  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.
