Observational constraints on $\alpha$-Starobinsky inflation

TL;DR

This study revisits $ extalpha$-Starobinsky inflation using current cosmological data, numerically computes power spectra without slow-roll approximation, and constrains model parameters, finding current observations insufficient to tightly constrain $ extalpha$.

Contribution

The paper provides a numerical analysis of $ extalpha$-Starobinsky inflation with updated observational constraints, avoiding slow-roll approximation and exploring reheating scenarios.

Findings

Constraints on $ extalpha$ are weak, with $ extlog_{10} extalpha$ spanning a broad range.

No significant correlation between $N_{pivot}$ and $ extalpha$ was found.

Current data cannot tightly constrain the inflationary parameter $ extalpha$.

Abstract

In this work we revisit $\alpha$-Starobinsky inflation, also know as $E$-model, in the light of current CMB and LSS observations. The inflaton potential in the Einstein frame for this model contains a parameter $\alpha$ in the exponential, which alters the predictions for the scalar and tensor power spectra of Starobinsky inflation. We obtain these power spectra numerically without using slow-roll approximation and perform MCMC analysis to put constraints on parameters $M$ and $\alpha$ from Planck-2018, BICEP/Keck (BK18) and other LSS observations. We consider general reheating scenario by varying the number of e-foldings during inflation, $N_{pivot}$, along with the other parameters. We find $\log_{10}\alpha = 0.0^{+1.6}_{-5.6}$, $\log_{10}M= -4.91^{+0.69}_{-2.7}$ and $N_{pivot} = 53.2^{+3.9}_{-5}$ with $95\%$ C. L.. This implies that the present CMB and LSS observations are insufficient to constrain the parameter $\alpha$. We also find that there is no correlation between $N_{pivot}$ and $\alpha$.