Revival of the Deser-Woodard nonlocal gravity model: Comparison of the original nonlocal form and a localized formulation

Abstract

We examine the origin of two opposite results for the growth of perturbations in the Deser-Woodard (DW) nonlocal gravity model. One group previously analyzed the model in its original nonlocal form and showed that the growth of structure in the DW model is enhanced compared to general relativity (GR) and thus concluded that the model was ruled out. Recently, however, another group has reanalyzed it by localizing the model and found that the growth in their localized version is suppressed even compared to the one in GR. The question was whether the discrepancy originates from an intrinsic difference between the nonlocal and localized formulations or is due to their different implementations of the sub-horizon limit. We show that the nonlocal and local formulations give the same solutions for the linear perturbations as long as the initial conditions are set the same. The different implementations of the sub-horizon limit lead to different transient behaviors of some perturbation variables; however, they do not affect the growth of matter perturbations at the sub-horizon scale much. In the meantime, we also report an error in the numerical calculation code of the former group and verify that after fixing the error the nonlocal version also gives the suppressed growth. Finally, we discuss two alternative definitions of the effective gravitational constant taken by the two groups and some open problems.

15 pages, 4 figures; v3: matches the published version in PRD, typos fixed

References in corpus (36)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data
• A Parameterized Post-Friedmann Framework for Modified Gravity
• Modified non-local-F(R) gravity as the key for the inflation and dark energy
• Cosmological perturbations and structure formation in nonlocal infrared modifications of general relativity
• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• On the Growth of Perturbations as a Test of Dark Energy
• The Parameterized Post-Friedmann Framework for Theories of Modified Gravity: Concepts, Formalism and Examples
• Dynamics of Nonlocal Cosmology
• Accelerating cosmologies from non-local higher-derivative gravity
• Phantom and non-phantom dark energy: The cosmological relevance of non-locally corrected gravity
• Localization of nonlocal theories
• Reconstructing the Distortion Function for Nonlocal Cosmology
• Newtonian limit of nonlocal cosmology
• Non-local quantum effects in cosmology 1: Quantum memory, non-local FLRW equations and singularity avoidance
• Generalised Quadratic Curvature, Non-Local Infrared Modifications of Gravity and Newtonian Potentials
• Screening of cosmological constant in non-local gravity
• Dynamics in Nonlocal Cosmological Models Derived from String Field Theory
• Non-local gravity and comparison with observational datasets
• Nonlinear structure formation in Nonlocal Gravity
• Constraining Generalized Non-local Cosmology from Noether Symmetries
• Field equations and cosmology for a class of nonlocal metric models of MOND
• Reconstruction Procedure in Nonlocal Cosmological Models
• Nonlocal Teleparallel Cosmology
• Running of Newton's constant and non integer powers of the d'Alembertian
• Nonlocal Metric Realizations of MOND
• Stability analysis and future singularity of the $m^{2}R{\square }^{-2}R$ model of non-local gravity
• Determining Cosmology for a Nonlocal Realization of MOND
• A Caveat on Building Nonlocal Models of Cosmology
• Quantum Gravity inspired nonlocal gravity model
• On Nonlocal Modified Gravity and its Cosmological Solutions
• Gravity Induced Non-Local Effects in the Standard Model
• Quantum Aspects of Nonlocal Approach to the Cosmological Constant Problem
• An Improved Cosmological Model
• Nonlocal effective actions in semiclassical gravity: thermal effects in stationary geometries
• Gravitational Quantum Effects and Nonlocal Approach to the Cosmological Constant Problem

Cited by in corpus (22)

• Testing General Relativity in Cosmology
• Nonlocal gravity. Conceptual aspects and cosmological predictions
• Testing nonlocal gravity with Lunar Laser Ranging
• Nonlocal Cosmology II --- Cosmic acceleration without fine tuning or dark energy
• Observational Constraints in Nonlocal Gravity: the Deser-Woodard Case
• Primordial bouncing cosmology in the Deser-Woodard nonlocal gravity
• De Sitter and Power-law Solutions in Non-local Gauss-Bonnet Gravity
• Addressing Cosmological Tensions by Non-Local Gravity
• Testing non-local gravity by clusters of galaxies
• Newtonian approximation and possible time-varying $G$ in nonlocal gravities
• Black hole quasinormal modes and isospectrality in Deser-Woodard nonlocal gravity
• Structure Formation in Nonlocal MOND
• Scalar-tensor nonlocal gravity
• Do the Spirits Rise?
• Galaxy rotation curves in the $\mu$-deformation based approach to dark matter
• Hamiltonian Formalism for Nonlocal Gravity Models
• Modified Gravity and Dark Energy models Beyond $w(z)$CDM Testable by LSST
• Does nonlocal gravity yield divergent gravitational energy-momentum fluxes?
• Late-times asymptotic equation of state for a class of nonlocal theories of gravity
• The Case for Nonlocal Modifications of Gravity
• Reconstruction Procedure for Nonlocal Gauss-Bonnet Models
• Accelerated expansion as manifestation of gravity: when Dark Energy belongs to the left