Reheating constraints to WIMPflation
  Analyses of inflation models are usually conducted assuming a specific
range---e.g., $N_k \simeq 50-60$--of the number $N_k$ of $e$-folds of
inflation. However, the analysis can also be performed by taking into account
constraints imposed by the physics of reheating. In this paper, we apply this
analysis to a class of "WIMPflation" models in which the inflaton also plays
the role of dark matter. Our analysis also updates prior WIMPflation work with
more recent Planck 2018 data. With this new analysis, inflaton potentials
$V(\phi)=\lambda\phi^4$ and $\lambda \phi_0^4[1-\cos(\phi/\phi_0)]^2$ are ruled
out, while $V(\phi)=\lambda \phi_0^4\{1-\exp[-(\phi/\phi_0)^2]\}^2$ is slightly
disfavored, and $V(\phi)=\lambda\phi_0^4\tanh^4(\phi/\phi_0)$ is only viable
for certain reheating conditions. In addition, we also discuss for the first
time the effect of post-reheating entropy production (from, e.g., cosmological
phase transitions) in this reheating-physics analysis. When accounted for, it
decreases the number of $e$-folds through $\Delta N_k=-(1/3)\ln(1+\gamma)$,
where $\gamma\equiv\delta s/s$ is the fractional increase in entropy. We
discuss briefly the possible impact of entropy production to inflation-model
constraints in earlier work.
