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 $\Lambda\rm{CDM}$ cosmological model. Along with the usual six parameters, we simultaneously vary different combinations of additional parameters, including the running of the scalar spectral index $\alpha_s$, its running of running $\beta_s$, the tensor amplitude $r$ and the spatial curvature $\Omega_k$. 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 non-zero $\alpha_s$ and $\beta_s$ at the level of 2.9$\sigma$ and 2.7$\sigma$, respectively. Anyway, this preference is reduced when the tensor amplitude can vary in the model or $\beta_s$ 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.