Power-Law Bounces in $f(R)$ Gravity: Analysis of the Ekpyrosis and Accelerating Regimes
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914188541034496 |
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| author | Das, Saurya Dunsby, Peter Haque, S. Shajidul Tema, Seturumane |
| author_facet | Das, Saurya Dunsby, Peter Haque, S. Shajidul Tema, Seturumane |
| contents | We investigate the dynamics of the Friedmann-Lemaître-Robertson-Walker spacetime within the framework of $f(R)$ gravity using a compact, model-independent dynamical systems approach. By assuming a power-law scale factor, we explore ekpyrotic and accelerating solutions to address the big bang singularity. Our analysis demonstrates that a cosmological bounce, characterized by a transition from contraction to expansion, possibly avoids the singularity without directly using the Raychaudhuri equation, unlike previous approaches using specific $f(R) \simeq R^n$ forms. We identify a key fixed point in the phase space corresponding to the bounce, supported by perturbation analysis and qualitative description of trajectories in the phase space. The results suggest that $f(R)$ gravity provides a robust framework for non-singular cosmologies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_00242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power-Law Bounces in $f(R)$ Gravity: Analysis of the Ekpyrosis and Accelerating Regimes Das, Saurya Dunsby, Peter Haque, S. Shajidul Tema, Seturumane General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory We investigate the dynamics of the Friedmann-Lemaître-Robertson-Walker spacetime within the framework of $f(R)$ gravity using a compact, model-independent dynamical systems approach. By assuming a power-law scale factor, we explore ekpyrotic and accelerating solutions to address the big bang singularity. Our analysis demonstrates that a cosmological bounce, characterized by a transition from contraction to expansion, possibly avoids the singularity without directly using the Raychaudhuri equation, unlike previous approaches using specific $f(R) \simeq R^n$ forms. We identify a key fixed point in the phase space corresponding to the bounce, supported by perturbation analysis and qualitative description of trajectories in the phase space. The results suggest that $f(R)$ gravity provides a robust framework for non-singular cosmologies. |
| title | Power-Law Bounces in $f(R)$ Gravity: Analysis of the Ekpyrosis and Accelerating Regimes |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.00242 |