Observational constraints and dynamical analysis of Kaniadakis
  horizon-entropy cosmology
  We study the scenario of Kanadiakis horizon entropy cosmology which arises
from the application of the gravity-thermodynamics conjecture using the
Kaniadakis modified entropy. The resulting modified Friedmann equations contain
extra terms that constitute an effective dark energy sector. We use data from
Cosmic chronometers, Supernova Type Ia, HII galaxies, Strong lensing systems,
and Baryon acoustic oscillations observations and we apply a Bayesian Markov
Chain Monte Carlo analysis to construct the likelihood contours for the model
parameters. We find that the Kaniadakis parameter is constrained around 0,
namely, around the value where the standard Bekenstein-Hawking is recovered.
Concerning the normalized Hubble parameter, we find
$h=0.708^{+0.012}_{-0.011}$, a result that is independently verified by
applying the $\mathbf{\mathbb{H}}0(z)$ diagnostic and, thus, we conclude that
the scenario at hand can alleviate the $H_0$ tension problem. Regarding the
transition redshift, the reconstruction of the cosmographic parameters gives
$z_T=0.715^{+0.042}_{-0.041}$. Furthermore, we apply the AICc, BIC and DIC
information criteria and we find that in most datasets the scenario is
statistical equivalent to $\Lambda$CDM one. Moreover, we examine the Big Bang
Nucleosynthesis (BBN) and we show that the scenario satisfies the corresponding
requirements. Additionally, we perform a phase-space analysis, and we show that
the Universe past attractor is the matter-dominated epoch, while at late times
the Universe results in the dark-energy-dominated solution. Finally, we show
that Kanadiakis horizon entropy cosmology accepts heteroclinic sequences, but
it cannot exhibit bounce and turnaround solutions.
