Rock 'n' Roll Solutions to the Hubble Tension
  Local measurements of the Hubble parameter are increasingly in tension with
the value inferred from a $\Lambda$CDM fit to the cosmic microwave background
(CMB) data. In this paper, we construct scenarios in which evolving scalar
fields significantly ease this tension by adding energy to the Universe around
recombination in a narrow redshift window. We identify solutions of $V \propto
\phi^{2 n}$ with simple asymptotic behavior, both oscillatory (rocking) and
rolling. These are the first solutions of this kind in which the field
evolution and fluctuations are consistently implemented using the equations of
motion. Our findings differ qualitatively from those of the existing
literature, which rely upon a coarse-grained fluid description. Combining CMB
data with low-redshift measurements, the best fit model has $n=2$ and increases
the allowed value of $H_0$ from 69.2 km/s/Mpc in $\Lambda$CDM to 72.3 km/s/Mpc
at $2\sigma$. Future measurements of the late-time amplitude of matter
fluctuations and of the reionization history could help distinguish these
models from competing solutions.
