Well, it must depend on time since it is dependent on a. I am unsure exactly how it would depend on space, but regardless if I assume T does depend on both I get
$$\frac{\partial f_{dm}}{\partial t}=-\frac{\dot{E}T-\dot{T}E}{T^2}e^{-E/T}$$
$$\frac{\partial f_{dm}}{\partial...
Homework Statement
Show that the temperature of non-relativistic matter scales as ##a^{-2}## in the absence of interactions. Start from the zero-order part of Eq. (4.68) and assume a form ##f_{dm} \propto e^{-E/T}=e^{-p^2/2mT}##. Note that his argument does not apply to electrons and protons...
Hey all. The title/name says it all. I am trying my best to improve my knowledge of Cosmology, GR, QFT, Statistical Field theory, and learn a bit about string theory. I have browsed through the site before and will be trying to soak up as much knowledge as possible.
Homework Statement
Show that Eq. (6.33) follows from Eq. (6.32) by changing variables from t to ##\eta##.
Homework Equations
(6.32) $$\frac{d^2\phi^{(0)}}{dt^2}+3H\frac{d\phi^{(0)}}{dt}+V'=0$$
(6.33) $$\ddot{\phi^{(0)}}+2aH\dot{\phi}^{(0)}+a^2V'=0$$
The Attempt at a Solution
So...