Loop-and-allied QG bibliography

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https://arxiv.org/abs/1610.07467
A new look at scalar perturbations in loop quantum cosmology: (un)deformed algebra approach using self dual variables
Jibril Ben Achour, Suddhasattwa Brahma, Julien Grain, Antonino Marciano
(Submitted on 24 Oct 2016)
Scalar cosmological perturbations in loop quantum cosmology (LQC) is revisited in a covariant manner, using self dual Ashtekar variables. For real-valued Ashtekar-Barbero variables, this `deformed algebra' approach has been shown to implement holonomy corrections from loop quantum gravity (LQG) in a consistent manner, albeit deforming the algebra of modified constraints in the process. This deformation has serious conceptual ramifications, not the least of them being an effective `signature-change' in the deep quantum regime. In this paper, we show that working with self dual variables lead to an undeformed algebra of hypersurface deformations, even after including holonomy corrections in the effective constraints. As a necessary consequence, the diffeomorphism constraint picks up non-perturbative quantum corrections thus hinting at a modification of the underlying space-time structure, a novel ingredient compared to the usual treatment of (spatial) diffeomorphisms in LQG. This work extends a similar result obtained in the context of spherically symmetric gravity coupled to a scalar field, suggesting that self dual variables could be better suited than their real counterparts to treat inhomogeneous LQG models.

 

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https://arxiv.org/abs/1610.08840
Signature change in loop quantum gravity: General midisuperspace models and dilaton gravity
Martin Bojowald, Suddhasattwa Brahma
(Submitted on 27 Oct 2016)
Models of loop quantum gravity based on real connections have a deformed notion of general covariance, which leads to the phenomenon of signature change. This result is confirmed here in a general analysis of all midisuperspace models without local degrees of freedom. As a subclass of models, 2-dimensional theories of dilaton gravity appear, but a larger set of examples is possible based only on the condition of anomaly freedom. While the classical dilaton gravity models are the only such systems without deformed covariance, they do give rise to signature change when holonomy modifications are included.

https://arxiv.org/abs/1610.08850
Signature change in 2-dimensional black-hole models of loop quantum gravity
Martin Bojowald, Suddhasattwa Brahma
(Submitted on 27 Oct 2016)
Signature change has been identified as a generic consequence of holonomy modifications in spherically symmetric models of loop quantum gravity with real connections, which includes modified Schwarzschild solutions. Here, this result is extended to 2-dimensional dilaton models and to different choices of canonical variables, including in particular the Callan-Giddings-Harvey-Strominger (CGHS) solution. New obstructions are found to coupling matter and to including operator-ordering effects in an anomaly-free manner.

 

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https://arxiv.org/abs/1610.09864
The information recovery problem
Valentina Baccetti, Viqar Husain, Daniel R. Terno
(Submitted on 31 Oct 2016)
The problem of rescuing unitary matter evolution on a black hole spacetime remains unresolved. We argue that some prominent cures are more troubling than the disease, demonstrate that their central element --- forming of the event horizon before the evaporation begins --- is not necessarily true, and describe a fully coupled matter-gravity system which is manifestly unitary.

https://arxiv.org/abs/1610.09681
Asymptotically Safe Grand Unification
Borut Bajc, Francesco Sannino
(Submitted on 30 Oct 2016)
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.

 

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https://arxiv.org/abs/1611.00785
The Geometry of Small Causal Cones
Ian Jubb
(Submitted on 2 Nov 2016)
We derive a formula for the spacetime volume of a small causal cone. We use this formula within the context of causal set theory to construct causal set expressions for certain geometric quantities relating to a spacetime with a spacelike hypersurface. We also consider a scalar field on the causal set, and obtain causal set expressions relating to its normal derivatives with respect to the hypersurface.

 

[kodama]

Emergent Gravity and the Dark Universe
Erik P. Verlinde
(Submitted on 7 Nov 2016 (v1), last revised 8 Nov 2016 (this version, v2))
Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional `dark' gravitational force describing the `elastic' response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton's constant and the Hubble acceleration scale a_0 =cH_0, and provide evidence for the fact that this additional `dark gravity~force' explains the observed phenomena in galaxies and clusters currently attributed to dark matter.
Comments: 5 figures
Subjects: High Energy Physics - Theory (hep-th)
Cite as: arXiv:1611.02269 [hep-th]

 

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https://arxiv.org/abs/1611.03668
The loop gravity string
Laurent Freidel, Alejandro Perez, Daniele Pranzetti
(Submitted on 11 Nov 2016)
In this work we study canonical gravity in finite regions for which we introduce a generalisation of the Gibbons-Hawking boundary term including the Immirzi parameter. We study the canonical formulation on a spacelike hypersuface with a boundary sphere and show how the presence of this term leads to an unprecedented type of degrees of freedom coming from the restoration of the gauge and diffeomorphism symmetry at the boundary. In the presence of a loop quantum gravity state, these boundary degrees of freedom localize along a set of punctures on the boundary sphere. We demonstrate that these degrees of freedom are effectively described by auxiliary strings with a 3-dimensional internal target space attached to each puncture. We show that the string currents represent the local frame field, that the string angular momenta represent the area flux and that the string stress tensor represents the two dimensional metric on the boundary of the region of interest. Finally, we show that the commutators of these broken diffeomorphisms charges of quantum geometry satisfy at each puncture a Virasoro algebra with central charge c=3. This leads to a description of the boundary degrees of freedom in terms of a CFT structure with central charge proportional to the number of loop punctures. The boundary SU(2) gauge symmetry is recovered via the action of the U(1)3 Kac-Moody generators (associated with the string current) in a way that is the exact analog of an infinite dimensional generalization of the Schwinger spin-representation. We finally show that this symmetry is broken by the presence of background curvature.

 

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https://arxiv.org/abs/1604.07818
Comments on the Sachdev-Ye-Kitaev model
Juan Maldacena, Douglas Stanford
(Submitted on 26 Apr 2016)
We study a quantum mechanical model proposed by Sachdev, Ye and Kitaev. The model consists of N Majorana fermions with random interactions of a few fermions at a time. It it tractable in the large N limit, where the classical variable is a bilocal fermion bilinear. The model becomes strongly interacting at low energies where it develops an emergent conformal symmetry. We study two and four point functions of the fundamental fermions. This provides the spectrum of physical excitations for the bilocal field.
The emergent conformal symmetry is a reparametrization symmetry, which is spontaneously broken to SL(2,R), leading to zero modes. These zero modes are lifted by a small residual explicit breaking, which produces an enhanced contribution to the four point function. This contribution displays a maximal Lyapunov exponent in the chaos region (out of time ordered correlator). We expect these features to be universal properties of large N quantum mechanics systems with emergent reparametrization symmetry.
This article is largely based on talks given by Kitaev \cite{KitaevTalks}, which motivated us to work out the details of the ideas described there.

https://arxiv.org/abs/1601.06768
The Spectrum in the Sachdev-Ye-Kitaev Model
Joseph Polchinski, Vladimir Rosenhaus
(Submitted on 25 Jan 2016)
The SYK model consists of N≫1 fermions in 0+1 dimensions with a random, all-to-all quartic interaction. Recently, Kitaev has found that the SYK model is maximally chaotic and has proposed it as a model of holography. We solve the Schwinger-Dyson equation and compute the spectrum of two-particle states in SYK, finding both a continuous and discrete tower. The four-point function is expressed as a sum over the spectrum. The sum over the discrete tower is evaluated.

https://arxiv.org/abs/1610.09758
An SYK-Like Model Without Disorder
Edward Witten
(Submitted on 31 Oct 2016 (v1), last revised 3 Nov 2016 (this version, v2))
Making use of known facts about "tensor models," it is possible to construct a quantum system without quenched disorder that has the same large n limit for its correlation functions and thermodynamics as the SYK model. This might be useful in further probes of this approach to holographic duality.

https://arxiv.org/abs/1611.04032
The complete 1/N expansion of a SYK--like tensor model
Razvan Gurau
(Submitted on 12 Nov 2016)
A SYK--like model close to the colored tensor models has recently been proposed \cite{Witten:2016iux}. Building on results obtained in tensor models \cite{GurSch}, we discuss the complete 1/N expansion of the model. We detail the two and four point functions at leading order. The leading order two point function is a sum over melonic graphs, and the leading order relevant four point functions are sums over dressed ladder diagrams. We then show that any order in the 1/N series of the two point function can be written solely in term of the leading order two and four point functions. The full 1/N expansion of arbitrary correlations can be obtained by similar methods.

 

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https://arxiv.org/abs/1611.05315
General Covariance from the Quantum Renormalization Group
Vasudev Shyam
(Submitted on 15 Nov 2016)
The Quantum renormalization group (QRG) is a realisation of holography through a coarse graining prescription that maps the beta functions of a quantum field theory thought to live on the `boundary' of some space to holographic actions in the `bulk' of this space. A consistency condition will be proposed that translates into general covariance of the gravitational theory in the D+1 dimensional bulk. This emerges from the application of the QRG on a planar matrix field theory living on the D dimensional boundary. This will be a particular form of the Wess--Zumino consistency condition that the generating functional of the boundary theory needs to satisfy. In the bulk, this condition forces the Poisson bracket algebra of the scalar and vector constraints of the dual gravitational theory to close in a very specific manner, namely, the manner in which the corresponding constraints of general relativity do. A number of features of the gravitational theory will be fixed as a consequence of this form of the Poisson bracket algebra. In particular, it will require the metric beta function to be of gradient form.

https://arxiv.org/abs/1611.05325
Transition probability spaces in loop quantum gravity
Xiao-Kan Guo
(Submitted on 15 Nov 2016)
We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability spaces. This is achieved by first checking such structures in covariant quantum mechanics, and then passing to spin foam models via the general boundary formulation. The transition probability space thus defined gives a simple way to reconstruct the Hilbert space of the canonical theory and the relevant quantum logical structure. Second, we show that the transition probability space and in particular the spin foam model are 2-categories. Then we discuss how to realize property transitions and causality in this categorical context in connection with presheaves on quantaloids and respectively causal categories. We conclude that transition probability spaces provide us with an alternative framework to understand various foundational questions of loop quantum gravity.

 

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https://arxiv.org/abs/1611.07009
Testing Quantum Black Holes with Gravitational Waves
Valentino F. Foit, Matthew Kleban
(Submitted on 21 Nov 2016)
We argue that near-future detections of gravity waves from merging black hole binaries will either confirm or conclusively rule out a long-standing proposal, originally due Bekenstein and Mukhanov, that the areas of black hole horizons are quantized in integer multiples of the Planck area times an O(1) constant \alpha. A single measurement of the "ring down" phase after a binary merger, if consistent with the predictions of classical general relativity, will rule out most or all (depending on the spin of the hole) of the extant proposals in the literature for the value of \alpha. A measurement of two such events for final black holes with substantially different spins will rule out the proposal for any \alpha.

 

[atyy]

https://arxiv.org/abs/1611.07849
General Relativity from Three-Forms in Seven Dimensions
Kirill Krasnov
(Submitted on 23 Nov 2016)
We consider a certain theory of 3-forms in 7 dimensions, and study its dimensional reduction to 4D, compactifying the 7-dimensional manifold on the 3-sphere of a fixed radius. We show that the resulting 4D theory is General Relativity (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian. Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of S^3. Realistic values of Lambda correspond to S^3 of Planck size.

 

[atyy]

https://arxiv.org/abs/1611.08915
Uncolored Random Tensors, Melon Diagrams, and the SYK Models
Igor R. Klebanov, Grigory Tarnopolsky
Comments: 23 pages, 18 figures
Certain models with rank-##3## tensor degrees of freedom have been shown by Gurau and collaborators to possesses a novel large ##N## limit, where ##g^(2)N^{3}## is held fixed. In this limit the perturbative expansion in the quartic coupling constant, ##g##, is dominated by a special class of "melon" diagrams. We study "uncolored" models of this type, which contain a single copy of real rank-##3## tensor. Its three indexes are distinguishable; therefore, the models possesses ##O(N)^{3}## symmetry with the tensor field transforming in the tri-fundamental representation. Such uncolored models also possesses the large ##N## limit dominated by the melon diagrams. The quantum mechanics of a real anti-commuting tensor therefore has a similar large N limit to the model recently introduced by Witten as an implementation of the Sachdev-Ye-Kitaev (SYK) model which does not require disorder. Gauging the ##O(N)^{3}## symmetry in our quantum mechanical model removes the non-singlet states; therefore, one can search for its well-defined gravity dual. We point out, however, that the model possesses a vast number of gauge-invariant operators involving higher powers of the tensor field, suggesting that the complete gravity dual will be intricate. We also discuss the quantum mechanics of a complex 3-index anti-commuting tensor, which has ##U(N)^{2}×O(N)## symmetry and argue that it is equivalent in the large ##N## limit to a version of SYK model with complex fermions. Finally, we discuss similar models of a commuting tensor in dimension ##d##. While the quartic interaction is not positive definite, we construct the large N Schwinger-Dyson equation for the two-point function and show that its solution is consistent with conformal invariance. We carry out a perturbative check of this result using the ##4−\epsilon## expansion.

 

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https://arxiv.org/abs/1611.09810
Phenomenology with fluctuating quantum geometries in loop quantum cosmology
Ivan Agullo, Abhay Ashtekar, Brajesh Gupt
(Submitted on 29 Nov 2016)
The goal of this paper is to probe phenomenological implications of large fluctuations of quantum geometry in the Planck era, using cosmology of the early universe. For the background (Friedmann, Lema\^{i}tre, Robertson, Walker) \emph{quantum} geometry, we allow `widely spread' states in which the \emph{relative} dispersions are as large as 168% in the Planck regime. By introducing suitable methods to overcome the ensuing conceptual and computational issues, we calculate the power spectrum PR(k) and the spectral index ns(k) of primordial curvature perturbations. These results generalize the previous work in loop quantum cosmology which focused on those states which were known to remain sharply peaked throughout the Planck regime. Surprisingly, even though the fluctuations we now consider are large, their presence does not add new features to the final PR(k) and ns(k): Within observational error bars, their effect is degenerate with a different freedom in the theory, namely the number of \emph{pre-inflationary} e-folds NB⋆ between the bounce and the onset of inflation. Therefore, with regard to observational consequences, one can simulate the freedom in the choice of states with large fluctuations in the Planck era using the simpler, sharply peaked states, simply by allowing for different values of NB⋆.

 

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https://arxiv.org/abs/1611.10281
Entanglement Entropy in Causal Set Theory
Rafael D. Sorkin, Yasaman K. Yazdi
(Submitted on 30 Nov 2016)
Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide in a natural manner the UV cutoff needed to render entanglement entropy finite. Defining entropy in a causal set is not straightforward because the type of canonical hypersurface-data on which definitions of entanglement typically rely is not available in a causal set. Instead, we will appeal to a more global expression given in arXiv:1205.2953 which, for a gaussian scalar field, expresses the entropy of a spacetime region in terms of the field's correlation function within that region. Carrying this formula over to the causal set, one obtains an entanglement entropy which is both finite and of a Lorentz invariant nature. Herein we evaluate this entropy for causal sets of 1+1 dimensions, and specifically for order-intervals ("causal diamonds") within the causal set, finding in the first instance an entropy that obeys a (spacetime) volume law instead of the expected (spatial) area law. We find, however, that one can obtain an area law by truncating the eigenvalues of a certain "Pauli-Jordan" operator that enters into the entropy formula. In connection with these results, we also study the "entropy of coarse-graining" generated by thinning out the causal set, and we compare it with what one obtains by similarly thinning out a chain of harmonic oscillators, finding the same, "universal" behaviour in both cases.

 

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https://arxiv.org/abs/1612.00266
Echoes from the Abyss: Evidence for Planck-scale structure at black hole horizons
Jahed Abedi, Hannah Dykaar, Niayesh Afshordi
(Submitted on 1 Dec 2016)
In classical General Relativity (GR), an observer falling into an astrophysical black hole is not expected to experience anything dramatic as she crosses the event horizon. However, tentative resolutions to problems in quantum gravity, such as the cosmological constant problem, or the black hole information paradox, invoke significant departures from classicality in the vicinity of the horizon. It was recently pointed out that such near-horizon structures can lead to late-time echoes in the black hole merger gravitational wave signals that are otherwise indistinguishable from GR. We search for observational signatures of these echoes in the gravitational wave data released by advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), following the three black hole merger events GW150914, GW151226, and LVT151012. In particular, we look for repeating damped echoes with time-delays of 8MlogM (+spin corrections, in Planck units), corresponding to Planck-scale departures from GR near their respective horizons. Accounting for the "look elsewhere" effect due to uncertainty in the echo template, we find tentative evidence for Planck-scale structure near black hole horizons at 2.9σ significance level (corresponding to false detection probability of 1 in 270). Future data releases from LIGO collaboration, along with more physical echo templates, will definitively confirm (or rule out) this finding, providing possible empirical evidence for alternatives to classical black holes, such as in firewall or fuzzball paradigms.

https://arxiv.org/abs/1612.00324
Quantum reduced loop gravity: extension to gauge vector field
Jakub Bilski, Emanuele Alesci, Francesco Cianfrani, Pietro Donà, Antonino Marciano
(Submitted on 1 Dec 2016)
Within the framework of Quantum Reduced Loop Gravity we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full Loop Quantum Gravity, while the matrix elements of the resulting operator between basis states are analytic coefficients. This analysis is the first step towards deriving the full quantum gravity corrections to the vector field semiclassical dynamics.

https://arxiv.org/abs/1612.00353
Time in quantum cosmology
Martin Bojowald, Theodore Halnon
(Submitted on 1 Dec 2016)
A cosmological model with two global internal times shows that time reparameterization invariance, and therefore covariance, is not guaranteed by deparameterization. In particular, it is impossible to derive proper-time effective equations from a single deparameterized model if quantum corrections from fluctuations and higher moments are included. The framework of effective constraints shows how proper-time evolution can consistently be defined in quantum cosmological systems, such that it is time reparameterization invariant when compared with other choices of coordinate time. At the same time, it allows transformations of moment corrections in different deparameterizations of the same model, indicating partial time reparameterization of internal-time evolution. However, in addition to corrections from moments such as quantum fluctuations, also factor ordering corrections may appear. The latter generically break covariance in internal-time formulations. Fluctuation effects in quantum cosmology are therefore problematic, in particular if derivations are made with a single choice of internal time or a fixed physical Hilbert space.

 

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https://arxiv.org/abs/1612.00551
A Classical and Spinorial Description of the Relativistic Spinning Particle
Trevor Rempel, Laurent Freidel
(Submitted on 2 Dec 2016)
In a previous work we showed that spin can be envisioned as living in a phase space that is dual to the standard phase space of position and momentum. In this work we demonstrate that the second class constraints inherent in this "Dual Phase Space" picture can be solved by introducing a spinorial parameterization of the spinning degrees of freedom. This allows for a purely first class formulation that generalizes the usual relativistic description of spinless particles and provides several insights into the nature of spin and its relationship with spacetime and locality. In particular, we find that the spin motion acts as a Lorentz contraction on the four-velocity and that, in addition to proper time, spinning particles posses a second gauge invariant observable which we call proper angle. Heuristically, this proper angle represents the amount of Zitterbewegung necessary for a spin transition to occur. Additionally, we show that the spin velocity satisfies a causality constraint, and even more stringently, that it is constant along classical trajectories. This leads to the notion of "half-quantum" states which violate the classical equations of motion, and yet do not experience an exponential suppression in the path integral. Finally we give a full analysis of the Poisson bracket structure of this new parametrization.

 

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https://arxiv.org/abs/1612.01084
Causal structures in cosmology
George Ellis, Jean-Philippe Uzan
(Submitted on 4 Dec 2016)
This article reviews the properties and limitations associated with the existence of particle, visual, and event horizons in cosmology in general and in inflationary universes in particular, carefully distinguishing them from `Hubble horizons'. It explores to what extent one might be able to probe conditions beyond the visual horizon (which is close in size to the present Hubble radius), thereby showing that visual horizons place major limits on what are observationally testable aspects of a multiverse, if such exists. Indeed these limits largely prevent us from observationally proving a multiverse either does or does not exist. We emphasize that event horizons play no role at all in observational cosmology, even in the multiverse context, despite some claims to the contrary in the literature.

https://arxiv.org/abs/1612.01236
Loop Quantum Cosmology: A brief review
Ivan Agullo, Parampreet Singh
(Submitted on 5 Dec 2016)
In the last decade, progress on quantization of homogeneous cosmological spacetimes using techniques of loop quantum gravity has led to insights on various fundamental questions and has opened new avenues to explore Planck scale physics. These include the problem of singularities and their possible generic resolution, constructing viable non-singular models of the very early universe, and bridging quantum gravity with cosmological observations. These results, which emerge from an interplay of sophisticated analytical and numerical techniques, has also led to valuable hints on loop quantization of black hole and inhomogeneous spacetimes. In this review, we provide a summary of this progress while focusing on concrete examples of the quantization procedure and phenomenology of cosmological perturbations.

https://arxiv.org/abs/1612.01296
Conformal anomalies and the Einstein Field Equations
Hadi Godazgar, Krzysztof A. Meissner, Hermann Nicolai
(Submitted on 5 Dec 2016)
We compute corrections to the Einstein field equations which are induced by the anomalous effective actions associated to the type A conformal anomaly, both for the (non-local) Riegert action, as well as for the local action with dilaton. In all cases considered we find that these corrections can be very large.

 

[atyy]

https://arxiv.org/abs/1612.01952
Why Our Universe is Comprehensible
James B. Hartle
(Submitted on 6 Dec 2016)
Einstein wrote memorably that `The eternally incomprehensible thing about the world is its comprehensibility.' This paper argues that the universe must be comprehensible at some level for information gathering and utilizing subsystems such as human observers to evolve and function.

 

[atyy]

https://arxiv.org/abs/1612.03851
A Supersymmetric SYK-like Tensor Model
Cheng Peng, Marcus Spradlin, Anastasia Volovich
(Submitted on 12 Dec 2016)
We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, "quarks" and "mesons". We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic "melon" diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.

 

[atyy]

https://arxiv.org/abs/1612.04002
Self-Dual Gravity and the Immirzi parameter
Javier Chagoya, M. Sabido
(Submitted on 13 Dec 2016)
Working in the first order formalism of gravity, we propose an action that combines the self and anti-self-dual parts of the curvature and comprises all the diffeomorphism invariant Lagrangians that one can consider in this formalism. The action that we propose is motivated by (A)dS gauge theories of gravity. We use this action to derive the (2+1)-dimensional version of the Immirzi parameter. Our derivation relates explicitly the Immirzi parameter to the existence of two classically equivalent actions for the description of gravity in (2+1) dimensions, namely the standard and exotic actions introduced by Witten in the description of (2+1) gravity as a gauge theory. This relation had been conjectured previously in the literature, but not derived.

https://arxiv.org/abs/1612.04334
Echoes of chaos from string theory black holes
Vijay Balasubramanian, Ben Craps, Bartłomiej Czech, Gábor Sárosi
(Submitted on 13 Dec 2016)
The strongly coupled D1-D5 conformal field theory is a microscopic model of black holes which is expected to have chaotic dynamics. Here, we study the weak coupling limit of the theory where it is integrable rather than chaotic. In this limit, the operators creating microstates of the lowest mass black hole are known exactly. We consider the time-ordered two-point function of light probes in these microstates, normalized by the same two-point function in vacuum. These correlators display a universal early-time decay followed by late-time sporadic behavior. To find a prescription for temporal coarse-graining of these late fluctuations we appeal to random matrix theory, where we show that a progressive time-average smooths the spectral form factor (a proxy for the 2-point function) in a typical draw of a random matrix. This coarse-grained quantity reproduces the matrix ensemble average to a good approximation. Employing this coarse-graining in the D1-D5 system, we find that the early-time decay is followed by a dip, a ramp and a plateau, in remarkable qualitative agreement with recent studies of the Sachdev-Ye-Kitaev (SYK) model. We study the timescales involved, comment on similarities and differences between our integrable model and the chaotic SYK model, and suggest ways to extend our results away from the integrable limit.

 

[atyy]

https://arxiv.org/abs/1612.04506
Towards a phase diagram for spin foams
Clement Delcamp, Bianca Dittrich
(Submitted on 14 Dec 2016)
One of the most pressing issues for loop quantum gravity and spin foams is the construction of the continuum limit. In this paper, we propose a systematic coarse-graining scheme for three-dimensional lattice gauge models including spin foams. This scheme is based on the concept of decorated tensor networks, which have been introduced recently. Here we develop an algorithm applicable to gauge theories with non-Abelian groups, which for the first time allows for the application of tensor network coarse-graining techniques to proper spin foams. The procedure deals efficiently with the large redundancy of degrees of freedom resulting from gauge symmetry. The algorithm is applied to 3D spin foams defined on a cubical lattice which, in contrast to a proper triangulation, allows for non--trivial simplicity constraints. This mimics the construction of spin foams for 4D gravity. For lattice gauge models based on a finite group we use the algorithm to obtain phase diagrams, encoding the continuum limit of a wide range of these models. We find phase transitions for various families of models carrying non--trivial simplicity constraints.

https://arxiv.org/abs/1612.04551
Testing loop quantum cosmology
Edward Wilson-Ewing
(Submitted on 14 Dec 2016)
Loop quantum cosmology predicts that quantum gravity effects resolve the big-bang singularity and replace it by a cosmic bounce. Furthermore, loop quantum cosmology can also modify the form of primordial cosmological perturbations, for example by reducing power at large scales in inflationary models or by suppressing the tensor-to-scalar ratio in the matter bounce scenario; these two effects are potential observational tests for loop quantum cosmology. In this article, I review these predictions and others, and also briefly discuss three open problems in loop quantum cosmology: its relation to loop quantum gravity, the trans-Planckian problem, and a possible transition from a Lorentzian to a Euclidean space-time around the bounce point.

 

[atyy]

https://arxiv.org/abs/1612.05364
Semi-classical analysis of black holes in Loop Quantum Gravity: Modelling Hawking radiation with volume fluctuations
Pierre Heidmann, Hongguang Liu, Karim Noui
(Submitted on 16 Dec 2016)
We introduce the notion of fluid approximation of a quantum spherical black hole in the context of Loop Quantum Gravity. In this limit, the microstates of the black hole are intertwiners between "large" representations ##s_{i}## which typically scale as ##s_{i}∼\sqrt{a_{H}}## where ##a_{H}## denotes the area of the horizon in Planck units. The punctures with large colors are, for the black hole horizon, similar to what are the fluid parcels for a classical fluid. We dub them puncels. Hence, in the fluid limit, the horizon is composed by puncels which are themselves interpreted as composed (in the sense of the tensor product) by a large number of more fundamental intertwiners. We study the spectrum of the euclidean volume acting on puncels and we compute its quantum fluctuations. Then, we propose an interpretation of black holes radiation based on the properties of the quantum fluctuations of the euclidean volume operator. We estimate a typical temperature of the black hole and we show that it scales as the Hawking temperature.

 

[atyy]

https://arxiv.org/abs/1612.06330
Quantum Chaos and Holographic Tensor Models
Chethan Krishnan, Sambuddha Sanyal, P. N. Bala Subramanian
(Submitted on 19 Dec 2016)
A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large-N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.

 

[kodama]

First test of Verlinde's theory of Emergent Gravity using Weak Gravitational Lensing measurements
Margot M. Brouwer, Manus R. Visser, Andrej Dvornik, Henk Hoekstra, Konrad Kuijken, Edwin A. Valentijn, Maciej Bilicki, Chris Blake, Sarah Brough, Hugo Buddelmeijer, Thomas Erben, Catherine Heymans, Hendrik Hildebrandt, Benne W. Holwerda, Andrew M. Hopkins, Dominik Klaes, Jochen Liske, Jon Loveday, John McFarland, Reiko Nakajima, Cristóbal Sifón, Edward N. Taylor
(Submitted on 9 Dec 2016 (v1), last revised 19 Dec 2016 (this version, v2))
Verlinde (2016) proposed that the observed excess gravity in galaxies and clusters is the consequence of Emergent Gravity (EG). In this theory the standard gravitational laws are modified on galactic and larger scales due to the displacement of dark energy by baryonic matter. EG gives an estimate of the excess gravity (described as an apparent dark matter density) in terms of the baryonic mass distribution and the Hubble parameter. In this work we present the first test of EG using weak gravitational lensing, within the regime of validity of the current model. Although there is no direct description of lensing and cosmology in EG yet, we can make a reasonable estimate of the expected lensing signal of low redshift galaxies by assuming a background LambdaCDM cosmology. We measure the (apparent) average surface mass density profiles of 33,613 isolated central galaxies, and compare them to those predicted by EG based on the galaxies' baryonic masses. To this end we employ the ~180 square degrees overlap of the Kilo-Degree Survey (KiDS) with the spectroscopic Galaxy And Mass Assembly (GAMA) survey. We find that the prediction from EG, despite requiring no free parameters, is in good agreement with the observed galaxy-galaxy lensing profiles in four different stellar mass bins. Although this performance is remarkable, this study is only a first step. Further advancements on both the theoretical framework and observational tests of EG are needed before it can be considered a fully developed and solidly tested theory.
Comments: 14 pages, 3 figures. Accepted for publication in MNRAS. Added references for section 1 and 6
Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Theory (hep-th)
DOI: 10.1093/mnras/stw3192
Cite as: arXiv:1612.03034 [astro-ph.CO]
(or arXiv:1612.03034v2 [astro-ph.CO] for this version)

 

[atyy]

https://arxiv.org/abs/1612.06872
Diffeomorphism-invariant averaging in quantum gravity and cosmology
Anthony W. H. Preston
(Submitted on 20 Dec 2016)
This thesis concerns research undertaken in two related topics concerning high-energy gravitational physics. The first is the construction of a manifestly diffeomorphism-invariant Exact Renormalization Group (ERG). This is a procedure that constructs effective theories of gravity by integrating out high-energy modes down to an ultraviolet cutoff scale without gauge-fixing. The manifest diffeomorphism invariance enables us to construct a fully background-independent formulation. This thesis will explore both the fixed-background and background-independent forms of the manifestly diffeomorphism-invariant ERG. The second topic is cosmological backreaction, which concerns the effect of averaging over high-frequency metric perturbations to the gravitational field equations describing the universe at large scales. This has been much studied the context of the unmodified form of General Relativity, but has been much less studied in the context of higher-derivative effective theories obtained by integrating out the high-energy modes of some more fundamental (quantum) theory of gravity. The effective stress-energy tensor for backreaction can be used directly as a diffeomorphism-invariant effective stress-energy tensor for gravitational waves without specifying the background metric.
This thesis will construct the manifestly diffeomorphism-invariant ERG and compute the effective action at the classical level in two different schemes. We will then turn to cosmological backreaction in higher-derivative gravity, deriving the general form of the effective stress-energy tensor due to inhomogeneity for local diffeomorphism-invariant effective theories of gravity. This an exciting research direction, as it begins the construction of a quantum theory of gravity as well as investigating possible implications for cosmology.

https://arxiv.org/abs/1612.07315
Towards apparent convergence in asymptotically safe quantum gravity
Tobias Denz, Jan M. Pawlowski, Manuel Reichert
(Submitted on 21 Dec 2016)
The asymptotic safety scenario in gravity is accessed within the systematic vertex expansion scheme for functional renormalisation group flows put forward in \cite{Christiansen:2012rx,Christiansen:2014raa}, and implemented in \cite{Christiansen:2015rva} for propagators and three-point functions. In the present work this expansion scheme is extended to the dynamical graviton four-point function. For the first time, this provides us with a closed flow equation for the graviton propagator: all vertices and propagators involved are computed from their own flows.
In terms of a covariant operator expansion the current approximation gives access to Λ, R, R2 as well as R2μν and higher derivative operators. We find a UV fixed point with three attractive and two repulsive directions, thus confirming previous studies on the relevance of the first three operators. In the infrared we find trajectories that correspond to classical general relativity and further show non-classical behaviour in some fluctuation couplings.
We also find signatures for the apparent convergence of the systematic vertex expansion. This opens a promising path towards establishing asymptotically safe gravity in terms of apparent convergence.

https://arxiv.org/abs/1612.07615
New Hamiltonians for loop quantum cosmology with arbitrary spin representations
Jibril Ben Achour, Suddhasattwa Brahma, Marc Geiller
(Submitted on 22 Dec 2016)
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the fundamental representation, and very little is known about the physics associated with higher spin labels. This constitutes an ambiguity whose understanding, we believe, is fundamental for connecting loop quantum cosmology to full theories of quantum gravity like loop quantum gravity, its spin foam formulation, or cosmological group field theory. We take a step in this direction by providing here a new closed formula for the Hamiltonian of flat FLRW models regularized in a representation of arbitrary spin. This expression is furthermore polynomial in the basic variables which correspond to well-defined operators in the quantum theory, takes into account the so-called inverse-volume corrections, and treats in a unified way two different regularization schemes for the curvature. After studying the effective classical dynamics corresponding to single and multiple spin Hamiltonians, we study the behavior of the critical density when the number of representations is increased, and the stability of the difference equations in the quantum theory.

https://arxiv.org/abs/1612.07331
Can quantum probes satisfy the weak equivalence principle?
Luigi Seveso, Matteo G. A. Paris
(Submitted on 21 Dec 2016)
We address the question whether, as a matter of principle, a quantum probe in a gravitational field may be considered as a test particle obeying the weak equivalence principle (WEP). To this aim we put forward a quantitative generalization of the WEP, which applies also to quantum systems, while maintaining the physical content of its classical formulation. Our formulation of the WEP is information-theoretic in nature, and requires that information about the mass of a probe, as obtained from position measurements, cannot increase in the presence of a gravitational field. More precisely, the generalized WEP states that the Fisher information of position measurements cannot increase in the presence of gravity, compared to its value for a free probe. Our results show that while in a uniform field quantum probes satisfy the WEP exactly, gravity gradients may encode nontrivial information about the mass in the particle's wavefunction, thus leading to violations of the WEP. We conclude that the WEP is untenable for a quantum particle described by a wavefunction, which rather behaves in analogy with a classical extended object.

https://arxiv.org/abs/1612.07629
More on the Bending of Light in Quantum Gravity
Dong Bai, Yue Huang
(Submitted on 22 Dec 2016)
We reconsider the long-range effects of the scattering of massless scalars and photons from a massive scalar object in quantum gravity. At the one-loop level, the relevant quantum mechanical corrections could be sorted into the graviton double-cut contributions, massless-scalar double-cut contributions and photon double-cut contributions. In arXiv:1410.7590 and 1609.07477 N.E.J.~Bjerrum-Bohr et al.~have considered explicitly the implications of the graviton double-cut diagrams on the gravitational bending of light and some classical formulations of the equivalence principle, using the modern double-copy constructions and on-shell unitarity techniques. In this article, we redo the analysis using the traditional Feynman diagrammatic approach and consider all three contributions. Our results on the graviton double-cut contributions agree with the aforementioned references, which acts as a nontrivial check of previous computations. Furthermore, it turns out that the massless-scalar double cut contributions and the photon double-cut contributions do leave non-vanishing quantum effects on the scattering amplitudes and the gravitational bending of light. Yet, we find that the general structure of the gravitational amplitudes and the quantum discrepancy of the equivalence principle suggested in the aforementioned references remain intact.

 

[kodama]

Holographic signatures of resolved cosmological singularities
Norbert Bodendorfer, Andreas Schäfer, John Schliemann
(Submitted on 20 Dec 2016)
The classical gravity approximation is often employed in AdS/CFT to study the dual field theory, as it allows for many computations. A drawback is however the generic presence of singularities in classical gravity, which limits the applicability of AdS/CFT to regimes where the singularities are avoided by bulk probes, or some other form of regularisation is applicable. At the same time, quantum gravity is expected to resolve those singularities and thus to extend the range of applicability of AdS/CFT also in classically singular regimes. This paper provides a proof of principle that such computations are already possible. We use a quantum corrected Kasner-AdS metric inspired by results from loop quantum gravity to compute the 2-point correlator in the geodesic approximation for a negative Kasner exponent. The correlator derived in the classical gravity approximation has previously been shown to contain a pole at finite distance as a signature of the singularity. Using the quantum corrected metric, we show explicitly how the pole is resolved and that a new subdominant long-distance contribution to the correlator emerges, caused by geodesics passing arbitrarily close to the resolved classical singularity. We stress that these results rely on several choices in the quantum corrected metric which allow for an analytic computation and may not hold in general. An alternative choice is presented where the correlator may remain singular even though the bulk singularity is resolved.
Comments: 14 pages
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
Cite as: arXiv:1612.06679 [hep-th]

 

[atyy]

https://arxiv.org/abs/1612.08800
Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects
David A. Craig, Parampreet Singh
(Submitted on 28 Dec 2016)
We explore the structure of the spin foam-like vertex expansion in loop quantum cosmology and discuss properties of the corresponding amplitudes, with the aim of elucidating some of the expansion's useful properties and features. We find that the expansion is best suited for consideration of conceptual questions and for investigating short-time, highly quantum behavior. In order to study dynamics at cosmological scales, the expansion must be carried to very high order, limiting its direct utility as a calculational tool for such questions. Conversely, it is unclear that the expansion can be truncated at finite order in a controlled manner.

https://arxiv.org/abs/1612.09521
The universe as a quantum gravity condensate
Daniele Oriti
(Submitted on 30 Dec 2016)
This is an introduction to the approach to the extraction of cosmological dynamics from full quantum gravity based on group field theory condensates. We outline its general perspective, which sees cosmology as the hydrodynamics of the fundamental quantum gravity degrees of freedom, as well as its concrete implementation within the group field theory formalism. We summarise recent work showing the emergence of a bouncing cosmological dynamics from a fundamental group field theory model, and provide a brief but complete survey of other results in the literature. Finally, we discuss open issues and directions for further research.

 

[kodama]

Loop-Corrected Virasoro Symmetry of 4D Quantum Gravity
Temple He, Daniel Kapec, Ana-Maria Raclariu, Andrew Strominger
(Submitted on 2 Jan 2017)
Recently a boundary energy-momentum tensor Tzz has been constructed from the soft graviton operator for any 4D quantum theory of gravity in asymptotically flat space. Up to an "anomaly" which is one-loop exact, Tzz generates a Virasoro action on the 2D celestial sphere at null infinity. Here we show by explicit construction that the effects of the IR divergent part of the anomaly can be eliminated by a one-loop renormalization that shifts Tzz.
Comments: 12 pages
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1701.00496 [hep-th]
(or arXiv:1701.00496v1 [hep-th] for this version)

Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections
Marcelo M. Amaral, Raymond Aschheim, Laurenţiu Bubuianu, Klee Irwin, Sergiu I. Vacaru, Daniel Woolridge
(Submitted on 7 Nov 2016)
The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/ aperiodic/ fractal / stochastic / (super) cluster / filament / polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such solutions are characterized by nonlinear symmetries of generating functions for generic off--diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi-Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.
Comments: latex2e, 11pt, 30 pages
Subjects: General Physics (physics.gen-ph)
Cite as: arXiv:1611.05295 [physics.gen-ph]

Moduli Structures, Separability of the Kinematic Hilbert Space and Frames in Loop Quantum Gravity
Bruno Carvalho, Daniel H. T. Franco
(Submitted on 28 Oct 2016)
We reassess the problem of separability of the kinematic Hilbert space in loop quantum gravity under a new mathematical point of view. We use the formalism of frames, a tool used in signal analysis, in order to remove the redundancy of the moduli structures in high valence graphs, without resorting to set extension of diffeomorphism group. For this, we introduce a local redundancy which encodes the concentration of frame vectors on the tangent spaces TpM around points of intersections p of smooth loops α in R3.
Subjects: General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
Cite as: arXiv:1610.09324 [gr-qc]
(or arXiv:1610.09324v1 [gr-qc] for this version)

Linking loop quantum gravity quantization ambiguities with phenomenology
Suddhasattwa Brahma, Michele Ronco, Giovanni Amelino-Camelia, Antonino Marciano
(Submitted on 25 Oct 2016)
Fundamental quantum gravity theories are known to be notoriously difficult to extract viable testable predictions out of. In this paper, we aim to incorporate putative quantum corrections coming from loop quantum gravity in deriving modified dispersion relations for particles on a deformed Minkowski spacetime. We show how different choices of the Immirzi parameter can, in some cases, serendipitously lead to different outcomes for such modifications, depending on the quantization scheme chosen. This allows one to differentiate between these quantization choices via testable phenomenological predictions.
Comments: 12 pages, 3 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1610.07865 [gr-qc]

 

[kodama]

Cosmological singularity resolution from quantum gravity: the emergent-bouncing universe
Emanuele Alesci, Gioele Botta, Francesco Cianfrani, Stefano Liberati
(Submitted on 21 Dec 2016)
Alternative scenarios to the Big Bang singularity have been subject of intense research for several decades by now. Most popular in this sense have been frameworks were such singularity is replaced by a bounce around some minimal cosmological volume or by some early constant volume quantum phase. This latter scenario was devised a long time ago and referred as an "emergent universe" (in the sense that our universe emerged from a static quantum phase) but was never derived from a rigorous quantum gravitational calculation. We show here that within an improved framework of canonical quantum gravity (the so called Quantum Reduced Loop Gravity) the Friedmann equations for cosmology are modified in such a way to replace the big bang singularity with a short bounce preceded by a metastable phase in which the universe is static and characteristically quantum in nature (having a typical size of a few tenths of Planck volumes). We call this hybrid scenario an "emergent-bouncing universe". Perspective developments and possible tests of this scenario are discussed in the end.
Comments: 5 pages, 3 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1612.07116 [gr-qc]
(or arXiv:1612.07116v1 [gr-qc] for this version)

Singularities and qualitative study in LQC
Llibert Aresté Saló, Jaume Amorós, Jaume de Haro
(Submitted on 16 Dec 2016 (v1), last revised 23 Dec 2016 (this version, v2))
This work contains a detailed analysis of singularities in General Relativity and in Loop Quantum Cosmology, yielding explicit analytical expressions for the energy density and the Hubble parameter for a given set of possible Equations of State. The case when the background is driven by a single scalar field is also considered, obtaining analytical expressions for the corresponding potential. And, in a given particular case, a qualitative study of the orbits in the associated phase space of the scalar field is performed.
Comments: 14 pages, 7 figures. New references added
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1612.05480 [gr-qc]

Viscous Chaplygin Gas Models as a Spherical Top-Hat Collapsing Fluids
Abdul Jawad, Ayesha Iqbal
(Submitted on 31 Oct 2016)
We study the spherical top-hat collapse in Einstein gravity and loop quantum cosmology by taking the non-linear evolution of viscous modified variable chaplygin gas and viscous generalized cosmic chaplygin gas. We calculate the equation of state parameter, square speed of sound, perturbed equation of state parameter, perturbed square speed of sound, density contrast and divergence of peculiar velocity in perturbed region and discussed their behavior. It is observed that both chaplygin gas models support the spherical collapse in Einstein as well as loop quantum cosmology because density contrast remains positive in both cases and the perturbed equation of state parameter remains positive at the present epoch as well as near future. It is remarked here that these parameters provide the consistence results for both chaplygin gas models in both gravities.
Comments: 19 pages; 12 figures. arXiv admin note: text overlap with arXiv:1110.6205, arXiv:1501.00486 by other authors
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Journal reference: Int. J. Mod. Phys. D 25(2016)1650074
DOI: 10.1142/S02182718165007

 

[kodama]

Towards apparent convergence in asymptotically safe quantum gravity
Tobias Denz, Jan M. Pawlowski, Manuel Reichert
(Submitted on 21 Dec 2016)
The asymptotic safety scenario in gravity is accessed within the systematic vertex expansion scheme for functional renormalisation group flows put forward in \cite{Christiansen:2012rx,Christiansen:2014raa}, and implemented in \cite{Christiansen:2015rva} for propagators and three-point functions. In the present work this expansion scheme is extended to the dynamical graviton four-point function. For the first time, this provides us with a closed flow equation for the graviton propagator: all vertices and propagators involved are computed from their own flows.
In terms of a covariant operator expansion the current approximation gives access to Λ, R, R2 as well as R2μν and higher derivative operators. We find a UV fixed point with three attractive and two repulsive directions, thus confirming previous studies on the relevance of the first three operators. In the infrared we find trajectories that correspond to classical general relativity and further show non-classical behaviour in some fluctuation couplings.
We also find signatures for the apparent convergence of the systematic vertex expansion. This opens a promising path towards establishing asymptotically safe gravity in terms of apparent convergence.
Comments: 24 pages, 6 figures
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1612.07315 [hep-th]
(or arXiv:1612.07315v1 [hep-th] for this version)

 

[atyy]

https://arxiv.org/abs/1701.01383
Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
Goffredo Chirco, Daniele Oriti, Mingyi Zhang
(Submitted on 5 Jan 2017)
We establish a dictionary between group field theory (thus, spin networks and random tensors) states and generalized random tensor networks. Then, we use this dictionary to compute the R\'{e}nyi entropy of such states and recover the Ryu-Takayanagi formula, in three different cases corresponding to three different truncations/approximations, suggested by the established correspondence.

 

[kodama]

Quantum gravity and Standard-Model-like fermions
Astrid Eichhorn, Stefan Lippoldt
(Submitted on 17 Nov 2016)
We discover that chiral symmetry does not act as an infrared attractor of the renormalization group flow under the impact of quantum gravity fluctuations. Thus, observationally viable quantum gravity models must respect chiral symmetry. In our truncation, asymptotically safe gravity does, as a chiral fixed point exists. A second non-chiral fixed point with massive fermions provides a template for models with dark matter. This fixed point disappears for more than 10 fermions, suggesting that an asymptotically safe ultraviolet completion for the standard model plus gravity enforces chiral symmetry.
Comments: 6 pages, 2 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1611.05878 [gr-qc]
Quantum-gravity effects on a Higgs-Yukawa model
Astrid Eichhorn, Aaron Held, Jan M. Pawlowski
(Submitted on 7 Apr 2016 (v1), last revised 13 Sep 2016 (this version, v2))
A phenomenologically viable theory of quantum gravity must accommodate all observed matter degrees of freedom and their properties. Here, we explore whether a toy model of the Higgs-Yukawa sector of the Standard Model is compatible with asymptotically safe quantum gravity. We discuss the phenomenological implications of our result in the context of the Standard Model. We analyze the quantum scaling dimension of the system, and find an irrelevant Yukawa coupling at a joint gravity-matter fixed point. Further, we explore the impact of gravity-induced couplings between scalars and fermions, which are non-vanishing in asymptotically safe gravity.
Comments: 13 pages + appendix, 10 figures, simplified basis for induced couplings
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph)
Journal reference: Phys. Rev. D 94, 104027 (2016)
DOI: 10.1103/PhysRevD.94.104027
Cite as: arXiv:1604.02041 [hep-th]
(or arXiv:1604.02041v2 [hep-th] for this version)

 

[kodama]

Quantum gravity on foliated spacetime - asymptotically safe and sound
Jorn Biemans, Alessia Platania, Frank Saueressig
(Submitted on 15 Sep 2016 (v1), last revised 17 Oct 2016 (this version, v2))
Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the ADM-formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the UV-non-Gaussian fixed point characteristic for Asymptotic Safety the setting exhibits a second non-Gaussian fixed point with a positive Newton's constant and real critical exponents. The new fixed point alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well-defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the ϵ-expansion around two dimensions, Monte Carlo simulations based on Lattice Quantum Gravity, and the discretized Wheeler-deWitt equation.
Comments: 7 pages, 3 figures. Conclusions slightly modified
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1609.04813 [hep-th]
(or arXiv:1609.04813v2 [hep-th] for this version)

 

[atyy]

https://arxiv.org/abs/1701.02282
Some Clarifications on the Duration of Inflation in Loop Quantum Cosmology
Boris Bolliet, Aurélien Barrau, Killian Martineau, Flora Moulin
(Submitted on 9 Jan 2017)
The prediction of a phase of inflation whose number of e-folds is constrained is an important feature of loop quantum cosmology. This work aims at giving some elementary clarifications on the role of the different hypotheses leading to this conclusion. We show that the duration of inflation does not depend significantly on the modified background dynamics in the quantum regime. [/PLAIN]

https://arxiv.org/abs/1701.02037
(3+1)-dimensional topological phases and self-dual quantum geometries encoded on Heegard surfaces
Bianca Dittrich
(Submitted on 8 Jan 2017)
We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the (2+1)-dimensional Turaev-Viro theory and obtain the state space for the Crane-Yetter model with line defects.
This work has important applications for quantum gravity as well as the theory of topological phases in (3+1) dimensions. It provides a self-dual quantum geometry realization based on a vacuum state peaked on a homogeneously curved geometry. The state spaces and operators we construct here provide also an improved version of the Walker-Wang model, and simplify its analysis considerably.
We in particular show that the fusion bases of the (2+1)-dimensional theory lead to a rich set of bases for the (3+1)-dimensional theory. This includes a quantum deformed spin network basis, which in a loop quantum gravity context diagonalizes spatial geometry operators. We also obtain a dual curvature basis, that diagonalizes the Walker-Wang Hamiltonian.
Furthermore, the construction presented here can be generalized to provide state spaces for the recently introduced dichromatic four--dimensional manifold invariants.

 

[atyy]

https://arxiv.org/abs/1701.02311
Hypercuboidal renormalization in spin foam quantum gravity
Benjamin Bahr, Sebastian Steinhaus
(Submitted on 9 Jan 2017)
In this article we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion letter, in which the existence of a fixed point in the truncated RG flow for the model was reported. Here we repeat the analysis with various modifications, and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.

https://arxiv.org/abs/1701.02439
Discretization of 3d gravity in different polarizations
Maïté Dupuis, Laurent Freidel, Florian Girelli
(Submitted on 10 Jan 2017)
We study the discretization of 3d gravity with Λ=0 following the loop quantum gravity framework. In the process, we realize that different choices of polarization are possible. This allows to introduce a new discretization based on the triad as opposed to the connection as in the standard loop quantum gravity framework. We also identify the classical non-trivial symmetries of discrete gravity, namely the Drinfeld double, given in terms of momentum maps. Another choice of polarization is given by the Chern-Simons formulation of gravity. Our framework also provides a new discretization scheme of Chern-Simons, which keeps track of the link between the continuum variables and the discrete ones. We show how the Poisson bracket we recover between the Chern-Simons holonomies allows to recover the Goldman bracket. There is also a transparent link between the discrete Chern-Simons formulation and the discretization of gravity based on the connection (loop gravity) or triad variables (dual loop gravity).

 

[atyy]

https://arxiv.org/abs/1701.03029
Flowing to the continuum in discrete tensor models for quantum gravity
Astrid Eichhorn, Tim Koslowski
(Submitted on 11 Jan 2017)
Tensor models provide a way to access the path-integral for discretized quantum gravity in d dimensions. As in the case of matrix models for two-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group fixed point in a setup where the tensor size N serves as the Renormalization Group scale. We develop functional Renormalization Group tools for tensor models with a main focus on a rank-3 model for three-dimensional quantum gravity. We rediscover the double-scaling limit and provide an estimate for the scaling exponent. Moreover, we identify two additional fixed points with a second relevant direction in a truncation of the Renormalization Group flow. The new relevant direction might hint at the presence of additional degrees of freedom in the corresponding continuum limit.