November 13, 2025Open Access

Dark Energy from Catalan's Constant

Key Points

Dark energy density parameter derived shows good correlation with previous Planck findings.
The predicted value of 0.7084 aligns with 2018 observations, limited by standard deviation intervals.
This analysis presents a parameter-free form, avoiding fitting or additional assumptions.
Implications of Catalan's constant in cosmology call for further theoretical exploration.

Abstract

This short note shows that the dark–energy density parameter can be writtenin a parameter–free form: ΩΛ = 1 − G/π = 0.7084, where G = β(2) is Catalan’s constant (the value of the Dirichlet betafunction at s = 2). This prediction agrees with Planck 2018 observations within a few standard deviations.No free parameters or fitting are required.A full theoretical derivation will be presented in a separate paper.

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