A Higher-Derivative Hubble Parameter Dark Energy Model: Cosmological Analysis and Scalar Field Correspondence

TL;DR

This paper introduces a dark energy model based on higher derivatives of the Hubble parameter, analyzes its cosmological implications for different interactions, and establishes correspondences with various scalar field theories.

Contribution

It proposes a novel dark energy model involving higher derivatives of H, explores its cosmological behavior under multiple interaction scenarios, and links it to several scalar field frameworks.

Findings

Derived cosmological quantities for the model with and without interactions.

Analyzed the impact of different interaction terms on cosmic evolution.

Established scalar field correspondences for the proposed dark energy model.

Abstract

In this work, we study a Dark Energy (DE) energy density model which depends on the Hubble parameter squared $H^2$ and on its first, second and third time derivatives $\dot{H}$, $\ddot{H}$ and $\dddot{H}$. Considering a scale factor $a$ with a power-law dependence on the time (with $n$ indicating the power-law index), we obtain some important cosmological quantities as function of the , like the energy densities of Matter $\rho_m$ and of DE $\rho_D$, the fractional energy densities of DM $\Omega_m$ and of DE $\Omega_D$, the Hubble parameter squared $H^2$, the deceleration parameter $q$, the evolutionary form of the fractional energy density of DE $\Omega'_D$, the pressure of DE $p_D$ and the Equation of State (EoS) parameter of DE $\omega_D$, for both non interacting and interacting cases. For the interacting case, we consider 9 different interacting term $Q$, all functions of the Hubble parameter $H$ and/or of $\rho_m$ and $\rho_D$. Finally, we establish a correspondence between the DE model we study and some scalar field theories, including tachyon, k-essence, quintessence, Yang-Mills (YM) and Nonlinear Electrodynamics (NLED) fields.