Barrow Entropy Cosmology: an observational approach with a hint of
  stability analysis
  In this work, we use an observational approach and dynamical system analysis
to study the cosmological model recently proposed by Saridakis (2020), which is
based on the modification of the entropy-area black hole relation proposed by
Barrow (2020). The Friedmann equations governing the dynamics of the Universe
under this entropy modification can be calculated through the
gravity-thermodynamics conjecture. We investigate two models, one considering
only a matter component and the other including matter and radiation, which
have new terms compared to the standard model sourcing the late cosmic
acceleration. A Bayesian analysis is performed in which we use five
cosmological observations (observational Hubble data, type Ia supernovae, HII
galaxies, strong lensing systems, and baryon acoustic oscillations) to
constrain the free parameters of both models. From a joint analysis, we obtain
constraints that are consistent with the standard cosmological paradigm within
$2\sigma$ confidence level. In addition, a complementary dynamical system
analysis using local and global variables is developed which allows obtaining a
qualitative description of the cosmology. As expected, we found that the
dynamical equations have a de Sitter solution at late times.
