Conformal aspects of Palatini approach in Extended Theories of Gravity

Abstract

The debate on the physical relevance of conformal transformations can be faced by taking the Palatini approach into account to gravitational theories. We show that conformal transformations are not only a mathematical tool to disentangle gravitational and matter degrees of freedom (passing from the Jordan frame to the Einstein frame) but they acquire a physical meaning considering the bi-metric structure of Palatini approach which allows to distinguish between spacetime structure and geodesic structure. Examples of higher-order and non-minimally coupled theories are worked out and relevant cosmological solutions in Einstein frame and Jordan frames are discussed showing that also the interpretation of cosmological observations can drastically change depending on the adopted frame.

References in corpus (21)

• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• The Case for a Positive Cosmological Lambda-term
• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• Cosmological Results from High-z Supernovae
• Cosmological Tracking Solutions
• Curvature Quintessence
• The 2dF Galaxy Redshift Survey: The bias of galaxies and the density of the Universe
• Study of the anomalous acceleration of Pioneer 10 and 11
• Modified gravity with $\ln R$ terms and cosmic acceleration
• On Physical Equivalence between Nonlinear Gravity Theories
• 1/R Curvature Corrections as the Source of the Cosmological Acceleration
• Palatini form of 1/R gravity
• Accelerated Cosmological Models in Ricci squared Gravity
• $O(d,d)$-Covariant String Cosmology
• The Universality of Einstein Equations
• Gravitational potential in Palatini formulation of modified gravity
• The Newtonian limit of fourth and higher order gravity
• Recovering the effective cosmological constant in extended gravity theories
• Hyperextended Scalar-Tensor Gravity
• Palatini formulation of modified gravity with squared scalar curvature
• Gravitational Lensing and the Variability of G

Cited by in corpus (71)

• Extended Theories of Gravity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• f(R) Gravity and scalar-tensor theory
• Covariant conservation of energy momentum in modified gravities
• Matter instability in modified gravity
• The (pseudo)issue of the conformal frame revisited
• Cosmological perturbations in the Palatini formulation of modified gravity
• Spherical symmetry in $f(R)$-gravity
• de Sitter space and the equivalence between f(R) and scalar-tensor gravity
• Cosmological constraints on f(R) gravity theories within the Palatini approach
• Solar System experiments do not yet veto modified gravity models
• Fourth order gravity: equations, history, and applications to cosmology
• f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints
• Comparing Equivalent Gravities: common features and differences
• A viability criterion for modified gravity with an extra force
• Massive gravitational waves from f(R) theories of gravity: Potential detection with LISA
• Cosmology of hybrid metric-Palatini f(X)-gravity
• A bird's eye view of f(R)-gravity
• Physical non-equivalence of the Jordan and Einstein frames
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• Axially symmetric solutions in f(R)-gravity
• The phase space view of f(R) gravity
• f(R) Gravity with Torsion: The Metric-Affine Approach
• Precision Gravity Tests and the Einstein Equivalence Principle
• f(R) theories of gravity in Palatini approach matched with observations
• Unifying Einstein and Palatini gravities
• Dark energy exponential potential models as curvature quintessence
• The Palatini side of inflationary attractors
• Theory of gravitation theories: a no-progress report
• Curvature scalar instability in f(R) gravity
• Scale transformations in metric-affine geometry
• Ghost-free $F(R)$ bigravity and accelerating cosmology
• The cosmic snap parameter in f(R) gravity
• Higher-order gravity and the cosmological background of gravitational waves
• Conformally related metrics and Lagrangians and their physical interpretation in cosmology
• Acceleration of the universe in the Einstein frame of a metric-affine f(R) gravity
• Cosmological perturbations in Palatini modified gravity
• f(R) gravity with torsion: a geometric approach within the J-bundles framework
• The production of matter from curvature in a particular linearized high order theory of gravity and the longitudinal response function of interferometers
• Affine theory of gravitation
• Invariant Differential Operators for Non-Compact Lie Algebras Parabolically Related to Conformal Lie Algebras
• Matter stability in modified teleparallel gravity
• Conformal Transformations and Weak Field Limit of Scalar-Tensor Gravity
• Equivalence of non-minimally coupled cosmologies by Noether symmetries
• New class of hybrid metric-Palatini scalar-tensor theories of gravity
• Cosmology of non-minimal derivative coupling to gravity in Palatini formalism and its chaotic inflation
• The dynamical equivalence of modified gravity revisited
• The present universe in the Einstein frame, metric-affine R+1/R gravity
• Space-time deformations as extended conformal transformations
• Nonminimal coupling inflation with constant slow roll
• Gravitational energy-momentum pseudo-tensor in Palatini and metric $f(R)$ gravity
• Bounding $f(R)$ gravity by particle production rate
• Hojman Symmetry Approach for Scalar-Tensor Cosmology
• Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity
• Conformal and kinetic couplings as two Jordan frames of the same theory
• FRW string cosmological solutions via Hojman symmetry
• The effective Equation of State in Palatini $f(R)$ cosmology
• F(R) gravity in purely affine formulation
• Classical Euclidean wormhole solutions in Palatini $f(\tilde{R})$ cosmology
• Extended Geometric Trinity of Gravity
• Cosmological Dark sector from a Mimetic-Metric-Torsion perspective
• Mimetic-Metric-Torsion with induced Axial mode and Phantom barrier crossing
• Simple cosmological model with inflation and late times acceleration
• Hyperbolic inflation in the Jordan frame
• Dynamical system analysis in multiscalar-torsion cosmology
• On the longitudinal response function of interferometers for massive gravitational waves from a bimetric theory of gravity
• Equivalent Gravities and Equivalence Principle: Foundations and experimental implications
• Spin frame transformations and Dirac equations
• Covariant single-field formulation of effective cosmological bounces
• Extended Theories of Electrodynamics in $f(R)$ Gravity