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

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 $V_0{e}^{-\lambda \varphi /m_{\mathrm{pl}}}$. We derive an analytical relationship between the current equation of state parameter for the quintessence field and the potential parameter $\lambda$ required to realize 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 approximate analytical upper bound on the potential parameter $\lambda$ for current accelerated expansion. Concretely, we obtain $\lambda <1.94$ as an approximate analytic estimate by adopting ${\Omega }_{\varphi 0}=0.685$.

Comments: 19 pages, 6 figures, 1 table, to appear in JCAP