# How did pressure evolve in the (early) universe?

I am trying to derive how the cosmological pressure $$p(t)$$ evolved over time in the universe, especially in the radiation and matter dominated epochs. There are some very nice explanations how $$H(t)$$ evolved with time here and here and I am looking for a similar explanation for $$p$$ as derivation from the Friedmann equations. I will also need some clarifications, e.g. is $$p$$ purely a result of the radiation or does also have a contribution by the matter?

In the case of the radiation dominated epoch I guess I could simplify the second Friedman Equation

$$\frac{2R\ddot{R} + \dot{R}^2 + k}{R^2} - \Lambda = -8\pi p$$

by claiming $$p\gg \Lambda$$ and $$p\gg k$$ to

$$- \frac{1}{8\pi}\left (\frac{2 \ddot{R}}{R} + H^2 \right)=p$$

but I am not sure if I can then simplify more. And what assumptions could I use for in matter dominated epoch about the $$p$$? Or would it only make sense to set $$p \approx 0$$ in the matter dominated epoch? Thanks for your ideas about expressing the evolution of $$p$$!

• One thing is sure. There was a high negative pressure initially. This became positive at the moment of particle generation. Right now (since matter began to accelerate away from each other) it's negative again and growing. Pressure can be given by the vacuum fluctuations too. Jun 16, 2021 at 16:53