Constraints for the thawing and freezing potentials

TL;DR

This paper investigates the evolution of the dark energy equation of state in quintessence models with thawing and freezing potentials, using numerical simulations constrained by observational data to identify potential types.

Contribution

It introduces a method to classify scalar potentials based on their $w(z)$ evolution and observational constraints, aiding future identification of dark energy models.

Findings

Allowed regions in $dw/da$ vs. $d^2w/da^2$ space are identified.

Some solutions exhibit thawing behavior within freezing potentials.

Numerical $w(z)$ fits observational constraints from Planck 2015.

Abstract

We study the accelerating present universe in terms of the time evolution of the equation of state $w(z)$ (redshift $z$) due to thawing and freezing scalar potentials in the quintessence model. The values of $dw/da$ and $d^2w/da^2$ at scale factor of $a = 1$ are associated with two parameters of each potential. For five type scalar potentials, the scalar fields $Q$ and $w$ as function of time $t$ and/or $z$ are numerically calculated under the fixed boundary condition of $w(z=0)=-1+\Delta$. The observational constraint $w_{obs}$ (Planck 2015) is imposed to test whether the numerical $w(z)$ is in $w_{obs}$. Some solutions show the thawing features in the freezing potentials. Mutually exclusive allowed regions in $dw/da$ vs. $d^2w/da^2$ diagram are obtained in order to identify the likely scalar potential and even the potential parameters by future observational tests.