Non-variational scalar field cosmology: Exact Bianchi I solutions for near-minimal scalar fields
Abstract
The purpose of this work is to investigate spatially homogeneous and flat cosmological solutions of the Einstein equations coupled to a non-variational ``near-minimal'' scalar field. This coupling model represents a minimal departure from standard theory by decoupling the scalar field's self-interaction term from the derivative of its potential. By assuming a quadratic potential and a self-interaction term that is proportional to the potential, we derive four new exact Bianchi I solutions. We demonstrate that these solutions produce a diverse range of cosmological phenomena, including Big Bang, Big Crunch, and Big Rip singularities, as well as oscillatory (``cyclic'') behaviour. For our exact solutions, these singularities occur in infinite proper time and hence are never truly reachable by an observer. To assess the stability of these cosmologies, we perform a numerical stability analysis against spatially inhomogeneous perturbations of the mean curvature. We find that the oscillatory solution is unstable to perturbations of this type, as are solutions in possession of a crushing singularity. Conversely, solutions with a Big Rip singularity (at infinity) are stable to spatially inhomogeneous perturbations of the mean curvature.
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BibTeX
@misc{ritchie2026nonvariational,
title = {{Non-variational scalar field cosmology: Exact Bianchi I solutions for near-minimal scalar fields}},
author = {Joshua Ritchie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.02078},
eprint = {2605.02078},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.02078},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Non-variational scalar field cosmology: Exact Bianchi I solutions for near-minimal scalar fields
AU - Joshua Ritchie
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2605.02078
UR - https://arxiv.org/abs/2605.02078
AB - The purpose of this work is to investigate spatially homogeneous and flat cosmological solutions of the Einstein equations coupled to a non-variational ``near-minimal'' scalar field. This coupling model represents a minimal departure from standard theory by decoupling the scalar field's self-interaction term from the derivative of its potential. By assuming a quadratic potential and a self-interaction term that is proportional to the potential, we derive four new exact Bianchi I solutions. We demonstrate that these solutions produce a diverse range of cosmological phenomena, including Big Bang, Big Crunch, and Big Rip singularities, as well as oscillatory (``cyclic'') behaviour. For our exact solutions, these singularities occur in infinite proper time and hence are never truly reachable by an observer. To assess the stability of these cosmologies, we perform a numerical stability analysis against spatially inhomogeneous perturbations of the mean curvature. We find that the oscillatory solution is unstable to perturbations of this type, as are solutions in possession of a crushing singularity. Conversely, solutions with a Big Rip singularity (at infinity) are stable to spatially inhomogeneous perturbations of the mean curvature.
ER -