Reconstructing sign-switching dark energy histories: Scalar-field regularity, conditional potential comparison, and representative dynamics
Abstract
Phenomenologically similar sign-switching dark-energy histories need not have comparable scalar-field realizations. We reconstruct minimally coupled scalars with fixed kinetic sign for three prescribed histories: the error-function model (ECDM), the compact smooth-step model (SSCDM), and the ladder-like model (LΛCDM). Continuous negative-to-positive density crossings select the phantom branch. ECDM yields a smooth on-shell potential at every finite redshift; its equation-of-state pole at the density zero is only a ratio singularity. Exact SSCDM has a regular trajectory but a C1, non-C2 endpoint potential, V−Ve∝|ϕ−ϕe|4/3. Its non-Lipschitz force permits delayed departures from frozen plateaus, so the reconstructed potential and plateau data do not uniquely generate the prescribed history. The exact Ladder requires distributional kinetic stress and has no ordinary classical realization in the adopted one-field action. In conditional synthetic comparisons, the sigmoid--Gaussian family ranks highest for ECDM and the generalized axion-like family for SSCDM, although the fitted axion exponents n<1/2 imply a divergent endpoint force. Representative regular forward solutions exhibit negative-to-positive scalar-density crossings, with the potential zero preceding the density zero. In a closure test, unretuned evolution of the top-ranked ECDM template tracks the target approximately, max|ΔΩ̃ϕ|≃0.16. Closure fails structurally for compact SSCDM: no potential with a locally Lipschitz force can reproduce its exact finite-duration frozen plateaus from exactly frozen initial data. Field-map existence, invertibility, and endpoint regularity must be assessed before interpreting a phenomenological history as scalar dynamics. The phantom action is used only as a homogeneous effective proxy.
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BibTeX
@misc{adil2026reconstructing,
title = {{Reconstructing sign-switching dark energy histories: Scalar-field regularity, conditional potential comparison, and representative dynamics}},
author = {Shahnawaz A. Adil and Özgür Akarsu and Mariam Bouhmadi-López and Beñat Ibarra-Uriondo and Nihan Katırcı and J. Alberto Vázquez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09261},
eprint = {2609.09261},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09261},
}
RIS
TY - UNPB
TI - Reconstructing sign-switching dark energy histories: Scalar-field regularity, conditional potential comparison, and representative dynamics
AU - Shahnawaz A. Adil
AU - Özgür Akarsu
AU - Mariam Bouhmadi-López
AU - Beñat Ibarra-Uriondo
AU - Nihan Katırcı
AU - J. Alberto Vázquez
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09261
UR - https://arxiv.org/abs/2609.09261
AB - Phenomenologically similar sign-switching dark-energy histories need not have comparable scalar-field realizations. We reconstruct minimally coupled scalars with fixed kinetic sign for three prescribed histories: the error-function model (ECDM), the compact smooth-step model (SSCDM), and the ladder-like model (LΛCDM). Continuous negative-to-positive density crossings select the phantom branch. ECDM yields a smooth on-shell potential at every finite redshift; its equation-of-state pole at the density zero is only a ratio singularity. Exact SSCDM has a regular trajectory but a C^1, non-C^2 endpoint potential, V−V_e∝|ϕ−ϕ_e|^4/3. Its non-Lipschitz force permits delayed departures from frozen plateaus, so the reconstructed potential and plateau data do not uniquely generate the prescribed history. The exact Ladder requires distributional kinetic stress and has no ordinary classical realization in the adopted one-field action. In conditional synthetic comparisons, the sigmoid--Gaussian family ranks highest for ECDM and the generalized axion-like family for SSCDM, although the fitted axion exponents n<1/2 imply a divergent endpoint force. Representative regular forward solutions exhibit negative-to-positive scalar-density crossings, with the potential zero preceding the density zero. In a closure test, unretuned evolution of the top-ranked ECDM template tracks the target approximately, max|ΔΩ̃_ϕ|≃0.16. Closure fails structurally for compact SSCDM: no potential with a locally Lipschitz force can reproduce its exact finite-duration frozen plateaus from exactly frozen initial data. Field-map existence, invertibility, and endpoint regularity must be assessed before interpreting a phenomenological history as scalar dynamics. The phantom action is used only as a homogeneous effective proxy.
ER -