Holographic Dark Energy Interacting with Two Fluids and Validity of Generalized Second Law of Thermodynamics

TL;DR

This paper models holographic dark energy interacting with dark matter and another dark energy component, analyzing thermodynamic laws and entropy to understand cosmic evolution and the validity of the generalized second law.

Contribution

It introduces a general cosmological model with two interaction terms between holographic dark energy, dark matter, and an unknown component, exploring thermodynamics and entropy bounds.

Findings

GSL validity depends on bounds on the deceleration parameter q.

Derived entropy expressions for interacting dark energy components.

Established conditions for the decay of dark energy into dark matter and other components.

Abstract

We have considered a cosmological model of holographic dark energy interacting with dark matter and another unknown component of dark energy of the universe. We have assumed two interaction terms $Q$ and $Q'$ in order to include the scenario in which the mutual interaction between the two principal components (i.e., holographic dark energy and dark matter) of the universe leads to some loss in other forms of cosmic constituents. Our model is valid for any sign of $Q$ and $Q'$. If $Q<Q'$, then part of the dark energy density decays into dark matter and the rest in the other unknown energy density component. But if $Q>Q'$, then dark matter energy receives from dark energy and from the unknown component of dark energy. Observation suggests that dark energy decays into dark matter. Here we have presented a general prescription of a cosmological model of dark energy which imposes mutual interaction between holographic dark energy, dark matter and another fluid. We have obtained the equation of state for the holographic dark energy density which is interacting with dark matter and other unknown component of dark energy. Using first law of thermodynamics, we have obtained the entropies for holographic dark energy, dark matter and other component of dark energy, when holographic dark energy interacting with two fluids (i.e., dark matter and other component of dark energy). Also we have found the entropy at the horizon when the radius ($L$) of the event horizon measured on the sphere of the horizon. We have investigated the GSL of thermodynamics at the present time for the universe enveloped by this horizon. Finally, it has been obtained validity of GSL which implies some bounds on deceleration parameter $q$.