Nonlinear stability of cosmological solutions in massive gravity

Abstract

We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type--I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions.

28 pages ; v2. Minor changes to match the published version

References in corpus (25)

• Resummation of Massive Gravity
• Massive gravity: nonlinear instability of the homogeneous and isotropic universe
• Inflationary perturbations in anisotropic backgrounds and their imprint on the CMB
• Acausality of Massive Gravity
• Quasi-Dilaton: Theory and Cosmology
• Instability of the ACW model, and problems with massive vectors during inflation
• Cosmological perturbations in Massive Gravity and the Higuchi bound
• Self-accelerating Massive Gravity: Exact solutions for any isotropic matter distribution
• Anisotropic Friedmann-Robertson-Walker universe from nonlinear massive gravity
• Evidence for and Obstructions to Non-Linear Partially Massless Gravity
• Nonlinear Partially Massless from Massive Gravity?
• Cosmological Perturbations in Extended Massive Gravity
• Cosmological solutions of massive gravity on de Sitter
• Cosmologies of extended massive gravity
• Aspects of the UV/IR correspondence : energy broadening and string fluctuations
• Gravitational wave signal from massive gravity
• Search for stopped long-lived particles produced in pp collisions at sqrt(s) = 7 TeV
• Cosmology and perturbations in massive gravity
• Vector instabilities and self-acceleration in the decoupling limit of massive gravity
• Anisotropic universes in the ghost-free bigravity
• Self-accelerating Massive Gravity: Time for Field Fluctuations
• All Fierz-Paulian massive gravity theories have ghosts or superluminal modes
• Dynamical analysis of the cosmology of mass-varying massive gravity
• Self-accelerating solutions in massive gravity on an isotropic reference metric
• On Cosmic No-hair in Bimetric Gravity and the Higuchi Bound

Cited by in corpus (89)

• Beyond the Cosmological Standard Model
• Massive Gravity
• A Critical Review of Classical Bouncing Cosmologies
• Universal Resistivity from Holographic Massive Gravity
• Anisotropic stress as signature of non-standard propagation of gravitational waves
• Bimetric gravity is cosmologically viable
• Dark Energy in light of Multi-Messenger Gravitational-Wave astronomy
• On couplings to matter in massive (bi-)gravity
• Phantom dark energy from non-local infrared modifications of General Relativity
• Cosmological Stability Bound in Massive Gravity and Bigravity
• Bimetric gravity doubly coupled to matter: theory and cosmological implications
• Viable cosmology in bimetric theory
• Towards consistent extension of quasidilaton massive gravity
• Non-local massive gravity
• Cosmological Perturbations in Extended Massive Gravity
• Massive Gravity Acausality Redux
• FRW Cosmological Perturbations in Massive Bigravity
• Higher Derivative Gravity and Conformal Gravity From Bimetric and Partially Massless Bimetric Theory
• New Kinetic Interactions for Massive Gravity?
• The Cosmology of Interacting Spin-2 Fields
• Spherically symmetric static solutions in a non-local infrared modification of General Relativity
• Generalized quasi-dilaton theory
• Cosmology of bigravity with doubly coupled matter
• Non-local gravity and comparison with observational datasets. II. Updated results and Bayesian model comparison with $\Lambda$CDM
• Quasi-dilaton non-linear massive gravity: Investigations of background cosmological dynamics
• Cosmological perturbations and observational constraints on nonlocal massive gravity
• Cosmological investigations of (extended) nonlinear massive gravity schemes with non-minimal coupling
• Integrated Sachs-Wolfe effect in massive bigravity
• Higher dimensional nonlinear massive gravity
• Stability of the Self-accelerating Universe in Massive Gravity
• CMB Scale Dependent Non-Gaussianity from Massive Gravity during Inflation
• Canonical structure of Tetrad Bimetric Gravity
• Mild bounds on bigravity from primordial gravitational waves
• A new quasidilaton theory of massive gravity
• Stable FLRW solutions in Generalized Massive Gravity
• $F(R)$ nonlinear massive theories of gravity and their cosmological implications
• Cosmology of F(R) nonlinear massive gravity
• Cosmological viability of massive gravity with generalized matter coupling
• No consistent bimetric gravity?
• Stability of the Early Universe in Bigravity Theory
• Cosmology in General Massive Gravity Theories
• Generalized massive gravity in arbitrary dimensions and its Hamiltonian formulation
• Cosmological perturbations in Gauss-Bonnet quasi-dilaton massive gravity
• Anisotropic instability in a higher order gravity theory
• Effective Field Theory of Broken Spatial Diffeomorphisms
• Reconstruction method of $f(R)$ gravity for isotropic and anisotropic spacetimes
• Minimal theory of massive gravity and constraints on the graviton mass
• Interacting spin-2 fields in the Stueckelberg picture
• Consistent metric combinations in cosmology of massive bigravity
• Conformal symmetry and nonlinear extensions of nonlocal gravity
• Long Range Effects in Gravity Theories with Vainshtein Screening
• The Komar mass function in the de-Rham-Gabadadze-Tolley non-linear theory of massive gravity
• Cosmology in rotation-invariant massive gravity with non-trivial fiducial metric
• Matter coupling in partially constrained vielbein formulation of massive gravity
• Hamiltonian Formalism of Bimetric Gravity In Vierbein Formulation
• Observational bounds on extended minimal theories of massive gravity: New limits on the graviton mass
• Nonderivative Modified Gravity: a Classification
• Stable Cosmology in Generalised Massive Gravity
• $f(T)$ non-linear massive gravity and the cosmic acceleration
• Coupling between Galileon and massive gravity with composite metrics
• Coleman-de Luccia instanton in dRGT massive gravity
• Extended DBI massive gravity with generalized fiducial metric
• Cosmology in Brans-Dicke-de Rham-Gabadadze-Tolley massive gravity
• Non-linear dynamics of the minimal theory of massive gravity
• Role of matter in extended quasidilaton massive gravity
• On the viability of bigravity cosmology
• Galileons Coupled to Massive Gravity: General Analysis and Cosmological Solutions
• Cosmology in massive gravity with effective composite metric
• Generalising the matter coupling in massive gravity: a search for new interactions
• Stable cosmology in ghost-free quasidilaton theory
• Cosmology of Dirac-Born-Infeld dRGT massive gravity
• Aller guten Dinge sind drei: Cosmology with three interacting spin-2 fields
• New Quasidilaton theory in Partially Constrained Vielbein Formalism
• Black Holes in Multi-Metric Gravity
• Cosmology of Massive Gravity and its Extensions
• Nonlinear anisotropy growth in Bianchi-I spacetime in metric $f(R)$ cosmology
• Anisotropic deformations of spatially open cosmology in massive gravity theory
• Translation invariant time-dependent solutions to massive gravity
• Extended minimal theories of massive gravity
• Perturbations of Cosmological and Black Hole Solutions in Massive gravity and Bi-gravity
• Boulware-Deser ghost in extended quasidilaton massive gravity
• Primordial fluctuations from inflation in dRGT bimetric theory of gravity
• Cosmological evolutions of $F(R)$ nonlinear massive gravity
• Bi-Connected Gauss-Bonnet Gravity
• Note About Consistent Extension of Quasidilaton Massive Gravity
• Black Holes in Multi-Metric Gravity II: Hairy Solutions and Linear Stability of the Non- and Partially Proportional Branches
• Effective Fluid FLRW Cosmologies of Minimal Massive Gravity
• $G_3$ -- interacting scalar tensor dark energy
• Cosmological aspects of cubic Galileon massive gravity