I am following up Weinberg Cosmology book, but I have one question.(adsbygoogle = window.adsbygoogle || []).push({});

In chapter 3.1, we have Eq (3.1.3) and (3.1.4)

[itex] s(T) = \frac{\rho(T) + p(T)}{T} [/itex]

[itex] T\frac{dp(T)}{dT} = \rho(T) + p(T) [/itex]

In Eq (3.1.5), we have the Fermi-Dirac or Bose-Einstein distributions.

[itex] n(p, T) = \frac{4 \pi g p^2}{(2 \pi \hbar)^3} \frac{1}{exp(\sqrt{p^2 + m^2} / k_B T) \pm 1} [/itex].

From using this number distribution, the author said we have the energy density and pressure of a particle mass m are given by Eq (3.1.6) and (3.1.7).

[itex] \rho(T) = \int n(p, T) dp \sqrt{p^2 + m^2} [/itex]

[itex] p(T) = \int n(p, T) dp \frac{p^2}{3\sqrt{p^2 + m^2}} [/itex]

Here, energy density is straightforward by the definition of number density.

But, for pressure, the author said it can be derived from Eq(3.1.4), the second equation on this post.

However, I cannot derive this pressure equation using Eq(3.1.4). Can somebody help me do this?

Thank you.

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# Questions on Weinberg Cosmology Book

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