Density perturbations in general modified gravitational theories

Abstract

We derive the equations of linear cosmological perturbations for the general Lagrangian density $f(R,\varphi ,X)/2+L_c$, where $R$ is a Ricci scalar, $\varphi$ is a scalar field, and $X=-(\nabla \varphi {)}^2/2$ is a field kinetic energy. We take into account a nonlinear self-interaction term $L_c$ recently studied in the context of "Galileon" cosmology, which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasi-static approximation on sub-horizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds. Our analysis includes most of modified gravity models of dark energy proposed in literature and thus it is convenient to test the viability of such models from both theoretical and observational points of view.

17 pages, no figures

References in corpus (123)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Dynamics of dark energy
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
• f(R) Theories Of Gravity
• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• Cosmological parameters from SDSS and WMAP
• f(R) theories
• 4D Gravity on a Brane in 5D Minkowski Space
• The Supernova Legacy Survey: Measurement of Omega_M, Omega_Lambda and w from the First Year Data Set
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• The galileon as a local modification of gravity
• Essentials of k-essence
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space
• Chameleon Cosmology
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Kinetically Driven Quintessence
• Curvature Quintessence
• Disappearing cosmological constant in f(R) gravity
• Quintessence and the Rest of the World
• Perturbations in k-inflation
• Covariant Galileon
• Cosmological parameter analysis including SDSS Ly-alpha forest and galaxy bias: constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy
• Observational Constraints on the Nature of the Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey
• Reconstruction of a scalar-tensor theory of gravity in an accelerating universe
• Ghost Condensation and a Consistent Infrared Modification of Gravity
• Measuring the Baryon Acoustic Oscillation scale using the SDSS and 2dFGRS
• Cosmic Growth History and Expansion History
• Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
• Conditions for the cosmological viability of f(R) dark energy models
• Strong Interactions and Stability in the DGP Model
• Scaling solutions in general non-minimal coupling theories
• The Cosmology of Generalized Modified Gravity Models
• Curvature quintessence matched with observational data
• Do consistent $F(R)$ models mimic General Relativity plus $\Lambda$?
• The Large Scale Structure of f(R) Gravity
• Nonperturbative Continuity in Graviton Mass versus Perturbative Discontinuity
• Classical and Quantum Consistency of the DGP Model
• Cosmological scaling solutions of non-minimally coupled scalar fields
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Scalar-tensor gravity in an accelerating universe
• Measuring the dark side (with weak lensing)
• A discriminating probe of gravity at cosmological scales
• Extended Quintessence
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Dilatonic ghost condensate as dark energy
• Quintessence without scalar fields
• Large Scale Structure as a Probe of Gravitational Slip
• Quintessence, the Gravitational Constant, and Gravity
• The pattern of growth in viable f(R) cosmologies
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• Probing Newton's Constant on Vast Scales: DGP Gravity, Cosmic Acceleration and Large Scale Structure
• f(R) Gravity and Chameleon Theories
• Distinguishing Modified Gravity from Dark Energy
• Dynamics of Linear Perturbations in f(R) Gravity
• Galileon Cosmology
• How to determine an effective potential for a variable cosmological term
• Solar system and equivalence principle constraints on f(R) gravity by chameleon approach
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• Scalar-Tensor Gravity and Quintessence
• Dark Energy and Dark Gravity
• Phantom crossing, equation-of-state singularities, and local gravity constraints in f(R) models
• Classical evolution and quantum generation in generalized gravity theories including string corrections and tachyon: Unified analyses
• Searching for modified growth patterns with tomographic surveys
• Observational Tests of Modified Gravity
• Structure formation in the DGP cosmological model
• Probing Cosmic Acceleration Beyond the Equation of State: Distinguishing between Dark Energy and Modified Gravity Models
• Stability of Cosmological Solution in f(R) Models of Gravity
• Cosmological observations in scalar-tensor quintessence
• More on ghosts in DGP model
• Exponential Gravity
• Self-Accelerating Universe in Galileon Cosmology
• Testing Gravity Against Early Time Integrated Sachs-Wolfe Effect
• Current constraints on the cosmic growth history
• Separating Dark Physics from Physical Darkness: Minimalist Modified Gravity vs. Dark Energy
• f(R) actions, cosmic acceleration and local tests of gravity
• Testing General Relativity with Current Cosmological Data
• Dark energy and cosmological solutions in second-order string gravity
• Constraints on scalar-tensor models of dark energy from observational and local gravity tests
• Cosmological perturbations in a generalized gravity including tachyonic condensation
• Ghosts, Instabilities, and Superluminal Propagation in Modified Gravity Models
• Modified-Source Gravity and Cosmological Structure Formation
• The Newtonian limit at intermediate energies
• Probing modifications of General Relativity using current cosmological observations
• Weak lensing in scalar-tensor theories of gravity
• On the evolution of density perturbations in f(R) theories of gravity
• Non-linear Evolution of Matter Power Spectrum in Modified Theory of Gravity
• Two Windows on Acceleration and Gravitation: Dark Energy or New Gravity?
• Large-Scale Tests of the DGP Model
• The dispersion of growth of matter perturbations in f(R) gravity
• Aspects of cosmological expansion in F(R) gravity models
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• Matter density perturbations in modified gravity models with arbitrary coupling between matter and geometry
• The growth of matter perturbations in f(R) models
• Fully Covariant Van Dam-Veltman-Zakharov Discontinuity, and Absence Thereof
• Cosmic expansion and growth histories in Galileon scalar-tensor models of dark energy
• Evolution of linear cosmological perturbations and its observational implications in Galileon-type modified gravity
• Non-linear interactions in a cosmological background in the DGP braneworld
• A Dynamical Approach to the Cosmological Constant
• Is Modified Gravity Required by Observations? An Empirical Consistency Test of Dark Energy Models
• Observational signatures of Jordan-Brans-Dicke theories of gravity
• A Unified Approach to Cosmic Acceleration
• The growth of matter perturbations in some scalar-tensor DE models
• Consistency test of general relativity from large scale structure of the Universe
• Tests of Gravity from Imaging and Spectroscopic Surveys
• Phantom boundary crossing and anomalous growth index of fluctuations in viable f(R) models of cosmic acceleration
• Theoretical Priors On Modified Growth Parametrisations
• Constraining Modified Gravity and Growth with Weak Lensing
• Cosmological perturbations of a perfect fluid and noncommutative variables
• Analytic solution for matter density perturbations in a class of viable cosmological f(R) models
• Newton's constant in f(R,R_{μν}R^{μν},\Box R) theories of gravity and constraints from BBN
• A step towards testing general relativity using weak gravitational lensing and redshift surveys
• New Parametrization for the Scale Dependent Growth Function in General Relativity
• Characterizing the linear growth rate of cosmological density perturbations in an f(R) model
• Constraining DGP Gravity from Observational Data
• Scalar mode propagation in modified gravity with a scalar field
• Modifying Gravity at Low Redshift
• Gravity in the dynamical approach to the cosmological constant

Cited by in corpus (105)

• Beyond the Cosmological Standard Model
• Cosmology and Fundamental Physics with the Euclid Satellite
• Cosmology and fundamental physics with the Euclid satellite
• Dark Energy
• Cosmological Tests of Modified Gravity
• Imperfect Dark Energy from Kinetic Gravity Braiding
• G-inflation: inflation driven by the Galileon field
• Cosmology of a covariant Galileon field
• Conditions for the cosmological viability of the most general scalar-tensor theories and their applications to extended Galileon dark energy models
• Effective gravitational couplings for cosmological perturbations in the most general scalar-tensor theories with second-order field equations
• Tension and constraints on modified gravity parametrizations of $G_{\text{eff}}(z)$ from growth rate and Planck data
• Dark energy in Horndeski theories after GW170817: A review
• The Imperfect Fluid behind Kinetic Gravity Braiding
• Cosmology of the Galileon from Massive Gravity
• Cosmology in generalized Proca theories
• Generalized Galileon cosmology
• Inflationary non-Gaussianities in the most general second-order scalar-tensor theories
• Higgs G-inflation
• Generic instabilities of non-singular cosmologies in Horndeski theory: a no-go theorem
• Observational constraints on Galileon cosmology
• Inflation and primordial non-Gaussianities of "generalized Galileons"
• Beyond generalized Proca theories
• Primordial non-Gaussianity from the DBI Galileons
• Matter perturbations in Galileon cosmology
• Effective gravitational couplings for cosmological perturbations in generalized Proca theories
• Modified gravity a la Galileon: Late time cosmic acceleration and observational constraints
• Primordial non-Gaussianities in general modified gravitational models of inflation
• Dynamics of Inflation and Dark Energy from $F(R,\mathcal{G})$ Gravity
• Constraints on Shift-Symmetric Scalar-Tensor Theories with a Vainshtein Mechanism from Bounds on the Time Variation of G
• The Paths of Gravity in Galileon Cosmology
• de Sitter Galileon
• Vainshtein mechanism in second-order scalar-tensor theories
• Growth of matter perturbations in non-minimal teleparallel dark energy
• Primordial non-Gaussianity from G-inflation
• A new perspective on Dark Energy modeling via Genetic Algorithms
• Late time approaches to the Hubble tension deforming $H(z)$, worsen the growth tension
• Constraints on dissipative unified dark matter
• Galileon inflation evades the no-go for PBH formation in the single-field framework
• A Galileon Design of Slow Expansion
• FRW and Bianchi type I cosmology of f-essence
• Primordial fluctuations and non-Gaussianities from multifield DBI Galileon inflation
• Effective field theory of modified gravity with two scalar fields: dark energy and dark matter
• Large Scale Structures in Kinetic Gravity Braiding Model That Can Be Unbraided
• Chameleon dark energy models with characteristic signatures
• Cosmological constraints on extended Galileon models
• Consistent perturbations in an imperfect fluid
• Disformal transformation of cosmological perturbations
• Cosmology of the selfaccelerating third order Galileon
• Conserved cosmological perturbation in Galileon models
• Cosmology in generalized Horndeski theories with second-order equations of motion
• Chaotic inflation in modified gravitational theories
• Constraints on f(R) theory and Galileons from the latest data of galaxy redshift surveys
• A Galileon Design of Slow Expansion: II
• Primordial non-Gaussianity from ultra slow-roll Galileon inflation
• Testing deviations from $\Lambda$CDM with growth rate measurements from 6 Large Scale Structure Surveys at $\mathbf{z}=0.06$ to 1
• Cosmological perturbations and observational constraints on nonlocal massive gravity
• Scalar induced gravity waves from ultra slow-roll Galileon inflation
• Anisotropic cosmological solutions in massive vector theories
• Possibility of realizing weak gravity in redshift space distortion measurements
• Cosmology in beyond-generalized Proca theories
• Observational constraints on non-minimally coupled Galileon model
• Late-time constraints on modified Gauss-Bonnet cosmology
• Bispectrum of cosmological density perturbations in the most general second-order scalar-tensor theory
• Observational signatures of the theories beyond Horndeski
• Realisation of the ultra-slow roll phase in Galileon inflation and PBH overproduction
• Stability of scalar perturbations in scalar-torsion $f(T,\varphi )$ gravity theories in the presence of a matter fluid
• Gravitational Collapse in Cubic Horndeski Theories
• Spherical Collapse in covariant Galileon theory
• Slow-roll inflation in generalized scalar-torsion gravity
• Large fluctuations and Primordial Black Holes
• Goldstone's Theorem and Hamiltonian of Multi-galileon Modified Gravity
• The WiggleZ Dark Energy Survey: constraining the evolution of Newton's constant using the growth rate of structure
• Dynamical systems of modified Gauss-Bonnet gravity: cosmological implications
• Third order solutions of the cosmological density perturbations in the Horndeski's most general scalar-tensor theory with the Vainshtein mechanism
• Stability of relativistic stars with scalar hairs
• Spherical Accretion of Matter by Charged Black Holes on f(T) Gravity
• Exact theory for the Rezzolla-Zhidenko metric and self-consistent calculation of quasinormal modes
• Cosmological disformal transformations to the Einstein frame and gravitational couplings with matter perturbations
• Revisiting the dynamics of interacting vector-like dark energy
• Weak lensing probe of cubic Galileon model
• Can the degeneracies in the gravity sector be broken?
• Observed galaxy power spectrum in cubic Galileon model
• Density perturbations in $f(R,\varphi )$-gravity with an application to the (varying power)-law model
• Generalized Galileon Model -- cosmological reconstruction and the Vainshtein mechanism --
• An extended analysis for a generalized Chaplygin gas model
• Cosmological stability in $f(\varphi ,\mathcal{G})$ gravity
• Cosmological Tests of $f(R,G,T)$ Dark Energy Model in FRW Universe
• The Music of the Aetherwave - B-mode Polarization in Einstein-Aether Theory
• Complete density perturbations in the Jordan-Fierz-Brans-Dicke theory
• On existence of a possible Lorentz invariant modified gravity in Weitzenböck spacetime
• Galileon intermediate inflation
• A study on Cubic Galileon Gravity Using N-body Simulations
• Chaotic Inflation and Reheating in Generalized Scalar-Tensor Gravity
• Primordial Black Holes Dark Matter and Secondary Gravitational Waves from Warm Higgs-G Inflation
• Phi Zeta Delta: Growth of Perturbations in Parameterized Gravity for an Einstein-de Sitter Universe
• A family of solutions to the inverse problem in gravitation: building a theory around a metric
• 21 cm power spectrum in interacting cubic Galileon model
• Gödel-type solutions within the $f(R,Q,P)$ gravity
• First and second order cosmological perturbations in light mass Galileon models
• Gauge Issues in Extended Gravity and f(R) Cosmology
• Dynamics of entropy perturbations in assisted dark energy with mixed kinetic terms
• Coupled vector Gauss-Bonnet theories and hairy black holes
• Geometrical deformation of brane matter field within $f(R,Q,P)$ gravity
• Consistency Relation and Non-Gaussianity in a Galileon Inflation
• Reheating after relaxation of large cosmological constant