New simple and accurate quintessence approximations

TL;DR

This paper introduces new simple and highly accurate approximations for quintessence solutions, significantly reducing computational complexity and enabling direct analytical calculations of key cosmological parameters.

Contribution

The authors develop novel approximations for quintessence models that are more accurate and simpler than existing methods, allowing for analytical expressions of CPL parameters from scalar potentials.

Findings

Achieve ~0.1% maximum relative errors in key cosmological functions

Approximate solutions are derived directly from scalar field potentials

Enable analytical computation of CPL parameters for quintessence models

Abstract

We derive new approximations for quintessence solutions that are simpler and an order of magnitude more accurate than anything available in the literature, which from an observational perspective \emph{makes numerical calculations superfluous}. For example, our tracking quintessence approximation yields $\sim 0.1\%$ maximum relative errors of $H(z)/H_0$ and $\Omega_\mathrm{m}(z)$ for the observationally viable inverse power law scalar field potentials, and similarly for viable thawing quintessence models using two slow-roll parameters. The approximations are trivially computed from the scalar field potential and as an application we give \emph{analytic} expressions for the CPL parameters calculated from an arbitrary scalar field potential for thawing and tracking quintessence models.