# Friedmann's Acceleration Equation

1. Jun 1, 2014

### johnnnyboy92

The acceleration equation is:

$\frac{\ddot{a}}{a}$ = -$\frac{4πG}{3c^2}$(ε+3P)

According to this equation, if we have a positive pressure, then the expansion of the universe will slow down. I'm confuse about this because I think of positive pressure resulting from the random thermal motions of particles pushing out in a container for example. The greater this pressure is, the greater the force the walls will feel outward. So how can the universe slow down if the pressure is positive?

2. Jun 2, 2014

### Staff: Mentor

According to general relativity, the pressure contributes to the overall gravitational field; more pressure means more gravitational attraction to slow the outwards acceleration.

3. Jun 2, 2014

### George Jones

Staff Emeritus
Very roughly ...

In Newtonian gravity, mass is the source of gravity. Because of the equivalence of mass and energy, in general relativity, mass and energy are sources for gravity.

Consider the ideal gas equation $PV=NkT$ as an example. The higher the pressure, the higher the temperature and thus thermal energy.

4. Jun 2, 2014

### johnnnyboy92

ohhhh, I see now. Correct me if my interpretation of your answers is wrong, but for cosmology, the mathematical relation between pressure and energy density, where we deal with dilute gases, is the equation of state is P=wε. And, since we are dealing with general relativity, like you guys said, then the positive pressure means there's going to be more energy density. If there's more energy, then space-time is curved causing the expansion to slow down because there's more gravity according to Einstein.