The analytical approach in testing the Kaniadakis cosmology

We know that a quantum-corrected cosmological scenario can emerge based on its corrected Friedmann equations corresponding to the corrected entropy of cosmic-horizon using the gravity-thermodynamics conjecture in deriving those equations. In this right, the Kaniadakis entropy associated with the apparent horizon of Friedmann-Robertson-Walker (FRW) Universe leads to a corrected Friedmann equation which contains a correction term as Ω K a = α ( H 2 + k a 2 ) − 1 H 2 where α ≡ K 2 π 2 2 G 2 (K is the Kaniadakis parameter). Here, we derive the analytical relations between the energy density parameters Ω m , Ω Λ (and the ratio density Ω of correction term) and the geometrical cosmological parameters { q , j } . This leads to getting Ω K a = j − 1 4 ( q + 1 ) 2 − ( j − 1 ) which enables us to put constrains on Ω K a 0 using the measurable parameters { q 0 , j 0 } and H. It also reveals some interesting aspects of the Kaniadakis cosmology by explaining that the correction term plays different roles both in the presence and in the absence of the cosmological constant Λ. This term plays the role of dark energy in the absence of the cosmological constant Λ, while in the presence of this component, it plays the role of a small correction to dark energy. The value of Ω then determines the amount of the deviation of Kaniadakis model from the concordance ΛCDM model. As a result, the value of j is found to be close to unit for vanishing cosmological constant Λ = 0 and the maximum value of Ω K a 0 ; thereby we get ( j 0 − 1 ) ≃ 0.137 and ( j 0 − 1 ) ≃< 10 − 3 for the case of Λ = 0 and Λ ≠ 0 , respectively. That is, the jerk parameter j can be used as a useful tool to test the Kaniadakis cosmology using the observational studies.