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.