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arXiv · 2603.14693

Background-level reconstruction of scalar-field potentials from dark-energy histories and comparison with analytic potential families

Shahnawaz A. Adil·Miguel A. Zapata·Özgür Akarsu·J. Alberto Vazquez
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Abstract

We present a unified \emph{background-level} framework that maps a prescribed late-time dark-energy density history $ρ_{\rm de}(z)$ onto an effective scalar-field description in a spatially flat FLRW universe. Working directly with $ρ_{\rm de}(z)$, we reconstruct the associated field trajectory $ϕ(z)$, and field-space potential $V(ϕ)$, together with a null energy condition (NEC) consistency check. We apply the method to three benchmark histories: (i) the Chevallier--Polarski--Linder (CPL) form; (ii) a smooth mirror AdS$\rightarrow$dS sign-switching profile in which $ρ_{\rm de}$ crosses zero at $z_\dagger$, interpolating between a positive late-time plateau and a negative high-$z$ plateau ($Λ_{\rm s}$CDM-like at the background level); and (iii) a shifted-$\tanh$ emergent profile that remains positive definite and approaches $ρ_{\rm de}\to 0^{+}$ at high redshift. Finally, treating the reconstructed potential, $V_{\rm tar}(ϕ)$, as a target, we perform Bayesian model comparison directly in \emph{potential space} and rank representative analytic potential families by their Bayesian evidence. For CPL (restricting to the single-valued phantom branch for the potential-space comparison), the exponential potential has the highest evidence in the baseline analysis, while the shifted-$\tanh$ and hilltop quartic forms remain close competitors; for the sign-switching $\tanh$ target, the shifted-$\tanh$ potential is strongly preferred, and the emergent profile yields the same qualitative ranking. These results provide a practical dictionary between phenomenological expansion histories and the scalar-field potential shapes required to reproduce them at the background level.

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Shahnawaz A. Adil, Miguel A. Zapata, Özgür Akarsu, J. Alberto Vazquez. 2026-07-14. Background-level reconstruction of scalar-field potentials from dark-energy histories and comparison with analytic potential families. https://doi.org/10.1016/j.dark.2026.102387

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