Conformal and kinetic couplings as two Jordan frames of the same theory

Abstract

Non-minimal scalar-tensor (ST) theories may admit an Einstein frame representation, where gravity is described by the Einstein-Hilbert action plus the scalar sector. Some STs become just {\em minimal} Einstein-scalar (MES) theories, notable examples are Brans-Dicke and $R{\varphi }^2$. ST theories with {\em derivative} coupling can also be reduced to an Einstein frame by disformal transformations, but, as a rule, their scalar sector will contain higher derivative terms. Here we draw attention to a new Palatini kinetically coupled theory which can be reduced to pure MES by an invertible disformal transformation. This theory can then be converted into the Jordan frame of another ST, $R{\varphi }^2$, which also admits an invertible transformation to MES. Two theories, each of which is dual to MES, will be {\em sequentially dual} to each other and can be considered as two different Jordan frames of the same theory. Both chosen theories violate null energy condition. Transforming the same singular MES solutions, we find the desingularization signs in both Jordan frames, but these are more pronouned in the framework of kinetic theory, leading, in the cosmological case, to Genesis-type behavior.

arXiv comment25 pages

References in corpus (79)

• Extended Theories of Gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• The Standard Model Higgs boson as the inflaton
• From k-essence to generalised Galileons
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Black holes, gravitational waves and fundamental physics: a roadmap
• Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
• Horndeski theory and beyond: a review
• Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
• The Relation between Physical and Gravitational Geometry
• Exploring gravitational theories beyond Horndeski
• General second order scalar-tensor theory, self tuning, and the Fab Four
• On Physical Equivalence between Nonlinear Gravity Theories
• Power-counting and the Validity of the Classical Approximation During Inflation
• New Model of Inflation with Non-minimal Derivative Coupling of Standard Model Higgs Boson to Gravity
• Extended Gravity Theories and the Einstein-Hilbert Action
• Does backreaction enforce the averaged null energy condition in semiclassical gravity?
• Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations
• The conformal frame freedom in theories of gravitation
• Galilean Genesis: an alternative to inflation
• Dark Energy and Modified Gravity in Degenerate Higher-Order Scalar-Tensor (DHOST) theories: a review
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Exact cosmological solutions with nonminimal derivative coupling
• Cosmology with Nonminimal Derivative Couplings
• Disformal invariance of second order tensor-scalar theories: framing the Horndeski action
• The Null Energy Condition and its violation
• Induced gravity inflation in the standard model of particle physics
• Cosmology with a stiff matter era
• Non-minimal coupling of the scalar field and inflation
• Question of quantum equivalence between Jordan frame and Einstein frame
• Hybrid metric-Palatini gravity
• Disformal Transformations, Veiled General Relativity and Mimetic Gravity
• Nonminimal Derivative Couplings and Inflation in Generalized Theories of Gravity
• Ghosts in metric-affine higher order curvature gravity
• Nonminimal Derivative Coupling and the Recovering of Cosmological Constant
• Some aspects of the cosmological conformal equivalence between ``Jordan Frame'' and ``Einstein Frame''
• Derivative-dependent metric transformation and physical degrees of freedom
• Palatini formulation of modified gravity with a nonminimal curvature-matter coupling
• Lovelock Gravity at the Crossroads of Palatini and Metric Formulations
• Disformal Inflation
• Ostrogradsky in Theories with Multiple Fields
• Unification of inflation and cosmic acceleration in the Palatini formalism
• Conformal aspects of Palatini approach in Extended Theories of Gravity
• The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier
• Theory of gravitation theories: a no-progress report
• Metric-affine Gravity and Inflation
• General Non-minimal Kinetic coupling to gravity
• Superinflation, quintessence, and nonsingular cosmologies
• Dynamical Aspects of Generalized Palatini Theories of Gravity
• Realistic cosmological scenario with non-minimal kinetic coupling
• Cosmological disformal invariance
• Solving higher curvature gravity theories
• Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
• Quantum equivalence of $f(R)$ gravity and scalar-tensor theories
• Disformal Gravity Theories: A Jordan Frame Analysis
• Conformally related metrics and Lagrangians and their physical interpretation in cosmology
• Singularity theorems from weakened energy conditions
• General invertible transformation and physical degrees of freedom
• Equivalence between Palatini and metric formalisms of f(R)-gravity by divergence free current
• Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
• Stationary axisymmetric spacetimes with a conformally coupled scalar field
• Scalar-tensor gravity and conformal continuations
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Genesis with general relativity asymptotics in beyond Horndeski theory
• On the (non-)uniqueness of the Levi-Civita solution in the Einstein-Hilbert-Palatini formalism
• On the singularities of gravity in the presence of non-minimally coupled scalar fields
• Exact Conformal Scalar Field Cosmologies
• A Singularity-Free Cosmological Model with a Conformally Coupled Scalar Field
• Energy conditions and classical scalar fields
• Cosmology of non-minimal derivative coupling to gravity in Palatini formalism and its chaotic inflation
• Ghost-free Palatini derivative scalar-tensor theory: desingularization and the speed test
• Hybrid Higgs Inflation: The Use of Disformal Transformation
• A singularity theorem for Einstein-Klein-Gordon theory
• Slow-Roll Inflation in Scalar-Tensor Models
• Wyman's "other" scalar field solution, Sultana's generalization, and their Brans-Dicke and $R^2$ relatives
• On the equivalence between different canonical forms of F(R) theory of gravity
• Dynamical analysis for a scalar-tensor model with kinetic and non-minimal couplings
• Comparing metric and Palatini approaches to vector Horndeski theory
• Possible resolution of a spacetime singularity with field transformations

Cited by in corpus (5)

• Palatini-Higgs inflation with non-minimal derivative coupling
• Implications of Palatini gravity for inflation and beyond
• Coupled dark energy model inspired from general conformal transformation
• Scalar fields with derivative coupling to curvature in the Palatini and the metric formulation
• Supergravity $p$-branes with scalar charge