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arXiv · 2605.05122

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

Naoto Maki·Kazunori Kohri
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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 $V_0 e^{-λϕ/m_{\mathrm{pl}}}$. We derive an analytical relationship between the current equation of state parameter for the quintessence field and the potential parameter $λ$ required to realize radiation and matter domination. Our results provide a useful analytical relation for inferring the potential parameter $λ$ 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 $λ$ for current accelerated expansion. Concretely, we obtain $λ<1.94$ as an approximate analytic estimate by adopting $Ω_{\phi0}=0.685$.

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BibTeXRIS

Naoto Maki, Kazunori Kohri. 2026-09-07. Exponential Quintessence: Analytic Relationship Between the Current Equation of State Parameter and the Potential Parameter. https://doi.org/10.1088/1475-7516%2F2026%2F09%2F086

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