Disformal transformations in a Palatini extension of Horndeski's gravity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910046413127680 |
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| author | Kozak, Aleksander |
| author_facet | Kozak, Aleksander |
| contents | In this paper, we extend Horndeski's theory into the Palatini approach, assuming that the metric tensor and the (symmetric) connection are a priori independent objects. We introduce an additional transformation of the connection and write down the action functional being form-invariant under both the disformal transformation of the metric and the new transformation of the connection. We show that such a theory reduces on-shell to a metric subclass of Horndeski's gravity called kinetic gravity braiding. We also introduce an invariant metric and connection, and demonstrate that quantities defined in such a way lead to a metric theory. In the second part of the paper, we consider a simple cosmological model within the theory and explore its potential links with $ k$-essence-type theories, with a non-trivial coupling between the scalar field and the matter part of the action in the Einstein frame. We show that there exists a model that reproduces late-time cosmic acceleration, approaching asymptotically the de Sitter phase, motivating further study of the theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08401 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Disformal transformations in a Palatini extension of Horndeski's gravity Kozak, Aleksander General Relativity and Quantum Cosmology In this paper, we extend Horndeski's theory into the Palatini approach, assuming that the metric tensor and the (symmetric) connection are a priori independent objects. We introduce an additional transformation of the connection and write down the action functional being form-invariant under both the disformal transformation of the metric and the new transformation of the connection. We show that such a theory reduces on-shell to a metric subclass of Horndeski's gravity called kinetic gravity braiding. We also introduce an invariant metric and connection, and demonstrate that quantities defined in such a way lead to a metric theory. In the second part of the paper, we consider a simple cosmological model within the theory and explore its potential links with $ k$-essence-type theories, with a non-trivial coupling between the scalar field and the matter part of the action in the Einstein frame. We show that there exists a model that reproduces late-time cosmic acceleration, approaching asymptotically the de Sitter phase, motivating further study of the theories. |
| title | Disformal transformations in a Palatini extension of Horndeski's gravity |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.08401 |