# Thermodynamic potential and energy density in cosmic models

1. Oct 19, 2012

### mjka

I'm reading this paper

http://arxiv.org/abs/0911.1728

It's about the authors' consideration of the Mass Varying Neutrino model with a new approach that try to explain the cosmic acceleration then.

I often encounter the thermodynamic potential during reading and re-calculating the equations. However, I'm not sure I got its meaning right, also the relation of thermodynamic potential and energy density. According to D part in Section I, the energy density is $\rho = \frac{\partial\Omega}{\partial m}$ where Ω is the thermodynamic potential density and m is the mass.

However, with that definition I couldn't achieve (72),(73) later.

By the way, I found how to evaluate the integral (31) but couldn't do that with (73), which is $\int_k^\inf \frac{z^2\sqrt{z^2-k^2}}{e^z+1}dz$.

Any help would be appreciate. Thank you!