The Neutrino Puzzle: Anomalies, Interactions, and Cosmological Tensions
  New physics in the neutrino sector might be necessary to address anomalies
between different neutrino oscillation experiments. Intriguingly, it also
offers a possible solution to the discrepant cosmological measurements of $H_0$
and $\sigma_8$. We show here that delaying the onset of neutrino free-streaming
until close to the epoch of matter-radiation equality can naturally accommodate
a larger value for the Hubble constant $H_0=72.3 \pm 1.4$ km/s/Mpc and a lower
value of the matter fluctuations $\sigma_8=0.786\pm 0.020$, while not degrading
the fit to the cosmic microwave background (CMB) damping tail. We achieve this
by introducing neutrino self-interactions in the presence of a non-vanishing
sum of neutrino masses. This strongly interacting neutrino cosmology prefers
$N_{\rm eff} = 4.02 \pm 0.29$, which has interesting implications for particle
model-building and neutrino oscillation anomalies. We show that the absence of
the neutrino free-streaming phase shift on the CMB can be compensated by
shifting the value of other cosmological parameters, hence providing an
important caveat to the detections made in the literature. Due to their impact
on the evolution of the gravitational potential at early times,
self-interacting neutrinos and their subsequent decoupling leave a rich
structure on the matter power spectrum. In particular, we point out the
existence of a novel localized feature appearing on scales entering the horizon
at the onset of neutrino free-streaming. While the interacting neutrino
cosmology provides a better global fit to current cosmological data, we find
that traditional Bayesian analyses penalize the model as compared to the
standard cosmological. Our analysis shows that it is possible to find radically
different cosmological models that nonetheless provide excellent fits to the
data, hence providing an impetus to thoroughly explore alternate cosmological
scenarios.
