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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.02078 |
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| _version_ | 1866909011595493376 |
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| author | Ritchie, Joshua |
| author_facet | Ritchie, Joshua |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02078 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-variational scalar field cosmology: Exact Bianchi I solutions for near-minimal scalar fields Ritchie, Joshua General Relativity and Quantum Cosmology 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. |
| title | Non-variational scalar field cosmology: Exact Bianchi I solutions for near-minimal scalar fields |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.02078 |