Bayesian Analysis of a Generalized Starobinsky Model with Reheating Constraints

We study a generalization of the the Starobinsky model adding a term of the form $R^{2p}$ to the Einstien-Hilbert action. We take the power $p$ as a parameter of the model and explore the constraints from CMB plus BAO data through a Bayesian analysis, thus exploring a range of values for the exponent parameter. We incorporate a reheating phase to the model through the background matter content (equation of state) and the duration of this period (number of $e$-foldings of reheating). We find that incorporating information from reheating imposes constraints on cosmological quantities, more stringent than the case of no reheating when tested with the Planck+BAO data. The inferred value of the exponent parameter is statistically consistent with $p=1$, favoring the original Starobinsky potential. Moreover, we report tighter constraints on $p$ and the number of $e$-folds in comparison with previous works. The obtained values for other inflationary observational parameters, such as the scalar spectral index $n_s$ and the scalar amplitude of perturbations $A_s$, are consistent with prior measurements. Finally we present the alternative use of consistency relations in order to simplify the parameter space and test the generalized Starobinsky potential even more efficiently.