A Unified Dynamical Systems Framework for Cosmology in $f(Q)$ Gravity: Generic Features Beyond the Coincident Gauge
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909963816796160 |
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| author | Dutta, Jibitesh Khyllep, Wompherdeiki Chakraborty, Saikat Gregoris, Daniele Karwan, Khamphee |
| author_facet | Dutta, Jibitesh Khyllep, Wompherdeiki Chakraborty, Saikat Gregoris, Daniele Karwan, Khamphee |
| contents | We present a unified dynamical systems framework for spatially flat FLRW cosmology in $f(Q)$ gravity, covering all three connection branches via a single set of Hubble-normalised variables without fixing $f(Q)$ \textit{a priori}. This connection-agnostic, model-independent approach enables direct comparison across branches and reveals generic structural features that are not apparent in model or connection-specific analyses. Beyond fixed points, we identify invariant submanifolds, model-independent trajectories, and viable phase-space regions common to multiple branches. For a broad class of viable $f(Q)$ models, we find generic de Sitter attractors and matter-dominated points in non-coincident branches, ensuring late-time acceleration without fine-tuning. An invariant submanifold is shown to reproduce $Λ$CDM-like backgrounds despite dynamics distinct from GR, offering a geometric origin for cosmic acceleration detectable only at the perturbation level. On this submanifold, a first integral enables analytic reconstruction of the dynamical connection and uncovers hidden conservation laws. While trivial connections display strong parameter dependence, nontrivial branches often exhibit parameter-independent behaviour. We also analyse the variation of the effective gravitational coupling $κ_{\text{eff}}=\frac{1}{f_Q}$ across branches, providing observational constraints that bridge theory and data. Applying the framework to $f(Q)=αQ+β(-Q)^n$, we recover late-time acceleration and $Λ$CDM-like behaviour without vacuum energy. Finally, we propose a general route for extending dynamical systems analysis to broader classes of $f(Q)$ models using the $m_i$-hierarchy method, which enables closure of the autonomous system for models previously inaccessible to standard approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Unified Dynamical Systems Framework for Cosmology in $f(Q)$ Gravity: Generic Features Beyond the Coincident Gauge Dutta, Jibitesh Khyllep, Wompherdeiki Chakraborty, Saikat Gregoris, Daniele Karwan, Khamphee General Relativity and Quantum Cosmology We present a unified dynamical systems framework for spatially flat FLRW cosmology in $f(Q)$ gravity, covering all three connection branches via a single set of Hubble-normalised variables without fixing $f(Q)$ \textit{a priori}. This connection-agnostic, model-independent approach enables direct comparison across branches and reveals generic structural features that are not apparent in model or connection-specific analyses. Beyond fixed points, we identify invariant submanifolds, model-independent trajectories, and viable phase-space regions common to multiple branches. For a broad class of viable $f(Q)$ models, we find generic de Sitter attractors and matter-dominated points in non-coincident branches, ensuring late-time acceleration without fine-tuning. An invariant submanifold is shown to reproduce $Λ$CDM-like backgrounds despite dynamics distinct from GR, offering a geometric origin for cosmic acceleration detectable only at the perturbation level. On this submanifold, a first integral enables analytic reconstruction of the dynamical connection and uncovers hidden conservation laws. While trivial connections display strong parameter dependence, nontrivial branches often exhibit parameter-independent behaviour. We also analyse the variation of the effective gravitational coupling $κ_{\text{eff}}=\frac{1}{f_Q}$ across branches, providing observational constraints that bridge theory and data. Applying the framework to $f(Q)=αQ+β(-Q)^n$, we recover late-time acceleration and $Λ$CDM-like behaviour without vacuum energy. Finally, we propose a general route for extending dynamical systems analysis to broader classes of $f(Q)$ models using the $m_i$-hierarchy method, which enables closure of the autonomous system for models previously inaccessible to standard approaches. |
| title | A Unified Dynamical Systems Framework for Cosmology in $f(Q)$ Gravity: Generic Features Beyond the Coincident Gauge |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2508.09530 |