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 $V_0{e}^{-\hat{I}»\ddot{I}•/m_{\mathrm{pl}}}$. We derive an analytical relationship between the current equation of state parameter for the quintessence field and the potential parameter $\hat{I}»$ required to realize sufficient duration of radiation and matter domination. Our results provide a useful analytical relation for inferring the potential parameter $\hat{I}»$ from the observed current equation of state parameter. Furthermore, based on this framework, we provide a new analytical upper bound on the potential parameter $\hat{I}»$ for current accelerated expansion. Concretely, we obtain $\hat{I}»<1.94$ by adopting $\hat{I}{\text{c◯}}_{\varphi 0}=0.685$.

19 pages, 6 figures, 1 table