On the Emergence of Einstein's Gravity from f(R) Gravity through Cosmological Evolution
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| Format: | Preprint |
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2026
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| author | Chattopadhyay, Gahan Sengupta, Soumitra |
| author_facet | Chattopadhyay, Gahan Sengupta, Soumitra |
| contents | $f(R)$-Gravity, a simple generalization of Einstein's General theory of Relativity has been considered in the context of Cosmology as one of the approaches to explain phenomena such as early-time inflation and late-time accelerated expansion of the Universe purely from the Gravity sector. In this work, we have considered a class of $f(R)$-Gravity theories with $f(R)=R+αR^n$ and it's dual scalar tensor theory in the Einstein frame. We have shown that in an isotropic and homogeneous background, for both positive and negative integral values of $n$, the extra scalar degree of freedom of the $f(R)$-theory (manifested as the scalar field in the Einstein frame action) dynamically freezes out due to cosmological evolution, resulting in the survival of only the Einstein-Hilbert term and a cosmological constant at most. This implies that all gravity models given as $R + αR^n$ inevitably evolve into pure Einstein gravity with a cosmological constant term through cosmological evolution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_01395 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Emergence of Einstein's Gravity from f(R) Gravity through Cosmological Evolution Chattopadhyay, Gahan Sengupta, Soumitra General Relativity and Quantum Cosmology $f(R)$-Gravity, a simple generalization of Einstein's General theory of Relativity has been considered in the context of Cosmology as one of the approaches to explain phenomena such as early-time inflation and late-time accelerated expansion of the Universe purely from the Gravity sector. In this work, we have considered a class of $f(R)$-Gravity theories with $f(R)=R+αR^n$ and it's dual scalar tensor theory in the Einstein frame. We have shown that in an isotropic and homogeneous background, for both positive and negative integral values of $n$, the extra scalar degree of freedom of the $f(R)$-theory (manifested as the scalar field in the Einstein frame action) dynamically freezes out due to cosmological evolution, resulting in the survival of only the Einstein-Hilbert term and a cosmological constant at most. This implies that all gravity models given as $R + αR^n$ inevitably evolve into pure Einstein gravity with a cosmological constant term through cosmological evolution. |
| title | On the Emergence of Einstein's Gravity from f(R) Gravity through Cosmological Evolution |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2601.01395 |