Palatini frames in scalar-tensor theories of gravity

Abstract

A new systematic approach extending the notion of frames to the Palatini scalar-tensor theories of gravity in various dimensions n>2 is proposed. We impose frame transformation induced by the group action which includes almost-geodesic and conformal transformations. We characterize theories invariant with respect to these transformations dividing them up into solution-equivalent subclasses (group orbits). To this end, invariant characteristics have been introduced. Unlike in the metric case, it turns out that the dimension four admitting the largest transformation group is rather special for such theories. The formalism provides new frames that incorporate non-metricity. The case of Palatini F(R)-gravity is considered in more detail.

arXiv comment39 pages, LaTeX. v3: New essentially modified version. Attention: We have found wrong coefficients in the transformation formula for the function B(ϕ) on page 11. This mistake led us to the incorrect statement in Appendix B that the transformations are only consistent in spacetime dimension D=4 or under some constraints on the parameters

References in corpus (57)

• Dynamics of dark energy
• f(R) Theories Of Gravity
• f(R) theories
• Extended Theories of Gravity
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• The Case for a Positive Cosmological Lambda-term
• The Confrontation between General Relativity and Experiment
• Properties of the Binary Black Hole Merger GW150914
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Dark Energy Dominance and Cosmic Acceleration in First Order Formalism
• f(R) Gravity and scalar-tensor theory
• Covariant conservation of energy momentum in modified gravities
• The conformal frame freedom in theories of gravitation
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• The (pseudo)issue of the conformal frame revisited
• Question of quantum equivalence between Jordan frame and Einstein frame
• The Universality of Einstein Equations
• Equivalence of the Einstein and Jordan frames
• Higgs inflation with loop corrections in the Palatini formulation
• Accelerated Cosmological Models in First-Order Non-Linear Gravity
• Physical non-equivalence of the Jordan and Einstein frames
• Palatini inflation in models with an $R^2$ term
• Covariant Effective Action for Loop Quantum Cosmology a la Palatini
• Inflation with $R^2$ term in the Palatini formalism
• Invariant quantities in the scalar-tensor theories of gravitation
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Unifying Einstein and Palatini gravities
• The Palatini side of inflationary attractors
• Universality of Einstein Equations for the Ricci Squared Lagrangians
• Constraints on f(R) Cosmology in the Palatini Formalism
• Quantum corrections to quartic inflation with a non-minimal coupling: metric vs. Palatini
• Coleman-Weinberg linear inflation: metric vs. Palatini formulation
• How (Not) to Palatini
• Higgs inflation in the Palatini formulation with kinetic terms for the metric
• New universal attractor in nonmininally coupled gravity: Linear inflation
• Inflationary Perturbations in Palatini Generalised Gravity
• Gravity and Scalar Fields
• Frame-Covariant Formulation of Inflation in Scalar-Curvature Theories
• A question mark on the equivalence of Einstein and Jordan frames
• Starobinsky cosmological model in Palatini formalism
• Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
• Cosmic acceleration from modified gravity with Palatini formalism
• Frame-invariant approach to higher-dimensional scalar-tensor gravity
• Invariant slow-roll parameters in scalar-tensor theories
• Lorentz invariance and the zero-point stress-energy tensor
• Non-locality of the C- and D-theories
• Inflationary cosmology with Chaplygin gas in Palatini formalism
• Frame Transformations of Gravitational Theories
• Filtering out the cosmological constant in the Palatini formalism of modified gravity
• Cosmology of non-minimal derivative coupling to gravity in Palatini formalism and its chaotic inflation
• A new extended quintessence
• Ghost-free Palatini derivative scalar-tensor theory: desingularization and the speed test
• Pauli-Zeldovich cancellation of the vacuum energy divergences, auxiliary fields and supersymmetry
• Extended Cosmology in Palatini f(R)-theories
• Galaxy Rotation Curves via Conformal Factors
• Comparing metric and Palatini approaches to vector Horndeski theory
• Non-minimal derivative coupling in Palatini cosmology: acceleration in chaotic inflation potential

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