Cosmological constraints on slow roll inflation: An update

Abstract

In light of the most recent cosmological observations, we provide new updated constraints on the slow roll inflation in different extended scenarios beyond the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmological model. Along with the usual six parameters, we simultaneously vary different combinations of additional parameters, including the running of the scalar spectral index ${\ensuremath{\alpha}}_{s}$, its running of running ${\ensuremath{\beta}}_{s}$, the tensor amplitude $r$ and the spatial curvature ${\mathrm{\ensuremath{\Omega}}}_{k}$. From the Planck 2018 data, we find no evidence for a scalar running or a running of running, while analyzing the Atacama Cosmology Telescope data combined with WMAP 9-years observations data we find a preference for nonzero ${\ensuremath{\alpha}}_{s}$ and ${\ensuremath{\beta}}_{s}$ at the level of $2.9\ensuremath{\sigma}$ and $2.7\ensuremath{\sigma}$, respectively. Anyway, this preference is reduced when the tensor amplitude can vary in the model or ${\ensuremath{\beta}}_{s}$ is fixed to zero. The upper bound on $r$ is only slightly affected by the additional parameters while the differences in the datasets can remarkably change the compatibility among the different inflationary models, sometimes leading to discordant conclusions.