Curvature–Matter Feedback in Semiclassical Cosmology: A Reduced Mathematical Framework for Geometry-Induced Quantum Matter Production
- 1Department of Mathematics and Education, Universidad a Distancia de Madrid (UDIMA), 28400 Madrid, Spain
Abstract
Quantum fields on a time-dependent geometry can undergo particle production, but this does not establish a self-amplifying response of the geometry. We study a conditional two-amplitude closure for a signed curvature perturbation and a signed renormalized stress response. The physical assumptions are specified through constrained projection, a low-frequency response expansion, and a stable single-pole approximation; none is asserted to hold for every semiclassical state. A quantitative memory-remainder estimate and a conditional scalar-field example make the scope of this approximation explicit. For the resulting cooperative reaction–diffusion system, a weighted spectral argument identifies the first loss of stability with the homogeneous mode. For the homogeneous cubic completion, a coercive gradient potential proves global existence and convergence to an equilibrium, including asymptotic stability at the critical parameter. We also establish the local spatial bifurcation, distinguish quintic corrections from a degenerate bifurcation, and classify a constant symmetry-breaking perturbation. Renormalization of the cosmological constant, conservation, higher-curvature terms, and the distinction between physical and effective-theory runaway solutions are treated explicitly. The contribution is a response-level diagnostic and its mathematical limitations, rather than a new microscopic theory or an observational cosmological prediction.
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BibTeX
@article{palencia2026curvaturematter,
title = {{Curvature–Matter Feedback in Semiclassical Cosmology: A Reduced Mathematical Framework for Geometry-Induced Quantum Matter Production}},
author = {José Luis Díaz Palencia},
journal = {Axioms},
year = {2026},
month = oct,
doi = {10.3390/axioms15100735},
url = {https://www.mdpi.com/2075-1680/15/10/735},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Curvature–Matter Feedback in Semiclassical Cosmology: A Reduced Mathematical Framework for Geometry-Induced Quantum Matter Production
AU - José Luis Díaz Palencia
PY - 2026
DA - 2026/10/01
JO - Axioms
DO - 10.3390/axioms15100735
UR - https://www.mdpi.com/2075-1680/15/10/735
AB - Quantum fields on a time-dependent geometry can undergo particle production, but this does not establish a self-amplifying response of the geometry. We study a conditional two-amplitude closure for a signed curvature perturbation and a signed renormalized stress response. The physical assumptions are specified through constrained projection, a low-frequency response expansion, and a stable single-pole approximation; none is asserted to hold for every semiclassical state. A quantitative memory-remainder estimate and a conditional scalar-field example make the scope of this approximation explicit. For the resulting cooperative reaction–diffusion system, a weighted spectral argument identifies the first loss of stability with the homogeneous mode. For the homogeneous cubic completion, a coercive gradient potential proves global existence and convergence to an equilibrium, including asymptotic stability at the critical parameter. We also establish the local spatial bifurcation, distinguish quintic corrections from a degenerate bifurcation, and classify a constant symmetry-breaking perturbation. Renormalization of the cosmological constant, conservation, higher-curvature terms, and the distinction between physical and effective-theory runaway solutions are treated explicitly. The contribution is a response-level diagnostic and its mathematical limitations, rather than a new microscopic theory or an observational cosmological prediction.
SN - 2075-1680
ER -