Comparing metric and Palatini approaches to vector Horndeski theory

Abstract

We compare cosmologic and spherically symmetric solutions to metric and Palatini versions of vector Horndeski theory. It appears that Palatini formulation of the theory admits more degrees of freedom. Specifically, homogeneous isotropic configuration is effectively bimetric, and static spherically symmetric configuration contains non-metric connection. In general, the exact solution in metric case coincides with the approximative solution in Palatini case. The Palatini version of the theory appears to be more complicated, but the resulting non-linearity may be useful: we demonstrate that it allows the specific cosmological solution to pass through singularity, which is not possible in metric approach.

14 pages, to be published in Int.J.Mod.Phys.D version 2 - minor changes: page format changed for a better view

References in corpus (13)

• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Metric-affine f(R) theories of gravity
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Palatini formulation of modified gravity with a nonminimal curvature-matter coupling
• Lovelock Gravity at the Crossroads of Palatini and Metric Formulations
• Unifying Einstein and Palatini gravities
• Palatini versus metric formulation in higher curvature gravity
• How (Not) to Palatini
• On new variational principles as alternatives to the Palatini method
• Non-minimal coupling for the gravitational and electromagnetic fields: black hole solutions and solitons
• Cosmologies in Horndeski's second-order vector-tensor theory
• Instabilities in Horndeski Yang-Mills inflation
• Generalized Einstein-Maxwell field equations in the Palatini formalism

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• Invariant quantities of Scalar-Tensor Theories for stellar structure
• Conformal and kinetic couplings as two Jordan frames of the same theory
• Quartic Horndeski-Cartan theories in a FLRW universe
• Healthy Horndeski cosmologies with torsion