Scalar Field Dark Energy Parametrization

TL;DR

This paper introduces a new scalar field-based parametrization for Dark Energy, allowing flexible evolution of the equation of state without specifying the potential, and connects it with scalar field dynamics and perturbations.

Contribution

It proposes a novel Dark Energy parametrization based on scalar field dynamics that does not require fixing the potential, enabling diverse evolution scenarios of the equation of state.

Findings

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

It maintains w within the bounds of -1 and 1 for canonical scalar fields.

The approach links the parametrization directly to the scalar potential V(φ).

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 $E_k=\dot\phi^2/2$ and potential $V$. The eq. of motion gives $x=(L/6)(V/3H^2)$ and with a solution $x=([1+2 L/3(1+y)]^{1/2}-1)(1+y)/2$ where $y\equiv \rm/V$ and $L\equiv (V'/V)^2 (1+q)^2,\, q\equiv\ddot\p/V'$. Since the universe is accelerating at present time we use the slow roll approximation in which case we have $|q|\ll 1$ and $L\simeq (V'/V)^2$. However, the derivation of $L$ 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 $V$. In fact $w$ 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. Furthermore, we also calculate the perturbations of DE and since the evolution of DE is motivated by the dynamics of a scalar field the homogenous and its perturbations can be used to determine the form of the potential and the nature of Dark Energy. Since our parametrization is on $L$ we can easily connect it with the scalar potential $V(\phi)$.