Observational Constraints on $$\boldsymbol{\alpha}$$-Starobinsky Inflation

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 $$\alpha$$ .