Dark Energy Parametrization motivated by Scalar Field Dynamics

TL;DR

This paper introduces a new dark energy parametrization based on scalar field dynamics, providing a flexible model for the equation of state that can mimic various evolutionary behaviors without specifying the potential explicitly.

Contribution

The authors develop an exact scalar field-based dark energy parametrization using a novel variable L, enabling diverse evolution scenarios without fixing the potential V.

Findings

The parametrization can produce increasing or decreasing w(z) over time.

It is consistent with current acceleration and the slow roll approximation.

The model links the equation of state to the scalar field potential through L.

Abstract

We propose a new Dark Energy parametrization based on the dynamics of a scalar field. We use an equation of state w=(x-1)/(x+1), with x=E_k/V, the ratio of kinetic energy E_k=\dotphi^2/2 and potential V. The equation of motion gives x=(L/6)(V/3H^2) and has a solution x=([(1+y)^2+2 L/3]^{1/2}-(1+y))/2 where y\equiv \rmm/V and L= (V'/V)^2 (1+q)^2, q=\ddotphi/V'. The resulting EoS is w=[6+ L- 6 \sqrt((1+y)^2+2L/3)]/(L+6y). Since the universe is accelerating at present time we use the slow roll approximation in which case we have |q|<< 1 and L\simeq (V'/V)^2. However, the derivation of w is exact and has no approximation. By choosing an appropriate ansatz for L we obtain a wide class of behavior for the evolution of Dark Energy without the need to specify the potential V. The EoS w can either grow and later decrease, or other way around, as a function of redshift and it is constraint between -1\leq w\leq 1 as for any canonical scalar field with only gravitational interaction. To determine the dynamics of Dark Energy we calculate the background evolution and its perturbations, since they are important to discriminate between different DE models. Our parametrization follows closely the dynamics of a scalar field scalar fields and the function L allow us to connect it with the potential V(phi) of the scalar field phi.