All particle species are in equilibrium at early times of the universe. But I didn't find any book that makes the difference of kinetic and chemical equilibrium clear. I have some of my own opinions and I hope to get your comments:
(1) kinetic equilibrium means the distribution function obeys...
In Dodelson's book, the equation for a scattering process ## a + b \Leftrightarrow c + d ## is given as
##a^{-3} \frac{ d (n_a a^3)}{d t}=-n^{\text{eq}}_a n^{\text{eq}}_b<\sigma v>(\frac{n_a n_b}{n^{\text{eq}}_a n^{\text{eq}}_b} - \frac{n_c n_d}{n^{\text{eq}}_c n^{\text{eq}}_d}) = - <\sigma...
Thanks. Since we are on this paper, I have a related question.
I am a little confused about how energy goes from inflaton to fermions. So during reheating, this paper says we can find the amplitude of fermion production from ##<f_i,\bar{f}_i|\phi \bar{\psi}_i\psi_i|0>##. Here ##\phi## is purely...
Do you mean thermodynamics or statistical distribution function doesn't work very well in this case? As to chemical potential, it is not constant. So how does it change with temperature?
I didn't say the net baryon number is determined from thermodynamics. I am trying to understand how the...
Thanks.
This question is from Phys.Lett. B117 (1982) 29
This is a 5-page paper and my question is from page two. The scalar is the inflaton which reheats the universe at the end of inflation by perturbative decaying. We can assume the potential energy of inflaton has only quadratic term. That's...
My equation is indeed from the quantum action. A fermion loop (##m_f<m_\phi/2##) will contribute a complex term to the effective potential, which means the free scalar particle is not the eigenstate of Hamiltonian. It will decay. I believe the Hamiltonian is also complex just like in quantum...
My question is not about baryogenesis. I am considering the era from some temperature when QCD phase transition has already finished, saying 100 MeV to nucleosynthesis at ##T\approx1## MeV. The correct density of baryons has already been generated by some unknown mechanism before this period.
I...
But when temperature is lower than mass the exponential dies out rather than being unity.
Do you mean nucleons have different temperature as photons during nucleosynthesis?
Thanks.
I need to find the evolution of its energy density ##\rho=\dot{\phi}^2/2+m^2\phi^2/2##. With complex solution for ##\phi##, I get complex energy density which doesn't make sense.
Before last scattering, the universe is opaque due to the very short mean free path of photons. There is no way for us to see earlier than last scattering. After last scattering, the density of electrons drops dramatically and photons can free stream almost all the way to us today. This is why...
When ##\Gamma << m##, the full solution is ##\phi(t)= A e^{imt-\Gamma t/2}+B e^{-imt+\Gamma t/2}##. It doesn't seem to be possible to make it real by constraining the two constant coefficients ##A## and ##B##.
Actually, this question is from Phys.Lett. B117 (1982) 29
But ##\phi## starts as a real field, how can it have complex solution?
In quantum mechanics, an imaginary part in Hamiltonian of some system indicates decaying amplitude. But isn't the total Hamiltonian of the whole system always real in order to obey unitarity? I don't know how to draw an...