Discordances in cosmology and the violation of slow-roll inflationary dynamics

We identify examples of single field inflationary trajectories beyond the slow-roll regime which improve the fit to Planck 2018 data compared to baseline $\Lambda$CDM model with power law form of primordial spectrum and at the same time alleviate existing tensions between different data sets in the estimate of cosmological parameters such as $H_0$ and $S_8$. A damped oscillation in the first Hubble flow function - or equivalently a feature in the potential - and the corresponding localized oscillations in the primordial power spectrum partially mimic the improvement in the fit of Planck data due to $A_L$ or $\Omega_K$. Compared to the baseline model, this model can lead simultaneously to larger value of $H_0$ and a smaller value of $S_8$, a trend which can be enhanced when the most recent SH0ES measurement for $H_0$ is combined with Planck and BK18 data. Large scale structure data and more precise CMB polarization measurements will further provide critical tests of this intermediate fast roll phase.