Covariant scalar-tensor theories beyond second derivatives
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908951773184000 |
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| author | Gorji, Mohammad Ali Petrov, Pavel Noui, Karim |
| author_facet | Gorji, Mohammad Ali Petrov, Pavel Noui, Karim |
| contents | We propose a covariant, gauge-independent construction of foliation-based scalar-tensor theories, yielding diffeomorphism-invariant operators involving only gradients on the hypersurfaces where the scalar field is constant, assumed to be spacelike. This defines a basis of independent invariants up to four derivatives of $ϕ$, including the first nontrivial parity-odd pseudoscalar at this order, with a straightforward extension to higher derivatives. Our framework goes beyond degenerate higher-order scalar-tensor (DHOST) theories and provides a nonlinear extension of U-DHOST (where $\nabla_μϕ$ is supposed to be timelike) directly in covariant form, without using unitary gauge as a starting point or imposing degeneracy a priori. After minimal coupling to gravity, we analyze the theory through its Hamiltonian constraint structure and linear cosmological perturbations about an FLRW background, and show that it propagates three physical degrees of freedom. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09170 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Covariant scalar-tensor theories beyond second derivatives Gorji, Mohammad Ali Petrov, Pavel Noui, Karim High Energy Physics - Theory Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology We propose a covariant, gauge-independent construction of foliation-based scalar-tensor theories, yielding diffeomorphism-invariant operators involving only gradients on the hypersurfaces where the scalar field is constant, assumed to be spacelike. This defines a basis of independent invariants up to four derivatives of $ϕ$, including the first nontrivial parity-odd pseudoscalar at this order, with a straightforward extension to higher derivatives. Our framework goes beyond degenerate higher-order scalar-tensor (DHOST) theories and provides a nonlinear extension of U-DHOST (where $\nabla_μϕ$ is supposed to be timelike) directly in covariant form, without using unitary gauge as a starting point or imposing degeneracy a priori. After minimal coupling to gravity, we analyze the theory through its Hamiltonian constraint structure and linear cosmological perturbations about an FLRW background, and show that it propagates three physical degrees of freedom. |
| title | Covariant scalar-tensor theories beyond second derivatives |
| topic | High Energy Physics - Theory Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.09170 |