Beyond (and back to) Palatini quadratic gravity and inflation
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arXiv
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| Format: | Preprint |
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2022
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| author | Dioguardi, Christian Racioppi, Antonio Tomberg, Eemeli |
| author_facet | Dioguardi, Christian Racioppi, Antonio Tomberg, Eemeli |
| contents | We study single-field slow-roll inflation embedded in Palatini $F(R)$ gravity where $F(R)$ grows faster than $R^2$. Surprisingly, the consistency of the theory requires the Jordan frame inflaton potential to be unbounded from below. Even more surprisingly, this corresponds to an Einstein frame inflaton potential bounded from below and positive definite. We prove that for all such Palatini $F(R)$'s, there exists a universal strong coupling limit corresponding to a quadratic $F(R)$ with the wrong sign for the linear term and a cosmological constant in the Jordan frame. In such a limit, the tensor-to-scalar ratio $r$ does not depend on the original inflaton potential, while the scalar spectral index $n_s$ does. Unfortunately, the system is ill-defined out of the slow-roll regime. A possible way out is to upgrade to a $F(R,X)$ model, with $X$ the Jordan frame inflaton kinetic term. Such a modification essentially leaves the inflationary predictions unaffected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11869 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Beyond (and back to) Palatini quadratic gravity and inflation Dioguardi, Christian Racioppi, Antonio Tomberg, Eemeli General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology We study single-field slow-roll inflation embedded in Palatini $F(R)$ gravity where $F(R)$ grows faster than $R^2$. Surprisingly, the consistency of the theory requires the Jordan frame inflaton potential to be unbounded from below. Even more surprisingly, this corresponds to an Einstein frame inflaton potential bounded from below and positive definite. We prove that for all such Palatini $F(R)$'s, there exists a universal strong coupling limit corresponding to a quadratic $F(R)$ with the wrong sign for the linear term and a cosmological constant in the Jordan frame. In such a limit, the tensor-to-scalar ratio $r$ does not depend on the original inflaton potential, while the scalar spectral index $n_s$ does. Unfortunately, the system is ill-defined out of the slow-roll regime. A possible way out is to upgrade to a $F(R,X)$ model, with $X$ the Jordan frame inflaton kinetic term. Such a modification essentially leaves the inflationary predictions unaffected. |
| title | Beyond (and back to) Palatini quadratic gravity and inflation |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2212.11869 |