Abstract <p>We revisit the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha\)</EquationSource>  </InlineEquation>-Starobinsky inflation, also known as the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(E\)</EquationSource>  </InlineEquation>-model, in the light of current CMB and LSS observations. The inflaton potential in the Einstein frame for this model contains a parameter <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\alpha\)</EquationSource>  </InlineEquation> 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 the slow-roll approximation, and perform MCMC analysis to put constraints on the parameters <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(M\)</EquationSource>  </InlineEquation> and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\alpha\)</EquationSource>  </InlineEquation> from Planck-2018, BICEP/Keck (BK18) and other LSS observations. We consider the general reheating scenario by varying the number of e-foldings during inflation, <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(N_{\textrm{privot}}\)</EquationSource>  </InlineEquation>, along with other parameters. We find <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\log_{10}\alpha=0.0^{+1.6}_{-5.6}\)</EquationSource>  </InlineEquation>, <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\log_{10}M=-4.91^{+0.69}_{-2.7}\)</EquationSource>  </InlineEquation>, and <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(N_{\textrm{privot}}=53.2^{+3.9}_{-5}\)</EquationSource>  </InlineEquation> with <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(95\%\)</EquationSource>  </InlineEquation> C.L. This implies that the present CMB and LSS observations are insufficient for constraining the parameter <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(\alpha\)</EquationSource>  </InlineEquation>. We also find that there is no correlation between <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(N_{\textrm{privot}}\)</EquationSource>  </InlineEquation> and <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(\alpha\)</EquationSource>  </InlineEquation>.</p>

Observational Constraints on \(\boldsymbol{\alpha}\)-Starobinsky Inflation

期刊论文
发表日期：

2025年12月3日

查看全文

Saisandri Saini,
Akhilesh Nautiyal

摘要

Abstract

We revisit the \(\alpha\) -Starobinsky inflation, also known as the \(E\) -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 the slow-roll approximation, and perform MCMC analysis to put constraints on the parameters \(M\) and \(\alpha\) from Planck-2018, BICEP/Keck (BK18) and other LSS observations. We consider the general reheating scenario by varying the number of e-foldings during inflation, \(N_{\textrm{privot}}\) , along with other parameters. We find \(\log_{10}\alpha=0.0^{+1.6}_{-5.6}\) , \(\log_{10}M=-4.91^{+0.69}_{-2.7}\) , and \(N_{\textrm{privot}}=53.2^{+3.9}_{-5}\) with \(95\%\) C.L. This implies that the present CMB and LSS observations are insufficient for constraining the parameter \(\alpha\) . We also find that there is no correlation between \(N_{\textrm{privot}}\) and \(\alpha\) .