Holographic dark energy in modified Kaniadakis cosmology

TL;DR

This work develops holographic dark energy within a modified Kaniadakis cosmology, incorporating KH entropy into the Friedmann equations with the Hubble radius as the IR cutoff. The KHDE density is $\rho_{DE}=3c^2M_p^2H^2+3\alpha M_p^2H^{-2}$, and the background dynamics are governed by $3M_p^2(H^2-\alpha H^{-2})=\rho_m+\rho_{DE}$ and $-2M_p^2\dot{H}(1+\alpha H^{-4})=(\rho_m+p_m+\rho_{DE}+p_{DE})$. In DE-dominated universes KHDE mimics a cosmological constant with $w_{DE}=-1$, and acceleration can occur with $L=H^{-1}$ even without DM–DE interaction; when interactions are included, the total EoS can cross the phantom line, and the stability and statefinder analyses reveal a rich phenomenology with $v_s^2$ often negative and trajectories departing from $\Lambda$CDM, though approaching $(r,s)=(1,0)$ in the future. Overall, KHDE in this thermodynamically consistent framework offers a potential microscopic link to the cosmological constant and a testable distinguishing signature from standard $\Lambda$CDM via statefinders and stability behavior.

Abstract

It is well-known that any modification to the entropy expression not only change the energy density of the holographic dark energy, but also modifies the cosmological field equations through thermodynamics-gravity correspondence. Here we propose a Kaniadakis holographic dark energy (KHDE) in the background of the modified Kaniadakis cosmology by incorporating the effects of Kaniadakis entropy into the Friedmann equations. We choose the Hubble radius, $L=H^{-1}$, as system's IR cutoff and determine the cosmological implications of this model. We first consider a dark energy (DE) dominated universe and reveal that this model mimics the cosmological constant with $w_{DE}=-1$. This implies that the theoretical origin of the cosmological constant, $Λ$, may be understood through KHDE in the context of Kaniadakis cosmology. Remarkably, we observe that in the absence of interaction between DE and dark matter (DM), and in contrast to HDE in standard cosmology, our model can explain the current acceleration of the cosmic expansion for the Hubble radius as IR cutoff. When the interaction between DE and DM is taken into account, we see that the total equation of state parameter (EoS), $w_{tot}=p_{tot}/ρ_{tot}$ can cross the phantom line at the present time. We also analyze the squared speed of sound, $v_s^2$, for this model and find out that $(v_s^2<0)$ for interacting KHDE. Investigating the statefinder, confirms the distinction between KHDE and $Λ$CDM model. It is seen that the statefinder diagram move away from the point of $\left\lbrace r,s\right\rbrace= \left\lbrace 1,0\right\rbrace$ with increasing the interaction parameter.

Figures (6)

• Figure 1: Evolution of $\Omega_{DE}$ (left panel) and (right panel) as a function of redshift, $z$, for both interacting and noninteracting KHDE for different values of ${b^2}$ in a flat Kaniadakis cosmology. Here, we set $\Omega^{0}_{DE}$= 0.7, and ${c^2} = 0.5$.
• Figure 2: Evolution of the difference between the $\Omega_{DE}$ values ($\Delta$) as a function of $z$, for different vales of ${b^2}$ in a flat Kaniadakis cosmology. Here, we set $\Omega^{0}_{DE}$= 0.7, and ${c^2} = 0.5$.
• Figure 3: Evolution of $w_{DE}$ (left panel) and $w_{tot}$ (right panel) as a function of $z$ for different choices of ${b^2}$ in a flat Kaniadakis cosmology. Here, we set $K=0.1$, $\Omega_{DE0}$= 0.7, and ${c^2} = 0.5$.
• Figure 4: Evolution of the deceleration parameter $q$ as a function of redshift, $z$, for KHDE in a flat Kaniadakis cosmology. Here, we set $\Omega_{DE0}$= 0.7, and ${c^2} = 0.5$.
• Figure 5: Evolution of the squared sound speed $\upsilon _s^2$ as a function of redshift, $z$, for non-interacting and interacting KHDE in a flat Kaniadakis cosmology. Here, we set $\Omega_{DE0}$= 0.7, and ${c^2} = 0.5$.