A Global Overview of Starobinsky Inflation beyond slow-roll with CMB-BAO data

We perform a global analysis of the Starobinsky inflation using most recent CMB data from ACT and SPT together with DESI BAO measurements. By directly solving the equations of motion, we find relatively stronger constraints on the model parameters than those obtained under the slow-roll approximation from the baseline $\mathrm{\Lambda }$CDM parameters $A_s$ and $n_s$. We translate these constraints into limits on the reheating temperature. We also discuss the dependence of the prior choices of the model parameters. Further, the correlation of the model parameters with the BAO parameter $r_{d}h$ is also studied. We further investigate the impact of the global analysis on the dimension-six $R^3$ modified Starobinsky model, deriving constraints on its additional parameters. Finally, we also provide parameter limits on the effective inflationary Hubble slow-roll (HSR) and potential slow-roll (PSR) parametrization.