New class of hybrid metric-Palatini scalar-tensor theories of gravity

Abstract

A class of scalar-tensor theories (STT) including a non-metricity that unifies metric, Palatini and hybrid metric-Palatini gravitational actions with non-minimal interaction is proposed and investigated from the point of view of their consistency with generalized conformal transformations. It is shown that every such theory can be represented on-shell by a purely metric STT possessing the same solutions for a metric and a scalar field. A set of generalized invariants is also proposed. This extends the formalism previously introduced in \cite{kozak2019}. We then apply the formalism to Starobinsky model, write down the Friedmann equations for three possible cases: metric, Palatini and hybrid metric-Palatini, and compare some inflationary observables.

arXiv comment34 pages in LaTeX, comments and references added, final version published in JCAP

References in corpus (97)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• f(R) theories
• Extended Theories of Gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Chameleon Cosmology
• Encyclopaedia Inflationaris
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Dark Energy Dominance and Cosmic Acceleration in First Order Formalism
• f(R) Gravity and scalar-tensor theory
• 1/R Curvature Corrections as the Source of the Cosmological Acceleration
• Covariant conservation of energy momentum in modified gravities
• The conformal frame freedom in theories of gravitation
• Cosmological dynamics of R^n gravity
• Solar system and equivalence principle constraints on f(R) gravity by chameleon approach
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• The (pseudo)issue of the conformal frame revisited
• Metric-Palatini gravity unifying local constraints and late-time cosmic acceleration
• Question of quantum equivalence between Jordan frame and Einstein frame
• Hybrid metric-Palatini gravity
• Massive gravitational waves from f(R) theories of gravity: Potential detection with LISA
• Higgs inflation with loop corrections in the Palatini formulation
• Accelerated Cosmological Models in First-Order Non-Linear Gravity
• Cosmology of hybrid metric-Palatini f(X)-gravity
• Physical non-equivalence of the Jordan and Einstein frames
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• Palatini inflation in models with an $R^2$ term
• Inflation with $R^2$ term in the Palatini formalism
• Generalized hybrid metric-Palatini gravity
• Invariant quantities in the scalar-tensor theories of gravitation
• $f(R)$ constant-roll inflation
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Dark matter and dark energy as a effects of Modified Gravity
• Einstein static Universe in hybrid metric-Palatini gravity
• The Palatini side of inflationary attractors
• Conformal aspects of Palatini approach in Extended Theories of Gravity
• Correspondence of $F(R)$ Gravity Singularities in Jordan and Einstein Frames
• Metric-affine Gravity and Inflation
• Is exponential gravity a viable description for the whole cosmological history?
• Constraints on f(R) Cosmology in the Palatini Formalism
• Quantum corrections to quartic inflation with a non-minimal coupling: metric vs. Palatini
• Resurrecting Quadratic Inflation with a non-minimal coupling to gravity
• Deceleration versus Acceleration Universe in Different Frames of $F(R)$ Gravity
• Coleman-Weinberg linear inflation: metric vs. Palatini formulation
• Rescuing Quartic and Natural Inflation in the Palatini Formalism
• CMB and Matter Power Spectra of Early f(R) Cosmology in Palatini Formalism
• Cosmological solutions in generalized hybrid metric-Palatini gravity
• A dynamical system analysis of hybrid metric-Palatini cosmologies
• How (Not) to Palatini
• Hidden Inflaton Dark Matter
• 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
• Tracing the high energy theory of gravity: an introduction to Palatini inflation
• Invariant solutions and Noether symmetries in Hybrid Gravity
• Accelerated Cosmological Models in Modified Gravity tested by distant Supernovae SNIa data
• Attractor Behaviour in Multifield Inflation
• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar
• Frame-Covariant Formulation of Inflation in Scalar-Curvature Theories
• Reconstructing the inflationary $f(R)$ from observations
• A question mark on the equivalence of Einstein and Jordan frames
• Dynamics of Linear Perturbations in the hybrid metric-Palatini gravity
• Palatini frames in scalar-tensor theories of gravity
• Inflation and dark energy from f(R) gravity
• A simple $F(\mathcal{R},\varphi )$ deformation of Starobinsky inflationary model
• Constant-roll inflation in scalar-tensor gravity
• Cosmological perturbations in Palatini modified gravity
• Starobinsky cosmological model in Palatini formalism
• Minimum main sequence mass in quadratic Palatini $f(\mathcal{R})$ gravity
• Towards distinguishing variants of non-minimal inflation
• Cosmic acceleration from modified gravity with Palatini formalism
• Transformation properties and general relativity regime in scalar-tensor theories
• Frame-invariant approach to higher-dimensional scalar-tensor gravity
• Invariant slow-roll parameters in scalar-tensor theories
• Polytropic stars in Palatini gravity
• Constant-roll in the Palatini-$R^2$ models
• 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
• Ghost-free Palatini derivative scalar-tensor theory: desingularization and the speed test
• A new extended quintessence
• On the Emergence of Accelerating Cosmic Expansion in f(R) Theories of Gravity
• The Palatini star: exact solutions of the modified Lane-Emden equation
• Galaxy Rotation Curves via Conformal Factors
• A simple model for explaining Galaxy Rotation Curves
• Asymptotically Weyl-Invariant Gravity

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• Palatini-Higgs inflation with non-minimal derivative coupling
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• Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
• Tachyonic Preheating in Palatini $R^2$ Inflation
• Palatini $R^2$ Quintessential Inflation
• Implications of Palatini gravity for inflation and beyond
• Gravitational dark matter production in Palatini preheating
• Stability criterion for white dwarfs in Palatini $f(R)$ gravity
• Metric-affine gravity effects on terrestrial (exo-)planets profiles
• Estimating the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S2, S38 and S55 stars: case of bulk mass distribution
• Weak-field regime of the generalized hybrid metric-Palatini gravity
• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
• Invariant quantities of Scalar-Tensor Theories for stellar structure
• General Einstein-Cartan quadratic gravity with derivative couplings
• Dynamical reconstruction of the $\Lambda$CDM model in hybrid metric-Palatini gravity
• Novel electrically charged wormhole, black hole and black bounce exact solutions in hybrid metric-Palatini gravity
• Scalar-tensor cosmologies in a minisuperspace formulation: a case study
• Gravitational wave propagation in generalized hybrid metric-Palatini gravity
• Is it possible to separate baryonic from dark matter within the $\Lambda$-CDM formalism?
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity
• On the "Legendre scalarization" of nonlinear gravity theories