Accelerating universe in Kaniadakis cosmology without need of dark energy

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.