Torsion, Frames and Quantum Bounces: Inflation and Ekpyrotic Contraction in Quantum Trajectory Cosmology with a Non-Minimally Coupled Scalar
Abstract
We study the de Broglie-Bohm quantum cosmology of a scalar field non-minimally coupled to a metric-compatible Riemann-Cartan geometry, comparing inflation with ekpyrotic contraction. The torsion trace is auxiliary and is eliminated algebraically before quantisation. The minisuperspace metric depends on the coupling F(ϕ) and a constant κ for an independent quadratic torsion term (κ=0 Einstein-Cartan, κ→∞ torsion-free). For every F, κ and potential this metric is conformally flat, so torsion acts only through the Einstein-frame kinetic function K(ϕ). Its curvature is therefore not a diagnostic of torsion, and the Laplace-Beltrami Wheeler-DeWitt equation, quantum potential and Bohmian trajectories are frame covariant. For a massless scalar the equation is solved exactly; in a two-packet state all 41 flux-weighted Bohmian trajectories bounce in the Einstein frame. In the Jordan frame the bounce at the symmetric event is independent of torsion and persists only for ξ<ξc (closed form); torsion changes the late-time exponent from 1−√(6ξ/(1+6ξ)) to 1−√(6ξ). The bounce comes from interference in the state, not from torsion. For exponential potentials, exact Wheeler-DeWitt solutions show that in the sector containing the ekpyrotic attractor no Bohmian trajectory bounces, and single-momentum states bounce only where the potential is negligible and end in the crunch. For quadratic inflation the torsion-specific shift of r is below one per cent. A single ekpyrotic field gives blue spectra, ns=3+2/(ε−1) and r=16ε, whatever the torsion, also for running ε. In an entropic two-field version the tilt shifts at order √ξ (non-minimal coupling) and ξ3/2 (torsion). Tensor modes cross the massless Bohmian bounce almost unchanged and stay blue.
Related
- The alternative scalar field dark sector of the Universe: Cosmological inflation, quintessence and ekpyrotic model in the framework of scalar-tensor cosmology
- Causal Horizons, Geodesic Completeness and Stability in Slow Contraction Cosmology
- Analysis of Phantom Cosmology With Different Potentials: Inflation and Isotropization
- Cosmology with a Non-minimally Coupled Dark Matter Fluid II. Cosmological Perturbations
- Reconciling axion quality with post-inflation cosmology
BibTeX
@misc{sengupta2026torsion,
title = {{Torsion, Frames and Quantum Bounces: Inflation and Ekpyrotic Contraction in Quantum Trajectory Cosmology with a Non-Minimally Coupled Scalar}},
author = {Rikpratik Sengupta and Paulo Vargas Moniz},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02036},
eprint = {2611.02036},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02036},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Torsion, Frames and Quantum Bounces: Inflation and Ekpyrotic Contraction in Quantum Trajectory Cosmology with a Non-Minimally Coupled Scalar
AU - Rikpratik Sengupta
AU - Paulo Vargas Moniz
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02036
UR - https://arxiv.org/abs/2611.02036
AB - We study the de Broglie-Bohm quantum cosmology of a scalar field non-minimally coupled to a metric-compatible Riemann-Cartan geometry, comparing inflation with ekpyrotic contraction. The torsion trace is auxiliary and is eliminated algebraically before quantisation. The minisuperspace metric depends on the coupling F(ϕ) and a constant κ for an independent quadratic torsion term (κ=0 Einstein-Cartan, κ→∞ torsion-free). For every F, κ and potential this metric is conformally flat, so torsion acts only through the Einstein-frame kinetic function K(ϕ). Its curvature is therefore not a diagnostic of torsion, and the Laplace-Beltrami Wheeler-DeWitt equation, quantum potential and Bohmian trajectories are frame covariant. For a massless scalar the equation is solved exactly; in a two-packet state all 41 flux-weighted Bohmian trajectories bounce in the Einstein frame. In the Jordan frame the bounce at the symmetric event is independent of torsion and persists only for ξ<ξ_c (closed form); torsion changes the late-time exponent from 1−√(6ξ/(1+6ξ)) to 1−√(6ξ). The bounce comes from interference in the state, not from torsion. For exponential potentials, exact Wheeler-DeWitt solutions show that in the sector containing the ekpyrotic attractor no Bohmian trajectory bounces, and single-momentum states bounce only where the potential is negligible and end in the crunch. For quadratic inflation the torsion-specific shift of r is below one per cent. A single ekpyrotic field gives blue spectra, n_s=3+2/(ε−1) and r=16ε, whatever the torsion, also for running ε. In an entropic two-field version the tilt shifts at order √ξ (non-minimal coupling) and ξ^3/2 (torsion). Tensor modes cross the massless Bohmian bounce almost unchanged and stay blue.
ER -