Power law $\alpha$-Starobinsky inflation

TL;DR

This paper introduces a generalized inflation model combining power law and alpha-Starobinsky features, constrains its parameters using recent cosmological data, and finds it mildly favored over the standard Starobinsky model.

Contribution

The work develops a novel inflationary model blending power law and alpha-Starobinsky features, and performs comprehensive observational constraints and Bayesian model comparison.

Findings

Model parameters constrained with Planck-2018, BICEP/Keck, DES, and BAO data.

Predictions for tensor-to-scalar ratio and spectral index are within observational bounds.

The proposed model is mildly favored over the standard Starobinsky inflation based on Bayesian evidence.

Abstract

In this work we consider a generalization of Starobinsky inflation obtained by combining power law ($R^\beta$), and $\alpha$-Starobinsky inflation ($E$-model). The Einstein frame potential for this model is that of power law Starobinsky inflation modified by a parameter $\alpha$ in the exponential. After computing power spectra for scalar and tensor perturbations numerically, we perform MCMC analysis to put constraints on the potential parameters $\alpha$, $\beta$ and $M$, and the number of e-foldings $N_{pivot}$ during inflation, using Planck-2018, BICEP/Keck (BK18), DES and BAO observations. We find $\log_{10}\alpha= 0.37^{+0.82}_{-0.85}$, $\beta = 1.969^{+0.020}_{-0.023}$, $M=\left(3.54^{+2.62}_{-1.73}\right)\times 10^{-5}$ and $N_{pivot} = 47\pm{10}$. With these mean values of the potential parameters $\alpha$ and $\beta$, and varying $N_{pivot}$ between $40$ to $55$, we also find that the $r-n_s$ predictions of our model lie well within the $1\sigma$ bounds of joint constraints from combined analysis of ACT, Planck-2018, BICEP and BAO observations. We compute the Bayesian evidences for our proposed model, power law Starobinsky inflation, $\alpha$-Starobinsky inflation and Starobinsky inflation. Considering the Starobinsky model as the base model, we calculate the Bayes factor and find that our proposed model is mildly favored by the CMB and LSS observations.