Future Rip Scenarios in Fractional Holographic Dark Energy

TL;DR

This paper explores the potential for late-time rip singularities in fractional holographic dark energy models, analyzing different cutoffs and interaction terms to identify conditions leading to big, little, and pseudo-rip scenarios.

Contribution

It introduces a comprehensive analysis of rip singularities in FHDE with various cutoffs, including the Hubble cutoff, and demonstrates the conditions under which different rip types occur.

Findings

Big rip occurs for fractional Lévys index 1<α≤2.

Pseudo-rip requires α>2, which is rejected for GO cutoff.

Little and pseudo-rip singularities can occur with Hubble cutoff and non-linear interaction Q.

Abstract

In this paper, we investigate the occurrence of late-time cosmological singularities, namely, the rip scenarios within the framework of interacting Fractional Holographic Dark Energy (FHDE). We start our investigation with the Granda-Oliveros (GO) cutoff, i.e., $L=(\gamma H^{2}+\delta\dot{H})^{-\frac{1}{2}}$, and highlight the range of allowed $\alpha$ (L\'evy's index) values for which big, little and pseudo rip can occur. In particular, we highlight the occurrence of a big rip for fractional values of the L\'evy's index in the allowed range $1<\alpha\leq2$. Moreover, we conclude that the occurrence of a pseudo-rip requires L\'evy's index to be $\alpha>2$. Therefore, we reject the possibility of pseudo-rip within the GO cutoff. Furthermore, we demonstrate that the occurrence of the little rip in FHDE equipped with a GO cutoff is rather contrived and requires a specific functional form of the IR cutoff $L\sim(\gamma H^{2}+g(H))^{-\frac{1}{2}}$, which belongs to a larger class of Nojiri-Odintsov (NO) cutoffs. To extend our perspective beyond the GO cutoff, we investigate the interacting FHDE framework equipped with the Hubble cutoff, i.e., $L=H^{-1}$, in developing an ansatz-based approach to the little and pseudo-rip singularities as they fail to appear in the GO cutoff. Within this approach, we invoke the expression of the Hubble parameter, $H(t)$, which corresponds to the little and pseudo-rip, into the cosmological parameters such as the Equation of State (EoS) and Squared Sound Speed (SSS) as a function of cosmic time $t$. We produce numerical plots of these parameters in both linear and non-linear $Q$ regimes, which supplement our theoretical findings. In summary, our results highlight the occurrence of little and pseudo-rip singularities within a Hubble cutoff for a non-linear $Q$ term within the FHDE framework.