Early mass varying neutrino dark energy: Nugget formation and Hubble
  anomaly
  We present a novel scenario, in which light ($\sim$ few \rm{eV}) dark
fermions (sterile neutrinos) interact with a scalar field like in mass varying
neutrino dark energy theories. As the $\rm{eV}$ sterile states naturally become
non-relativistic before the Matter Radiation Equality (MRE), we show that the
neutrino-scalar fluid develops strong perturbative instability followed by the
formation of neutrino-nuggets and the early dark energy behaviour disappears
around MRE. The stability of the nugget is achieved when the Fermi pressure
balances the attractive scalar force and we numerically find the mass and
radius of heavy cold nuggets by solving for the static configuration for the
scalar field. We find that for the case when DM nugget density is sub-dominant
and most of the early DE energy goes into scalar field dynamics, it can in
principle relax the Hubble anomaly. Especially when a kinetic energy dominated
phase appears after the phase transition, the DE density dilutes faster than
radiation and satisfy the requirements for solving $H_0$ anomaly. In our
scenario, unlike in originally proposed early dark energy theory, the dark
energy density is controlled by ($\rm{eV}$) neutrino mass and it does not
require a fine tuned EDE scale. We perform a MCMC analysis and confront our
model with Planck + SHOES and BAO data and find an evidence for non-zero
neutrino-scalar EDE density during MRE. Our analysis shows that this model is
in agreement of nearly 1.3$\sigma$ with SHOES measurement which is $H_0 = 74.03
\pm 1.42$ km/s/Mpc.
