Dual Effective Field Theory formulation of Metric--Affine and Symmetric Teleparallel Gravity
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914192505700352 |
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| author | Teruel, Ginés R. Pérez |
| author_facet | Teruel, Ginés R. Pérez |
| contents | We develop a unified algebraic and effective field theory (EFT) formulation for non--Riemannian extensions of General Relativity with an independent connection. For metric--affine $f(R,Q)$ gravity we show that the connection equations admit an exact matrix solution, whose square--root structure generates a convergent binomial/Neumann expansion in powers of the stress tensor $T_{μν}$. For the Eddington--inspired Born--Infeld (EiBI) theory we show that the connection can be solved algebraically as well, and that its determinantal field equations produce a parallel Neumann expansion with coefficients fixed by the underlying determinant operator. This allows us to rewrite the Einstein--like equations in the auxiliary metric as an effective Einstein equation for $g_{μν}$ with a local algebraic correction $(ΔT)_{μν}$ that follows from a dual EFT built from the invariants $\{T,\,T^2,\,T_{μν}T^{μν},\ldots\}$, organised by a characteristic density scale. We prove a convergence criterion based on the spectral radius of $\hat T^μ_ν$ and interpret EiBI gravity as a determinantal resummation of the same $T$--tower. Extending the framework to symmetric teleparallel $f(Q)$ gravity, we identify the EFT coefficients in terms of $f_Q$ and $f_{QQ}$ and present a background matching for $f(Q)=Q+αQ^2$. The resulting dual EFT provides a common algebraic language for metric--affine, Born--Infeld and non--metricity gravities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dual Effective Field Theory formulation of Metric--Affine and Symmetric Teleparallel Gravity Teruel, Ginés R. Pérez General Relativity and Quantum Cosmology We develop a unified algebraic and effective field theory (EFT) formulation for non--Riemannian extensions of General Relativity with an independent connection. For metric--affine $f(R,Q)$ gravity we show that the connection equations admit an exact matrix solution, whose square--root structure generates a convergent binomial/Neumann expansion in powers of the stress tensor $T_{μν}$. For the Eddington--inspired Born--Infeld (EiBI) theory we show that the connection can be solved algebraically as well, and that its determinantal field equations produce a parallel Neumann expansion with coefficients fixed by the underlying determinant operator. This allows us to rewrite the Einstein--like equations in the auxiliary metric as an effective Einstein equation for $g_{μν}$ with a local algebraic correction $(ΔT)_{μν}$ that follows from a dual EFT built from the invariants $\{T,\,T^2,\,T_{μν}T^{μν},\ldots\}$, organised by a characteristic density scale. We prove a convergence criterion based on the spectral radius of $\hat T^μ_ν$ and interpret EiBI gravity as a determinantal resummation of the same $T$--tower. Extending the framework to symmetric teleparallel $f(Q)$ gravity, we identify the EFT coefficients in terms of $f_Q$ and $f_{QQ}$ and present a background matching for $f(Q)=Q+αQ^2$. The resulting dual EFT provides a common algebraic language for metric--affine, Born--Infeld and non--metricity gravities. |
| title | Dual Effective Field Theory formulation of Metric--Affine and Symmetric Teleparallel Gravity |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2512.09516 |