Bayesian analysis of a generalized Starobinsky model with reheating constraints

Abstract

We study a generalization of 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 consitent 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 ns and the scalar amplitude of perturbations As , 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.