Chasing cosmic inflation: constraints for inflationary models and reheating insights

We investigate the impact of different choice of prior's range for the reheating epoch on cosmic inflation parameter inference in light of cosmic microwave background (CMB) anisotropy measurements from the {\em Planck} 2018 legacy release in combination with BICEP/Keck Array 2018 data and additional late-time cosmological observations such as uncalibrated Type Ia supernovae from the Pantheon catalogue, baryon acoustic oscillations and redshift space distortions from SDSS/BOSS/eBOSS. Here, we explore in particular the implications for the combination of reheating and inflationary-model parameter space considering $R+R^2$ inflation and a broad class of $\alpha$-attractor and D-brane models. Propagating the uncertainties due to an unknown reheating phase, these inflationary models completely cover the $n_{\rm s}$-$r$ parameter space allowed by {\em Planck} and BICEP/Keck data and represent good targets for future CMB and large-scale structure experiments. We perform a Bayesian model comparison of inflationary models, taking into account the reheating uncertainties assuming a conservative but accurate modelling of inflationary predictions. $R+R^2$ inflation, T-model $\alpha$-attractor inflation for $n=1$, E-model $\alpha$-attractor inflation for $n=1/2$, and KKLT inflation for $p=5$ are the better performing models, with none being preferred at a statistically significant level.