What is Cosmological constant: Definition and 188 Discussions

In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ), alternatively called Einstein's cosmological constant, is the energy density of space, or vacuum energy, that arises in Albert Einstein's field equations of general relativity. It is closely associated to the concept of dark energy.Einstein originally introduced the concept in 1917 to counterbalance the effects of gravity and achieve a static universe, a notion which was the accepted view at the time. Einstein abandoned the concept in 1931 after Hubble's confirmation of the expanding universe. From the 1930s until the late 1990s, most physicists assumed the cosmological constant to be equal to zero. That changed with the surprising discovery in 1998 that the expansion of the universe is accelerating, implying the possibility of a positive nonzero value for the cosmological constant.Since the 1990s, studies have shown that around 68% of the mass–energy density of the universe can be attributed to so-called dark energy. The cosmological constant Λ is the simplest possible explanation for dark energy, and is used in the current standard model of cosmology known as the ΛCDM model.
According to quantum field theory (QFT) which underlies modern particle physics, empty space is defined by the vacuum state which is a collection of quantum fields. All these quantum fields exhibit fluctuations in their ground state (lowest energy density) arising from the zero-point energy present everywhere in space. These zero-point fluctuations should act as a contribution to the cosmological constant Λ, but when calculations are performed these fluctuations give rise to an enormous vacuum energy. The discrepancy between theorized vacuum energy from quantum field theory and observed vacuum energy from cosmology is a source of major contention, with the values predicted exceeding observation by some 120 orders of magnitude, a discrepancy that has been called "the worst theoretical prediction in the history of physics". This issue is called the cosmological constant problem and it is one of the greatest mysteries in science with many physicists believing that "the vacuum holds the key to a full understanding of nature".

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  1. Willfrid Somogyi

    I Flat vs Open Universe: CMBR & Type Ia Supernovae

    So CMBR points to a flat universe, and this seems to be the generally accepted model. But in a flat universe is expansion not supposed to slow exponentially, stopping after an infinite time? How does this fit with the observation that distant type Ia supernovae show the universe's expansion to...
  2. G

    I Question about the cosmological constant

    Layman here, please excuse my ignorance. I believe to understand the basics of SR, GR, cosmic expansion, etc but questions come to mind now and then. As I understand, dark energy, the cosmological constant, vacuum energy, whatever you may call it, remains a constant per space volume unit. Empty...
  3. marcus

    A Atoms Of Space, Gravity and the Cosmological Constant

    This Invited Review article just came out: http://arxiv.org/abs/1603.08658 The Atoms Of Space, Gravity and the Cosmological Constant T. Padmanabhan (Submitted on 29 Mar 2016) I describe an approach which connects classical gravity with the quantum microstructure of spacetime. The field equations...
  4. davidbenari

    Finding an upper bound for the cosmological constant

    Homework Statement (Working with geometrised units) Consider the EFE ##G^{\alpha \beta }+\Lambda g^{\alpha \beta} = 8 \pi T^{\alpha \beta} ## work out (using weak-field considerations) an upper bound for the cosmological constant knowing that the radius of Pluto's orbit is 5.9 x 10^12 m...
  5. marcus

    A Could an entropic force help explain size of the cosmological constant?

    When we measure the cosmological constant Λ what we are really doing is measuring the longterm value of the Hubble rate, namely H∞, the distance expansion rate that the present rate H(t) is seen to be declining towards and leveling out at. It's convenient to write distance expansion rates as...
  6. bcrowell

    I Anthropic Lower Limit on Cosmological Constant

    Piran et al., "Cosmic explosions, life in the Universe and the Cosmological Constant," http://arxiv.org/abs/1508.01034 I thought this was interesting. If I'm understanding correctly, the idea is that satellite galaxies such as the Magellanic Clouds have low metallicity, which causes them to...
  7. Einstein's Cat

    Accurate Measurement of Cosmological Constant Value

    Could anyone please recommend a paper that accurately gives the value of the cosmological constant? Or else may you reply with values of the cosmological constant that you would you use in your research? Any help would be very much appreciated.
  8. Markus Hanke

    Gravitational Radiation and Cosmological Constant

    How come that, in the context of discussing the search for gravitational waves, I never see the cosmological constant mentioned ? We know that ##\Lambda \neq 0##, so this seems strange to me; in the presence of a non-vanishing constant, the background is not Ricci flat in the vacuum case, so...
  9. D

    Lorentz invariance of the Minkowski metric

    I understand that in order to preserve the inner product of two four vectors under a change of coordinates x^{\mu}\rightarrow x^{\mu^{'}}=\Lambda^{\mu^{'}}_{\,\, \nu}x^{\nu} the Minkowski metric must transform as \eta_{\mu^{'}\nu^{'}}=\Lambda^{\alpha}_{\,\...
  10. J

    Relationship Between Spatial Expansion and Gravity's Force?

    Fellow Nerds, I'm looking for a quantitative relationship between the gravitational strength of a point on a field and the speed of expansion of space at that point. Given a cosmological constant and a metric, is it possible to pinpoint a certain point of space and ask how quickly that space is...
  11. 1

    Evidence for a Cyclic Universe

    http://physics.princeton.edu/~steinh/lambda16.pdf In this research article the authors suggest a cyclic universe, specifically one involving collisions of higher dimensional branes (an idea taken out of string theory), could indirectly explain why the observed cosmological constant is so small...
  12. R

    Alternative hypotheses regarding dark energy?

    Currently, the favoured explanations for the accelerating expansion of the universe are the cosmological constant, and various scalar fields, most notably quintessence. All of these are mechanisms dependent on mathematical field properties. My question is: do any alternative hypotheses exist...
  13. Isaac0427

    Cosmological constant times the metric tensor

    In the EFE, what does adding Λgμν mean and why is it not included in the Einstein tensor?
  14. Shadowclan

    How can I apply probability to the cosmological constant?

    Hello! me and my friends were discussing a few ideas earlier this week and then we suddenly started talking about Einstein's biggest mistake. I was a bit lost because I am not all that familiar with the Cosmological constant and I was wondering how can probability be applied to that mistake?? I...
  15. yazanhomsi

    Dark energy and cosmological constant

    Hello everyone. I am having some problem with dark energy and the cosmological constant. The cosmological constant is a proposed form of dark energy. Alright, now the cosmological constant is is estimated by cosmologists to on the order of 10^-26 kilograms per cubic meters. But the density of...
  16. haael

    Susskind on supersymmetry vs. cosmological constant?

    In one book of Susskind I found the following claim and I wanted to ask for its basis. Susskind says that each kind of boson gives positive contribution to the cosmological constant (the lighter, the better). Each kind of fermion gives negative contribution to the cosmological constant. Thus...
  17. quantumfunction

    How different can quantum vacuums be?

    For instance our quantum vacuum has a certain Cosmological constant and the question is can there be other vacuums with different values and if so where's the evidence for this I would like to read it. How do you derive the Cosmological Constant through something like Quantum field theory or...
  18. RyanH42

    Has the Cosmological Constant Mystery Been Solved?

    I read a article now and It claims he found the cause of cosmological constant.Is that true ? The idea is actually good...
  19. B

    Interpretting the cosmological constant

    I am trying to wrap my brain around the idea of the cosmological constant, and how it gives the result of an accelerating universe. I have read different explanations for it, and in some it gives me the impression that it is an actual physical force, pushing everything away from everything...
  20. T

    Value of Cosmological Constant

    Hi. I was just curious about the current value of the cosmological constant. My astrophysics class lecture notes say on the order of 10^-122, but the Wikipedia article says 10^-35 s^-2. Could someone explain where the 10^-35 s^-2 value comes from? Thanks!
  21. E

    Cosmological constant term and metric tensor

    Why cosmological constant term ##\Lambda g_{uv}## in Einstein equation is proportional to ##g_{uv}##. Why it is even proportional to ##g_{uv}## in spacetime of MInkowski?
  22. Jorrie

    Marcus's 'no-pressure' model in different jacket

    In this thread, I would like to discuss: "which is more natural for a simple cosmological model: taking the long term Hubble time as a timescale (as Marcus has done), or taking the Hubble time as a timescale". I will start by paraphrasing Marcus' OP and replacing his '##\Lambda##-timescale' with...
  23. U

    How do I find the scale factor of cosmological constant?

    Homework Statement (a)Sketch how the contributions change with time (b)For no cosmological constant, how long will this universe exist? (c)How far would a photon travel in this metric? (d)Find particular density ##\rho_E## and scale factor (e)How would this universe evolve?[/B] Homework...
  24. S

    Godel Metric Cosmological Constant

    What is the cosmological constant for the Godel metric?
  25. Quarlep

    Does space-time have an energy itself?

    Is space time has a energy itself ? Thanks
  26. A

    How to calculate cosmological constant?

    I reading book, part about gravity. It is Landau-Lifschiz, "Theory of field". And I trying to understand how to calculate cosmological constant. Re-read part with introduction of cosmological constant several times, still not understood. Let's imagine function of space curvature, without...
  27. Quarlep

    Cosmological Constant and Vacuum Energy

    I was reading a book about cosmolgy.And there wrotes vacuum energy must be higher than cosmological constant 10100 times to satisfy (It may just the opposite ) observations. Is that true ?
  28. Q

    Dark energy and the Cosmological Constant

    So the Universe expanded very rapidly in its very first moments (inflation). The Universe then slowed down and is speeding up again, and Dark energy is supposed to be responsible for this accelerated expansion. The cosmological constant might as well be dark energy, but why is it still being...
  29. T

    What does a Cosmological Constant mean?

    Simplistically, the GR equation is G = k T + l g G represents the curvature of the fabric of space-time T is the stress energy tensor, representing the fluxes and densities of matter and energy g is the metric tensor So... In another thread, someone said that the cosmological constant...
  30. binbagsss

    Cosmological Constant, Einstein equation Quick Question

    So Einstein Equation: ##G_{uv}= 8 \pi G T_{uv} ##, Justifying the cosmological constant can be included is done by noting that ## \bigtriangledown^{a}g_{ab} =0 ## and so including it on the LHS, conservation of energy-momentum tensor still holds. I'm not sure why ## \bigtriangledown^{a}g_{ab}...
  31. V

    Couldn't you unify gravity & the cosmological constant?

    ...through inertial mass, namely to explain away the sameness of inertial and gravitational mass? If you assume that only inertial mass is a "real" effect, then gravity would simply become a fictious force arising from inertial mass holding matter back from expanding alongside spacetime during...
  32. K

    Solving expansion rate for a variant of the Friedmann equation

    Homework Statement For the equation H^2 = \frac{8 \pi G \rho_m}{3} + \frac{H}{r_c} how do I find the value of H for scale factor a \rightarrow \infty , and show that H acts as though dominated by \Lambda (cosmological constant) ? Homework Equations \rho_m \propto \frac{1}{a^3} H > 0...
  33. T

    The Cosmological Constant with Inflation is not Constant

    The title says a lot about my doubt. I don't know a lot about inflation maths but the idea is that in Inflation, I am seeing that the Cosmological Constant (ie Vacuum Energy) is not Constant in two ways: 1 With time; the Vacuum Energy was larger in the beginning and that triggered Inflation...
  34. ChrisVer

    Cosmological constant deceleration parameter

    Homework Statement Give q(t) the deceleration parameter, as a function of: \Omega_{\Lambda}, the cosmological constant density, and \bar{a}(t) = \frac{a(t)}{a(t_{0})}= 1+ H_{0} (t-t_{0}) - \frac{1}{2} q_{0} H_{0}^{2} (t-t_{0})^{2} where a's the scale factors have already defined τ =...
  35. J

    Energy density of the cosmological constant units question

    Hi Everyone! I need a bit of help with the following question please. How does the energy density of the cosmological constant Uλ=ρλc^2 have the required SI units if λ=4∏Gρ/c^2 I know that the energy density of the cosmological constant (Uλ)is essentially dark energy and the SI units...
  36. J

    Cosmic Dynamics - Cosmological Constant

    Suppose the energy density of the cosmological constant is equal to the present critical density ε\Lambda = εc,0 = 5200 MeV m-3. What is the total energy of the cosmological constant within a sphere 1 AU in radius? My answer: ε\Lambda = ET / V ET = ε\Lambda * V = (8.33 * 10-10...
  37. edpell

    Dark energy versus cosmological constant

    Are dark energy and the cosmological constant the same thing?
  38. marcus

    BOSS questions cosmological constant (undecided)

    The PF home page has some news items in the righthand margin and one is about this: http://arxiv.org/abs/1404.1801 The popular news account is this BBC piece: http://www.bbc.com/news/science-environment-26329320 "They find that some three billion years after the Big Bang, the cosmos was...
  39. J

    Cosmological Constant & Fine Tuning for Life

    Hi, I have some confusion about the cosmological constant (CC). From what I have read it is to do with the energy density throughout the entire universe which is thought to drive the expansion of the universe. If the CC were any smaller then matter would not have been able to form and since the...
  40. H

    Does the cosmological constant 'require' energy?

    I have a question about GR in a cosmological setting. If dark energy is assumed to be a true GR cosmological constant, does this require some kind of energy input. I am curious to know if this is just a 'curvature' of space somehow, or does it represent a continual addition of energy on some...
  41. G

    Not understanding cosmological constant in field theory

    The bare cosmological constant in field theory is needed to cancel the infinite vacuum zero-point energy. Then you get a renormalized cosmological constant. There are three quantites at play, Ω=E+Ω0, where E is the infinite vacuum zero-point energy, and Ω is the renormalized cosmological...
  42. K

    Two kinds of flatness? cosmological constant?

    I'm confused about the relationship between two seemingly different concepts of flatness of the universe. 1. Spatial flatness. This is the lack of any curvature on a large scale. Simple enough... 2. Energy density flatness. If the energy density is higher than a critical value, then the...
  43. J

    Units of cosmological constant

    The cosmological constant (Ʌ ) is equated to dark energy and has units of energy/volume. Why have I read that Ʌ equals the Hubble constant squared (H2) which has units of 1/sec2? There must be an obvious explanation.
  44. G

    Cosmological constant in qft

    The vacuum-vacuum expectation value in the absence of a source is in general not equal to 1, but exp[-iEt], where E is the energy of the vacuum. For some reason in QFT, we say E=0 (i.e., we normalize Z[0]=1, the generating functional), but we don't need to do this and one can in fact calculate E...
  45. F

    Cosmological constant and vacuum energy

    Since Omega-lambda is very close to Omega-matter, what could it mean if we assume they are exactly equal to each other. Also, let's assume they were always equal since coincident problem is unnatural.
  46. F

    Cosmological constant calculation

    I have always wondered about how cosmological constant is characterized. You often read the “cosmological constant measured to be ….”.So since it is still a hypothesis, shouldn't the statement read “cosmological constant calculated to be ….” . Or Is it that such semantics does not matter.
  47. A

    Is dark energy or dark matter created to keep the Cosmological constant

    A positive value for the cosmological constant was found by the studies of Adam G. Riess et al and Pearlmutter et al In terms of Planck units, and as a natural dimensionless value, the cosmological constant, λ, is on the order of 10−122 or 10−29 g/cm3 The cosmological constant has negative...
  48. Chronos

    Solution to the cosmological constant problem

    Padmanabhan is guilty of another interesting paper - Solution to the cosmological constant problem, http://arxiv.org/abs/1302.3226. Any thoughts?
  49. J

    Jacobsen's New Papers: Solving the Cosmological Constant Problem?

    reading these new jacobsen papers, yesterday. a few questions came up Does Jacobsen tries to solve Cosmological constant problem with these papers ? http://arxiv.org/pdf/1212.6821.pdf
  50. M

    Einstein tensor with the cosmological constant present.

    I can fairly well grasp the trace relationship between the Einstein tensor and the Ricci tensor, and see that Ricci tensor is a multiple of the metric. If the cosmological constant is included I don't get why the Einstein tensor shouldn't become a multiple of the metric (leaving out physical...
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