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 Markov chain Monte Carlo analysis to put constraints on the potential parameters $\alpha$, $\beta$ and $M$, and the number of e-foldings $N_{\text{pivot}}$ during inflation, using Planck 2018, BICEP/Keck, DES, and baryon acoustic oscillation (BAO) observations. We find ${\log }_{10}\alpha =0.37_{-0.85}^{+0.82}$, $\beta =1.969_{-0.023}^{+0.020}$, $M=(3.54_{-1.73}^{+2.62})\times {10}^{-5}$, and $N_{\text{pivot}}=47\pm 10$. With these mean values of the potential parameters $\alpha$ and $\beta$, and varying $N_{\text{pivot}}$ between 40 and 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 cosmic microwave background and large-scale structure observations.

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• Alternative gravity theories
• Cosmic microwave background
• Inflation
• Supergravity