Accelerating universe in Kaniadakis cosmology without need of dark energy

TL;DR

This paper proposes a Kaniadakis entropy-based cosmological model that explains the universe's accelerated expansion without dark energy or a cosmological constant, using corrected Friedmann equations and cosmographic parameters.

Contribution

It introduces a new cosmological scenario derived from Kaniadakis entropy, reconstructs model parameters analytically from cosmographic data, and demonstrates the correction term's role as dark energy.

Findings

The model reproduces observed cosmological parameters without dark energy.

Analytical reconstruction of parameters from cosmographic data is possible.

The correction term mimics dark energy effects in the universe's expansion.

Abstract

Taking into consideration of Kaniadakis entropy associated with the apparent horizon of Friedmann-Robertson-Walker (FRW) Universe and using the gravity-thermodynamics conjecture, a new cosmological scenarios emerges based on corrected Friedmann equations, which contains a correction term $ \alpha\left(H^2+\frac{k}{a^2}\right)^{-1}$ where $\alpha\equiv\frac{K^2 \pi^2}{2 G^2}$ and $K$ is Kaniadakis parameter. We show that it is possible to reconstruct the parameters of the model, in terms of cosmographic parameters$\{ q, j, s\}$ analytically. For the flat universe, the parameters can be reconstructed in terms of only two cosmographic parameters $\{q, j\}$. The advantage of this analytical reconstruction is that it provides the possibility to test observational measurements on Kaniadakis cosmology using directly measurable cosmographic parameters. As an interesting result is that without any assumption about the value of $\Lambda$, we found that the set $\{q_{0}=-0.708, j_{0}=1.137\}$ automatically gives $\Lambda\simeq0$ and $\{\Omega_{m0}\simeq0.325,\Omega_{\alpha0}=0.671\}$. This result is in excellent agrement with pervious observational studies. Reconstructing the evolution of deceleration parameter against redshift $z$ for these values, shows that the correction term could plays the role of dark energy without any dark energy component or cosmological constant $\Lambda$. Finally, we formulate the deviation parameter in terms of $\{q,j\}$ which reflects the deviation of the model from $\Lambda CDM$ model. We Show that the deviation factor is very sensitive to the jerk parameter $j$, while the $\Omega_{m0}$ is sensitive to deceleration parameter $q_{0}$. Hence, the set $\{j,q\}$ can be regarded as useful parameters to test the theoretical and observational studies in Kaniadakis cosmology.