How (Not) to Palatini

Abstract

We revisit the problem of defining non-minimal gravity in the first order formalism. Specializing to scalar-tensor theories, which may be disguised as `higher-derivative' models with the gravitational Lagrangians that depend only on the Ricci scalar, we show how to recast these theories as Palatini-like gravities. The correct formulation utilizes the Lagrange multiplier method, which preserves the canonical structure of the theory, and yields the conventional metric scalar-tensor gravity. We explain the discrepancies between the naïve Palatini and the Lagrange multiplier approach, showing that the naïve Palatini approach really swaps the theory for another. The differences disappear only in the limit of ordinary General Relativity, where an accidental redundancy ensures that the naïve Palatini works there. We outline the correct decoupling limits and the strong coupling regimes. As a corollary we find that the so-called `Modified Source Gravity' models suffer from strong coupling problems at very low scales, and hence cannot be a realistic approximation of our universe. We also comment on a method to decouple the extra scalar using the chameleon mechanism.

18 pages, LaTeX; added references and minor improvements in sec 4

References in corpus (6)

• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Constraining f(R) Gravity as a Scalar Tensor Theory
• f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints
• Lovelock Gravity at the Crossroads of Palatini and Metric Formulations
• The Cosmology of Ricci-Tensor-Squared Gravity in the Palatini Variational Approach
• The content of f(R) gravity

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• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• The viability of theories with matter coupled to the Ricci scalar
• Curvature singularities, tidal forces and the viability of Palatini f(R) gravity
• The Cauchy problem of f(R) gravity
• Microscopic and Macroscopic Behaviors of Palatini Modified Gravity Theories
• "Detuned" f(R) gravity and dark energy
• Aspects of Infrared Modifications of Gravity
• Palatini f(R) gravity as a fixed point