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 Γ = N/N , which leads to a second-order evolution equation for H. We propose a simple Γ that is naturally defined and that conforms to the thermodynamical conditions: (i) the entropy production rate starts at a maximum; (ii) the initial vacuum (for radiation) is a non-singular regular vacuum and (iii) 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.