Cosmological constraints on slow roll inflation: An update

In light of the most recent cosmological observations, we provide new updated constraints on the slow roll inflation in different extended scenarios beyond the ΛCDM cosmological model. Along with the usual six parameters, we simultaneously vary different combinations of additional parameters, including the running of the scalar spectral index αs, its running of running βs, the tensor amplitude r and the spatial curvature ωk. 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 αs and βs at the level of 2.9σ and 2.7σ, respectively. Anyway, this preference is reduced when the tensor amplitude can vary in the model or βs 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.