Power law $\alpha$-Starobinsky inflation

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.