Dark Energy predictions from GREA: Background and linear perturbation theory

General Relativistic Entropic Acceleration (GREA) theory provides a covariant formalism for out-of-equilibrium phenomena in GR, extending the Einstein equations with an entropic force that behaves like bulk viscosity with a negative effective pressure. In particular, the growth of entropy associated with the homogeneous causal horizon can explain the present acceleration of the Universe, without introducing a cosmological constant. The dynamics of the accelerated Universe is characterized by a single parameter $\alpha$, the ratio of the causal horizon to the curvature scale, which provides a unique history of the Universe distinguishable from that of LCDM. In particular, we explain the coincidence problem and the Hubble tension by shifting the coasting point to higher redshifts. All background observables are correlated among themselves due to their common dependence on $\alpha$. This scenario gives a specific evolution for the effective equation of state parameter, $w(a)$. Furthermore, we study the linear growth of matter perturbations in the context of a homogeneous expanding background driven by the entropy of the causal horizon. We find that the rate of growth of matter fluctuations in GREA slows down due to the accelerated expansion and alleviates the $\sigma_8$ tension of LCDM. We compute the growth function of matter fluctuations, the redshift space distortions in the galaxy correlation function, as well as the redshift evolution of the BAO scale, and find that the ISW effect is significantly larger than in LCDM. It is interesting to note that many of the tensions and anomalies of the standard model of cosmology are alleviated by the inclusion of this transient period of acceleration of the Universe based on known fundamental physics. In the near future we will be able to constrain this theory with present data from deep galaxy surveys.