Cosmological disformal transformations to the Einstein frame and gravitational couplings with matter perturbations

Abstract

The disformal transformation of metric $g_{\mu \nu }\to {\Omega }^2(\varphi )g_{\mu \nu }+\Gamma (\varphi ,X){\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$, where $\varphi$ is a scalar field with the kinetic energy $X={\partial }_{\mu }\varphi {\partial }^{\mu }\varphi /2$, preserves the Lagrangian structure of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories (which is the minimum extension of Horndeski theories). In the presence of matter, this transformation gives rise to a kinetic-type coupling between the scalar field $\varphi$ and matter. We consider the Einstein frame in which the second-order action of tensor perturbations on the isotropic cosmological background is of the same form as that in General Relativity and study the role of couplings at the levels of both background and linear perturbations. We show that the effective gravitational potential felt by matter perturbations in the Einstein frame can be conveniently expressed in terms of the sum of a General Relativistic contribution and couplings induced by the modification of gravity. For the theories in which the transformed action belongs to a class of Horndeski theories, there is no anisotropic stress between two gravitational potentials in the Einstein frame due to a gravitational de-mixing. We propose a concrete dark energy model encompassing Brans-Dicke theories as well as theories with the tensor propagation speed $c_{\mathrm{t}}$ different from 1. We clarify the correspondence between physical quantities in the Jordan/Einstein frames and study the evolution of gravitational potentials and matter perturbations from the matter-dominated epoch to today in both analytic and numerical approaches.

22 pages, 4 figures

References in corpus (42)

• Dynamics of dark energy
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Beyond the Cosmological Standard Model
• Covariant Galileon
• Healthy theories beyond Horndeski
• Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
• Imperfect Dark Energy from Kinetic Gravity Braiding
• Effective Field Theory for Inflation
• Exploring gravitational theories beyond Horndeski
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity
• Measuring the dark side (with weak lensing)
• Approaches to Understanding Cosmic Acceleration
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• Cosmological parameters from the comparison of peculiar velocities with predictions from the 2M++ density field
• Screening Modifications of Gravity through Disformally Coupled Fields
• Constraints on scalar-tensor models of dark energy from observational and local gravity tests
• Observables and unobservables in dark energy cosmologies
• Resilience of the standard predictions for primordial tensor modes
• Disformal Transformations, Veiled General Relativity and Mimetic Gravity
• Density perturbations in general modified gravitational theories
• Hamiltonian analysis of spatially covariant gravity
• The 6dF Galaxy Velocity Survey: Cosmological constraints from the velocity power spectrum
• Effective Theory of Interacting Dark Energy
• Disformal couplings and the dark sector of the universe
• Disformal Theories of Gravity: From the Solar System to Cosmology
• Constraining Disformally Coupled Scalar Fields
• Hamiltonian structure of scalar-tensor theories beyond Horndeski
• Effective field theory of modified gravity with two scalar fields: dark energy and dark matter
• A note on the equivalence of a barotropic perfect fluid with a K-essence scalar field
• Disformal transformation of cosmological perturbations
• Effective field theory approach to modified gravity including Horndeski theory and Hořava-Lifshitz gravity
• Shaken, not stirred: kinetic mixing in scalar-tensor theories of gravity
• Cosmology in generalized Horndeski theories with second-order equations of motion
• Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
• Possibility of realizing weak gravity in redshift space distortion measurements
• Observational signatures of the theories beyond Horndeski
• Cosmological Implications of the Effective Field Theory of Cosmic Acceleration
• Multi-disformal invariance of nonlinear primordial perturbations
• Induced geometry from disformal transformation
• Inflationary gravitational waves in the effective field theory of modified gravity

Cited by in corpus (16)

• Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
• Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations
• Hamiltonian analysis of higher derivative scalar-tensor theories
• Selected topics in scalar-tensor theories and beyond
• Effective Theory of Dark Energy at Redshift Survey Scales
• Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
• Disformal Gravity Theories: A Jordan Frame Analysis
• Invertible disformal transformations with higher derivatives
• Spatially covariant theories of gravity: disformal transformation, cosmological perturbations and the Einstein frame
• Disformally coupled inflation
• Conical singularities and the Vainshtein screening in full GLPV theories
• Coupled dark energy model inspired from general conformal transformation
• An issue with the classification of the scalar-tensor theories of gravity
• Constraining Violations of the Weak Equivalence Principle in the Dark Sector
• Disformal transformations as a change of units
• Exploring Self-Gravitating Cylindrical Structures in Modified Gravity: Insights from Scalar-Vector-Tensor Theory