All Questions
Tagged with cosmology statistical-mechanics
77
questions
0
votes
1
answer
58
views
Why can we use Bose-Einstein statistics in this expression for number density
In a system with $N$ particles in some volume $V$ in contact with a reservoir of temperature $T$, we find that
$$\bar{n_i}=\frac{g_i}{e^{\frac{{\epsilon}_i -\mu}{kT}} \pm 1}$$
depending on whether the ...
- 129
4
votes
2
answers
138
views
Why can photon be treated like gas?
In Cosmology, especially when studying Cosmic Dynamic, sometime we will treat photons as gas to calculate its pressure, but according to my understanding, photon and gas are nothing alike. Why can ...
- 411
5
votes
1
answer
75
views
Net particle number density for relativistic particles at finite chemical potential (tricky integral)
Question: How does one show that the chemical potential of relativistic fermions is negligible at high energies? In particular, I would like to show that the difference between the particle density $n$...
- 1,198
2
votes
5
answers
1k
views
A few questions about Boltzmann brains [closed]
So I've been thinking about Boltzmann brains and there are some questions which I wasn't able to answer online:
Given that Boltzmann brains only last for a split second, is experience (the notion or ...
- 185
2
votes
1
answer
195
views
Determining free Fermi/Bose gas chemical potentials, given temperature, number density, and baryon density
I'm attempting to recreate some plots of individual particle chemical potentials from S. Reddy et. al.'s paper on neutrino interactions in hot and dense matter (of the same title). The specifics aren'...
- 799
0
votes
0
answers
31
views
Poincaré recurrence in a closed universe? [duplicate]
Is it possible that the Poincaré recurrence applies to a closed universe (with a finite spacetime)? If it is, would this mean that a closed universe could eventually reach the same state as its ...
- 2,466
8
votes
2
answers
3k
views
Do Boltzmann brain thought experiments suggest literally anything can form randomly?
Do Boltzmann brain thought experiments suggest literally anything can form randomly?
What are the limitations to what random fluctuations can form? Literally any physical, material object?
Lastly, I ...
user353810
0
votes
1
answer
63
views
Integral on the solid angle of a function of the direction [closed]
I need to compute the integral
$$\int \frac{d^3q}{(2\pi)^3} \frac{q}{E}n^in^jn^k \frac{\partial g}{\partial x^i}$$
where $n^i$, $n^j$ and $n^k$ are the unit vectors and $g$ is a function of the ...
- 308
1
vote
1
answer
94
views
The content of early universe and max limit on the number of particles
When the size of the observable universe was small as a proton what was the physical content of it?
Was there a limit of particles in such a tiny volume with enormous high density and energy?
Can we ...
- 487
5
votes
3
answers
902
views
Why does the CMB have a spectrum like a black-body radiation?
Equilibrium distributions of particles (Maxwell, Boltzmann, Saha) are achieved by the particle collisions. On the other hand, photons do not interact with each other. From the introductory course in ...
- 51
1
vote
0
answers
36
views
Why are two assumptions for the approximation from the BE, FD to MB distribution and $T$ invariance in the Boltzmann equation reasonable?
As the title says, I can not understand whether the assumptions
are reasonable.
If an interaction $1+2\leftrightarrow 3+4$ is taken into account, the number variance in time is proportional to
$$|\...
4
votes
1
answer
132
views
Question about deriving the amount of pressure due to an element of momentum space in cosmology (Baumann Cosmology Book Eq. 3.10)
In Daniel Baumann's cosmology book Eq. (3.10) and cosmology lecture notes Eq. (3.2.18) he states that the pressure in the early universe can be defined as
$$P=\frac g{(2\pi)^3}\int d^3 p\ f(p)\times\...
- 394
0
votes
0
answers
40
views
Is the 2nd law of thermodynamics more of a likelihood than a law? [duplicate]
Given enough time, even extremely unlikely events are certain to happen. This includes spontaneous reduction in disorder.
As an example, given enough time, all the particles of a gas in a container ...
- 1,419
1
vote
0
answers
41
views
Internal degrees of freedom of a Weyl spinor
In statistical mechanics, we have formulas like
$$
n
=
\frac{g}{2\pi^2}
\int_m^\infty
\frac{E(E^2 - m^2)^{1/2}}{e^{(E - \mu)/T} \pm 1}\ dE
.
$$
where $g$ is the internal degrees of freedom. What is ...
- 574
1
vote
2
answers
264
views
What is the theoretical value of this phase space invariant?
So I wanted know how to theoretically calculate this phase space invariant (equation $3.31a$ )$R$ in our universe (FLRW metric) during the cosmological nucleosysthesis:
$$R = \int_{p} \frac{\mathcal{...
- 1,389