Observational constraints on power law Starobinsky inflation

Abstract

In this work we revisit power law, $\frac{1}{M^2}R^\beta$, inflation to find the deviations from $R^2$ inflation allowed by current CMB and LSS observations. We compute the power spectra for scalar and tensor perturbations numerically and perform MCMC analysis to put constraints on parameters $M$ and $\beta$ from Planck-2018, BICEP3 and other LSS observations. We consider general reheating scenario and also vary the number of e-foldings during inflation, $N_{pivot}$, along with the other parameters. We find $\beta = 1.966^{+0.035}_{-0.042}$, $M= \left(3.31^{+5}_{-2}\right)\times 10^{-5}$ and $N_{pivot} = 41^{+10}_{-10}$ with $95\%\, C.\, L.$. This indicates that the current observations allow deviation from Starobinsky inflation. The scalar spectral index, $n_s$, and tensor-to-scalar ratio, $r$, derived from these parameters, are consistent with the Planck and BICEP3 observations.