Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories

Abstract

With a scalar field non-minimally coupled to curvature, the underlying geometry and variational principle of gravity - metric or Palatini - becomes important and makes a difference, as the field dynamics and observational predictions generally depend on this choice. In the present paper we describe a classification principle which encompasses both metric and Palatini models of inflation, employing the fact that inflationary observables can be neatly expressed in terms of certain quantities which remain invariant under conformal transformations and scalar field redefinitions. This allows us to elucidate the specific conditions when a model yields equivalent phenomenology in the metric and Palatini formalisms, and also to outline a method how to systematically construct different models in both formulations that produce the same observables.

PRD accepted, title modified per journal's request, discussion and examples expanded, references added

References in corpus (24)

• The Standard Model Higgs boson as the inflaton
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Higgs inflation: consistency and generalisations
• The Unity of Cosmological Attractors
• Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Higgs-Palatini Inflation and Unitarity
• Higgs inflation with loop corrections in the Palatini formulation
• Preheating in Palatini Higgs inflation
• Invariant quantities in the scalar-tensor theories of gravitation
• Selected topics in scalar-tensor theories and beyond
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Lovelock Gravity at the Crossroads of Palatini and Metric Formulations
• Metric-affine Gravity and Inflation
• Minimal Higgs inflation with an $R^2$ term in Palatini gravity
• Coleman-Weinberg linear inflation: metric vs. Palatini formulation
• Deceleration versus Acceleration Universe in Different Frames of $F(R)$ Gravity
• Inflationary Perturbations in Palatini Generalised Gravity
• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar
• Frame Covariant Nonminimal Multifield Inflation
• Potential dominated scalar-tensor cosmologies in the general relativity limit: phase space view
• Filtering out the cosmological constant in the Palatini formalism of modified gravity
• Dynamical equivalence of $f(R)$ gravity in Jordan and Einstein frames
• Note on stability in conformally connected frames

Cited by in corpus (5)

• Stability criterion for white dwarfs in Palatini $f(R)$ gravity
• Universal Inflationary Attractors Implications on Static Neutron Stars
• Cooling process of brown dwarfs in Palatini f(R) gravity
• General slow-roll inflation in $f(R)$ gravity under the Palatini approach
• Relaxing inflation models with non-minimal coupling: A general study