Bayesian inference of the inflation and reheating model parameters

In this paper, we perform a Bayesian inference of the parameters of the Starobinsky inflationary model with subsequent reheating stage using the MCMC method and the observed data on the anisotropy of the cosmic microwave background collected by the Planck collaboration and on baryonic acoustic oscillations. The reheating stage is modeled by a single parameter Rᵣₑₕ, which contains a combination of the reheating temperature Tᵣₑₕ and the effective equation of state during reheating ω̄ᵣₑₕ. Using the modified Boltzmann code CLASS and the MontePython program with the GetDist package, we perform a direct analysis of the space of model parameters and obtain their posterior distributions. By computing the Kullback–Leibler divergence, we estimate the information gained by the parameter inference from the observed data. In the proposed parametrization, we achieve $7.73$ bits of information about the inflaton potential amplitude and $1.64$ bits of information about the reheating parameter. The results are compared with those existing in the literature implying that the specification of inflationary model allows to better constrain the reheating stage than in the model-independent approach to inflation. Finally, we draw constraints for the reheating temperature and average equation of state. Although the former can vary within $16$ orders of magnitude (in the $95%$ credible interval), for the latter there is a clear preference for the values larger than zero, meaning that the usual dust-like equation of state ω̄ᵣₑₕ = 0 is excluded at more than 2σ level.