Is there a Friedmann equation form with inflation?

[Buzz Bloom]

TL;DR Summary

I have been unable to find on the Internet any form of GR similar to the 4 Omegas Friedmann equation that includes a transition from an inflation era back to a radiation era. Is it known whether of not such a equation currently exists?

If it is known that such an equation exists, I would much appreciate seeing a link to a reference. If it is known that such an equation does not exist, I would much appreciate seeing a reference with an explanation of implications regarding the compatibility of general relativity with a transition from the inflation era to subsequent eras: radiation to matter to dark energy/cosmological constant.

 

[PeterDonis]

I have been unable to find on the Internet any form of GR similar to the 4 Omegas Friedmann equation that includes a transition from an inflation era back to a radiation era.

That's probably because it's cumbersome, at best, to describe such a transition in the form you are talking about. It's easier to use the more basic form of the Friedmann equations in terms of the energy density $\rho$ and the pressure $p$. The transition from inflation to radiation dominated involves a change in the equation of state that relates $\rho$ and $p$, from the inflation era's equation $p = - \rho$ to the radiation dominated $p = \rho / 3$. In terms of the 4 $\Omega$s, that would mean a discontinuous change in at least two of the $\Omega$s, $\Omega_\Lambda$ and $\Omega_r$ (the lambda and radiation $\Omega$s), and the 4 $\Omega$s form is not really set up to handle discontinuous changes like that.

 

[PeterDonis]

the compatibility of general relativity with a transition from the inflation era to subsequent eras: radiation to matter to dark energy/cosmological constant.

General relativity can describe all of these transitions just fine.