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Palatini versus metric formulation in higher curvature gravity

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arxiv 0804.4440 v2 pith:DERGOAZ2 submitted 2008-04-28 hep-th gr-qc

Monica Borunda , Bert Janssen , Mar Bastero-Gil This is my paper · ORCID
classification hep-thgr-qc
keywords palatinimetricequationsformalismclasscurvaturefindlovelock
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We compare the metric and the Palatini formalism to obtain the Einstein equations in the presence of higher-order curvature corrections that consist of contractions of the Riemann tensor, but not of its derivatives. We find that there is a class of theories for which the two formalisms are equivalent. This class contains the Palatini version of Lovelock theory, but also more Lagrangians that are not Lovelock, but respect certain symmetries. For the general case, we find that imposing the Levi-Civita connection as an Ansatz, the Palatini formalism is contained within the metric formalism, in the sense that any solution of the former also appears as a solution of the latter, but not necessarily the other way around. Finally we give the conditions the solutions of the metric equations should satisfy in order to solve the Palatini equations.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Inflation with nondynamic distortion to leading order in slow roll

    astro-ph.CO 2026-07 conditional novelty 6.0 of 10

    Nondynamic distortion integrated out of a 13-parameter metric-affine action sources the entire inflaton kinetic term; monomial models depend only on exponent ratio while α-attractors recover modified Starobinsky observables.

  2. Inflation with the Gauss-Bonnet term in the Palatini formulation

    astro-ph.CO 2026-03 accept novelty 5.0 of 10

    In Palatini gravity the inflaton–Gauss–Bonnet coupling yields a negative Chern–Simons-like kinetic correction and similar GW modifications, with metric-like behaviour unless the kinetic term nearly flips sign.

  3. Inflationary assessment of $F(\mathcal{R},\tilde{\mathcal{R}})$ Einstein-Cartan models

    gr-qc 2025-12 conditional novelty 5.0 of 10

    Adding cubic Holst-invariant terms to F(R,R̃) Einstein-Cartan inflation models systematically lowers the predicted spectral index n_s and tensor-to-scalar ratio r, restoring data compatibility in parameter regions whe...

  4. Constant-roll $\beta$-exponential inflation: Palatini formalism

    gr-qc 2026-01 reject novelty 4.0 of 10

    A parameter scan of constant-roll β-exponential inflation in Palatini R² gravity claims agreement with ACT/Planck contours, but the derivation is undermined by algebraic sign errors and an absent non-Gaussianity calculation.

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