Solving the Trans-Planckian Censorship Problem with a Power-law Tail in $R^2$ Inflation: A Dynamical System Approach
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| Format: | Preprint |
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2025
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| _version_ | 1866914036480737280 |
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| author | Odintsov, S. D. Oikonomou, V. K. Manouri, Eleni I. Papadopoulos, Asterios T. |
| author_facet | Odintsov, S. D. Oikonomou, V. K. Manouri, Eleni I. Papadopoulos, Asterios T. |
| contents | In this work we elaborate on solving the trans-Planckian censorship problem of standard slow-roll inflation by using a power-law inflationary tail generated by a scalar field with an exponential potential. We use a quantitative approach by studying in detail the phase space of a combined $F(R,ϕ)$ cosmological system, focusing on the de Sitter and power-law subspaces of the total phase space. As we show, the de Sitter subspace of the $F(R,ϕ)$ system shares the same fixed points as the vacuum $F(R)$ gravity system and the trajectories in the phase space tend to these fixed points. However, the power-law subspace is not stable and cannot be realized by the combined $F(R,ϕ)$ system. To this end, we propose a well-motivated phenomenological $F(R)$ gravity model for which the $R^2$ term is switched off below a critical curvature near the end of the $R^2$ slow-roll inflationary era, and below that critical curvature, only the Einstein-Hilbert gravity term and the scalar field remain in the effective inflationary Lagrangian. The remaining system can successfully realize a power-law tail of the $R^2$ slow-roll era. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_11387 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving the Trans-Planckian Censorship Problem with a Power-law Tail in $R^2$ Inflation: A Dynamical System Approach Odintsov, S. D. Oikonomou, V. K. Manouri, Eleni I. Papadopoulos, Asterios T. General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory In this work we elaborate on solving the trans-Planckian censorship problem of standard slow-roll inflation by using a power-law inflationary tail generated by a scalar field with an exponential potential. We use a quantitative approach by studying in detail the phase space of a combined $F(R,ϕ)$ cosmological system, focusing on the de Sitter and power-law subspaces of the total phase space. As we show, the de Sitter subspace of the $F(R,ϕ)$ system shares the same fixed points as the vacuum $F(R)$ gravity system and the trajectories in the phase space tend to these fixed points. However, the power-law subspace is not stable and cannot be realized by the combined $F(R,ϕ)$ system. To this end, we propose a well-motivated phenomenological $F(R)$ gravity model for which the $R^2$ term is switched off below a critical curvature near the end of the $R^2$ slow-roll inflationary era, and below that critical curvature, only the Einstein-Hilbert gravity term and the scalar field remain in the effective inflationary Lagrangian. The remaining system can successfully realize a power-law tail of the $R^2$ slow-roll era. |
| title | Solving the Trans-Planckian Censorship Problem with a Power-law Tail in $R^2$ Inflation: A Dynamical System Approach |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.11387 |