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.
