We identify examples of single field inflationary trajectories beyond the slow-roll regime that improve the fit to Planck 2018 data compared to a baseline $\mathrm{\Lambda }$ cold dark matter model with power law form of primordial spectrum and at the same time alleviate existing tensions between different datasets 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 ${\mathrm{\Omega }}_K$. Compared to the baseline model, this model can lead simultaneously to a larger value of $H_0$ and a smaller value of $S_8$, a trend that can be enhanced when the most recent SH0ES measurement for $H_0$ is combined with Planck and BICEP-Keck 2018 data. Large scale structure data and more precise cosmic microwave background polarization measurements will further provide critical tests of this intermediate fast-roll phase.

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• Cosmic microwave background
• Cosmological parameters
• Inflation