Exponential Quintessence: Analytic Relationship Between the Current Equation of State Parameter and the Potential Parameter

TL;DR

This paper derives an analytical relation linking the current dark energy equation of state to the exponential potential parameter in quintessence models, aiding observational inference.

Contribution

It provides a new analytical formula connecting the current equation of state parameter to the potential parameter in exponential quintessence models, including an upper bound on bb.

Findings

Derived an analytical relation between bb and current equation of state.

Provided an upper bound bb<1.94 for accelerated expansion.

Facilitates inference of potential parameters from observations.

Abstract

Motivated by the indications of time-varying dark energy equation of state reported from DESI, we investigate a quintessence model with an exponential potential $V_0 e^{-\lambda\phi/m_{\mathrm{pl}}}$. We derive an analytical relationship between the current equation of state parameter for the quintessence field and the potential parameter $\lambda$ required to realize sufficient duration of radiation and matter domination. Our results provide a useful analytical relation for inferring the potential parameter $\lambda$ from the observed current equation of state parameter. Furthermore, based on this framework, we provide a new analytical upper bound on the potential parameter $\lambda$ for current accelerated expansion. Concretely, we obtain $\lambda<1.94$ by adopting $\Omega_{\phi0}=0.685$.