The Observational Status of Simple Inflationary Models: an Update

We provide an update on five relatively well motivated inflationary models in which the inflaton is a Standard Model singlet scalar field. These include i) the textbook quadratic and quartic potential models but with additional couplings of the inflaton to fermions and bosons, which enable reheating and also modify the naive predictions for the scalar spectral index $n_s$ and $r$, ii) models with Higgs and Coleman-Weinberg potentials, and finally iii) a quartic potential model with non-minimal coupling of the inflaton to gravity. For $n_s$ values close to 0.96, as determined by the WMAP9 and Planck experiments, most of the considered models predict $r\gtrsim0.02$. The running of the scalar spectral index, quantified by $|\rm{d} n_s/\rm{d}\ln k|$, is predicted in these models to be of order $10^{-4}$--$10^{-3}$.