Early Mass-varying Neutrino Dark Energy: Nugget Formation and Hubble Anomaly

We present a novel scenario in which light (similar to few eV) dark fermions (sterile neutrinos) interact with a scalar field as in mass-varying neutrino dark energy theories. As the eV sterile states naturally become nonrelativistic 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 (EDE) behavior 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 dark matter nugget density is subdominant and most of the EDE go 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 satisfies the requirements for solving the H (0) anomaly. In our scenario, unlike in originally proposed early DE theory, the DE density is controlled by (eV) neutrino mass and it does not require a fine-tuned EDE scale. We perform a Markov Chain Monte Carlo analysis and confront our model with Planck + SHOES and baryon acoustic oscillation data and find evidence for a nonzero neutrino-scalar EDE density during MRE. Our analysis shows that this model is in agreement to nearly 1.3 sigma with SHOES measurement, which is H (0) = 74.03 +/- 1.42 km s(-1) Mpc(-1).