Inflationary cosmology and thermodynamics

We present a simple and thermodynamically consistent cosmology with a phenomenological model of quantum creation of radiation due to vacuum decay. Thermodynamics and Einstein's equations lead to an equation in which $H$ is determined by the particle number $N$. The model is completed by specifying the particle creation rate $\Gamma=\dot{N}/N$, which leads to a second-order evolution equation for $H$. We propose a simple $\Gamma$ that is naturally defined and that conforms to the thermodynamical conditions: (a) the entropy production rate starts at a maximum; (b) the initial vacuum (for radiation) is a non-singular regular vacuum; and (c) the creation rate is initially higher than the expansion rate $H$, but then falls below $H$. The evolution equation for $H$ then has a remarkably simple exact solution, in which a non-adiabatic inflationary era exits smoothly to the radiation era, without a reheating transition. For this solution, we give exact expressions for the cosmic scale factor, energy density of radiation and vacuum, temperature, entropy and super-horizon scalar perturbations.