Friedmann's Acceleration Equation

[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?

 

[Nugatory]

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?

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

 

[George Jones]

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.

 

[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.

 

[sardar]

I can understand your confusion regarding the relationship between positive pressure and the expansion of the universe. However, it is important to note that this equation is not describing the behavior of particles in a container, but rather the behavior of the entire universe.

The Friedmann's acceleration equation is a fundamental equation in cosmology that describes the evolution of the universe. The term "pressure" in this context refers to the pressure exerted by the matter and energy in the universe, which includes not only particles but also radiation and dark energy.

When the pressure is positive, it means that the matter and energy in the universe are pushing against each other, which can slow down the expansion of the universe. This is because the positive pressure contributes to the total energy density in the equation, which has a negative effect on the acceleration of the universe.

Furthermore, it is important to note that the expansion of the universe is not solely determined by pressure, but also by the overall energy density and curvature of the universe. So even though a positive pressure can slow down the expansion, it is not the only factor at play.

In summary, the Friedmann's acceleration equation is a complex equation that takes into account various factors in the universe, including pressure, to describe its evolution. While it may seem counterintuitive, a positive pressure can indeed contribute to the slowing down of the universe's expansion.