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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 V0 e−λϕ/mpl. 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 Ωϕ0=0.685.

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Cite

BibTeXRIS
BibTeX
@misc{maki2026exponential,
  title = {{Exponential Quintessence: Analytic Relationship Between the Current Equation of State Parameter and the Potential Parameter}},
  author = {Naoto Maki and Kazunori Kohri},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.05122},
  eprint = {2605.05122},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.05122},
}
RIS
TY  - UNPB
TI  - Exponential Quintessence: Analytic Relationship Between the Current Equation of State Parameter and the Potential Parameter
AU  - Naoto Maki
AU  - Kazunori Kohri
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2605.05122
UR  - https://arxiv.org/abs/2605.05122
AB  - 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_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_ϕ0=0.685.
ER  -