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arXiv · 2608.07878

Analytic Integration of the Lambert W Cosmic Fluid Model H(z) Formula

Ken Roberts·S. R. Valluri
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Abstract

The Lambert $W$ (LW) model for the cosmic fluid equation of state was proposed by S. Saha and K. Bamba in 2019-2020. A recent (early 2026) paper by Dubey, et al, carries out a new fit of the LW model to observational data, in order to estimate the model's parameters. That paper exhibits a formula for the logarithm of the relative Hubble factor at redshift $z$, $\ln(H(z)/H_0)$, which is based upon a numerical integration. That integral can be evaluated analytically, and we present the details in this working paper. The resulting analytic expression for $H(z)/H_0$ may be convenient for exploration of the LW model.

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Ken Roberts, S. R. Valluri. 2026-08-08. Analytic Integration of the Lambert W Cosmic Fluid Model H(z) Formula. https://arxiv.org/abs/2608.07878

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