  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.
