Bimodular Gravity: Unimodularising Bimetric Scalar-Tensor Gravity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909908770750464 |
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| author | Hallam, James Magueijo, João |
| author_facet | Hallam, James Magueijo, João |
| contents | It is the object of the present paper to unimodularise a disformal bimetric scalar-tensor theory, thereby defining what we call bimodular gravity. We impose one unimodular constraint per metric via multipliers $λ_{1,2}$ and show that two natural implementations-a dual fixed-determinant (BUG) and a dual diffeomorphism-invariant (BHT/BDUG) formulation-are classically inequivalent. In BUG the relative volume element $ν=\sqrt{1-2BX}$ is fixed, enforcing a kinematic constraint on the biscalar and we derive the "bimodular cosmological constant" $Λ=λ_1+νλ_2$. In BHT/BDUG, $λ_{1,2}$ are individually constant but $ν$ (hence $BX$) remains dynamical. Recasting the theory in an Einstein-frame form, we derive the biscalar sound speed and identify a subluminal domain $1+B(V+λ_2)>0$. At the background level, BUG admits constant-roll solutions governed by first-order flow, whereas BHT supports solutions with time-dependent roll. These structural differences yield distinct, in-principle testable predictions for the expansion history, the dark-energy equation of state, and the propagation of biscalar perturbations. Finally, we present a diffeomorphism-invariant completion that correlates the two HT volume forms, reproducing the $Λ$ of BUG on shell whilst maintaining full covariance. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_13562 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bimodular Gravity: Unimodularising Bimetric Scalar-Tensor Gravity Hallam, James Magueijo, João General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory It is the object of the present paper to unimodularise a disformal bimetric scalar-tensor theory, thereby defining what we call bimodular gravity. We impose one unimodular constraint per metric via multipliers $λ_{1,2}$ and show that two natural implementations-a dual fixed-determinant (BUG) and a dual diffeomorphism-invariant (BHT/BDUG) formulation-are classically inequivalent. In BUG the relative volume element $ν=\sqrt{1-2BX}$ is fixed, enforcing a kinematic constraint on the biscalar and we derive the "bimodular cosmological constant" $Λ=λ_1+νλ_2$. In BHT/BDUG, $λ_{1,2}$ are individually constant but $ν$ (hence $BX$) remains dynamical. Recasting the theory in an Einstein-frame form, we derive the biscalar sound speed and identify a subluminal domain $1+B(V+λ_2)>0$. At the background level, BUG admits constant-roll solutions governed by first-order flow, whereas BHT supports solutions with time-dependent roll. These structural differences yield distinct, in-principle testable predictions for the expansion history, the dark-energy equation of state, and the propagation of biscalar perturbations. Finally, we present a diffeomorphism-invariant completion that correlates the two HT volume forms, reproducing the $Λ$ of BUG on shell whilst maintaining full covariance. |
| title | Bimodular Gravity: Unimodularising Bimetric Scalar-Tensor Gravity |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.13562 |