Exploring generalized Starobinsky Model of Inflation: Observational Constraints

TL;DR

This paper investigates a generalized Starobinsky inflation model with power-law corrections, using observational data to constrain model parameters and confirm its viability within current cosmological bounds.

Contribution

The study introduces a generalized $f(R)$ inflation model with power-law corrections and provides observational constraints on its parameters using Planck, BICEP3, and BAO data.

Findings

Constraints on $eta$ and $M$ parameters from observational data.

Scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ within Planck bounds.

Deviations from the original Starobinsky model are observationally viable.

Abstract

We examine the power-law Starobinsky model, a generalized version of the Starobinsky inflation model, characterized by a power-law correction to Einstein gravity. Employing the $f(R)$ formalism, the scalar and tensor power spectra were numerically computed as functions of the dimensionless parameters $M$ and $\beta$. A Markov Chain Monte Carlo (MCMC) analysis was conducted using Planck-2018, BICEP3 and BAO observational data, yielding precise constraints on $\beta = 1.987^{+0.013}_{-0.016},\, 95\%\, C.\, L.$. and $ \log_{10}M = -4.72^{+0.21}_{-0.20}$. The derived scalar spectral index $n_s=0.9676^{+0.0069}_{-0.0068}$ and tensor-to-scalar ratio $r=0.0074^{+0.0061}_{-0.0044}$ lie within the bounds set by Planck observations. We analyse a general reheating scenario while keeping the number of e-folds during inflation, $N_{pivot}$, fixed. The analysis confirms that deviations from the Starobinsky $R^2$ model are observationaly viable, with implications for high-energy physics and supergravity-based inflationary models.