Can the Universe Change Signature When Gravity is Dynamical?
Abstract
Can a universe undergo a regular Euclidean-Lorentzian signature transition when the gravitational coupling itself is dynamical? We address this question in scalar-tensor gravity with nonminimal coupling F(ϕ)R. Although the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) sector can be mapped to the Einstein frame for F>0 and a nondegenerate scalar redefinition, not all transition properties are frame independent. For a finite, positive, and sufficiently regular conformal factor, the existence and transverse character of the type change are preserved, whereas the extrinsic geometry is not. We therefore use the Einstein frame as a solution-generating representation and impose total geodesy in the physical Jordan frame. We construct two exactly integrable classes of solutions. In the oscillator-ghost-oscillator branch, the scalar field is stationary at the transition and Jordan-frame total geodesy follows under suitable regularity assumptions on the conformal factor. In the critical exponential-potential branch, the scalar is generically nonstationary and total geodesy instead requires HE|Σ= 1/2 ( (dln F)/dψ )Σψ̇Σ. We also distinguish this condition from the stronger smoothness requirements of a Kossowski-Kriele-type transverse metric. Finally, while the canonical Einstein-frame scalar does not allow effective phantom evolution, the dynamical nonminimal coupling can generate a locally superaccelerating Jordan-frame regime near the transition when ((dln F)/dψ)Σ>0 for the chosen oscillator branch. Thus signature change persists beyond Einstein gravity, with regularity and effective cosmological behavior remaining intrinsically frame sensitive.
Versions
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BibTeX
@misc{heydarzade2026universe,
title = {{Can the Universe Change Signature When Gravity is Dynamical?}},
author = {Yaghoub Heydarzade},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08964},
eprint = {2609.08964},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08964},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Can the Universe Change Signature When Gravity is Dynamical?
AU - Yaghoub Heydarzade
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08964
UR - https://arxiv.org/abs/2609.08964
AB - Can a universe undergo a regular Euclidean-Lorentzian signature transition when the gravitational coupling itself is dynamical? We address this question in scalar-tensor gravity with nonminimal coupling F(ϕ)R. Although the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) sector can be mapped to the Einstein frame for F>0 and a nondegenerate scalar redefinition, not all transition properties are frame independent. For a finite, positive, and sufficiently regular conformal factor, the existence and transverse character of the type change are preserved, whereas the extrinsic geometry is not. We therefore use the Einstein frame as a solution-generating representation and impose total geodesy in the physical Jordan frame. We construct two exactly integrable classes of solutions. In the oscillator-ghost-oscillator branch, the scalar field is stationary at the transition and Jordan-frame total geodesy follows under suitable regularity assumptions on the conformal factor. In the critical exponential-potential branch, the scalar is generically nonstationary and total geodesy instead requires H_E|_Σ= 1/2 ( (dln F)/dψ )_Σψ̇_Σ. We also distinguish this condition from the stronger smoothness requirements of a Kossowski-Kriele-type transverse metric. Finally, while the canonical Einstein-frame scalar does not allow effective phantom evolution, the dynamical nonminimal coupling can generate a locally superaccelerating Jordan-frame regime near the transition when ((dln F)/dψ)_Σ>0 for the chosen oscillator branch. Thus signature change persists beyond Einstein gravity, with regularity and effective cosmological behavior remaining intrinsically frame sensitive.
ER -