Nonlocal Metric Realizations of MOND

Abstract

I discuss relativistic extensions of MOND in which the metric couples normally to matter. I argue that MOND might be a residual effect from the vacuum polarization of infrared gravitons produced during primordial inflation. If so, MOND corrections to the gravitational field equations would be nonlocal. Nonocality also results when one constructs metric field equations which reproduce the Tully-Fisher relation, along with sufficient weak lensing. I give the full field equations for the simplest class of models, and I specialize these equations to the geometries relevant for cosmology. I conclude by sketching the direction of future studies.

arXiv comment23 pages, no figures, uses LaTeX2e, written for a special issue of the Canadian Journal of Physics devoted to MOND

References in corpus (87)

• Planck 2013 results. XVI. Cosmological parameters
• Modified Gravity and Cosmology
• A direct empirical proof of the existence of dark matter
• Relativistic gravitation theory for the MOND paradigm
• Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• Modified Newtonian Dynamics as an Alternative to Dark Matter
• Scalar-Tensor-Vector Gravity Theory
• The Baryonic Tully-Fisher Relation of Galaxies with Extended Rotation Curves and the Stellar Mass of Rotating Galaxies
• Bouncing Universes in String-inspired Gravity
• Nonlocal Cosmology
• Modifying gravity with the Aether: an alternative to Dark Matter
• Large Scale Structure in Bekenstein's theory of relativistic Modified Newtonian Dynamics
• Modified non-local-F(R) gravity as the key for the inflation and dark energy
• Quantum Gravity Slows Inflation
• Stochastic Quantum Gravitational Inflation
• Bimetric MOND gravity
• Cosmological perturbations and structure formation in nonlocal infrared modifications of general relativity
• Non-local gravity and dark energy
• The MOG weak field approximation and observational test of galaxy rotation curves
• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• Stochastic Inflationary Scalar Electrodynamics
• Nonlocal action for long-distance modifications of gravity theory
• Leading Log Solution for Inflationary Yukawa
• Generalized ghost-free quadratic curvature gravity
• Accelerating cosmologies from non-local higher-derivative gravity
• The MOG Weak Field approximation II. Observational test of Chandra X-ray Clusters
• One Loop Vaccum Polarization in a Locally de Sitter Background
• Can Cosmic Structure form without Dark Matter?
• Reconstructing the Distortion Function for Nonlocal Cosmology
• Nonlocal Gravity Simulates Dark Matter
• The Fermion Self-Energy during Inflation
• Nonlocal Models of Cosmic Acceleration
• A Nonlocal Metric Formulation of MOND
• A formal framework for a nonlocal generalization of Einstein's theory of gravitation
• Non-local quantum effects in cosmology 1: Quantum memory, non-local FLRW equations and singularity avoidance
• The MOND limit from space-time scale invariance
• Problems for MOND in Clusters and the Ly-alpha Forest
• Reply to `Can infrared gravitons screen $\Lambda$?'
• Effective Nonlocal Euclidean Gravity
• Observational Viability and Stability of Nonlocal Cosmology
• Gravitons Enhance Fermions during Inflation
• Vector field models of modified gravity and the dark sector
• Nonlocal Effective Gravitational Field Equations and the Running of Newton's G
• Nonlocal metric formulations of MOND with sufficient lensing
• Dark energy and dark matter from nonlocal ghost-free gravity theory
• Screening of cosmological constant in non-local gravity
• Serendipitous discoveries in nonlocal gravity theory
• Non-Perturbative Models For The Quantum Gravitational Back-Reaction On Inflation
• Can infrared gravitons screen $\Lambda$?
• Vacuum polarization and photon mass in inflation
• How Cold Dark Matter Theory Explains Milgrom's Law
• Screening of cosmological constant in non-local cosmology
• Structure formation in a nonlocally modified gravity model
• De Sitter Universe in Nonlocal Gravity
• Nonlocal Modification of Newtonian Gravity
• Fading Gravity and Self-Inflation
• A Simple Operator Check of the Effective Fermion Mode Function during Inflation
• Apparent ghosts and spurious degrees of freedom in non-local theories
• Nonlocal Gravity and Structure in the Universe
• Cosmological fluctuation growth in bimetric MOND
• A generic problem with purely metric formulations of MOND
• Cosmological significance of one-loop effective gravity
• Field equations and cosmology for a class of nonlocal metric models of MOND
• Screening of cosmological constant for De Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities
• A Generic Test of Modified Gravity Models which Emulate Dark Matter
• Do Newton's G and Milgrom's a_0 vary with cosmological epoch ?
• A few cosmological implications of tensor nonlocalities
• Non-linear sigma model in de Sitter space
• A Phenomenological Model for the Early Universe
• A Gravitational Mechanism for Cosmological Screening
• Infra-red effects of Non-linear sigma model in de Sitter space
• Gravity Gets There First with Dark Matter Emulators
• Running of Newton's constant and non integer powers of the d'Alembertian
• New representation of the nonlocal ghost-free gravity theory
• Can a non-local model of gravity reproduce Dark Matter effects in agreement with MOND?
• Gravitational waves in bimetric MOND
• Applying MOG to lensing: Einstein rings, Abell 520 and the Bullet Cluster
• A Decisive test to confirm or rule out the existence of dark matter emulators using gravitational wave observations
• Post-Inflationary Evolution via Gravitation
• Quantum Gravity and Inflation
• One Loop Field Strengths of Charges and Dipoles on a Locally de Sitter Background
• FRW cosmology in Milgrom's bimetric theory of gravity
• A useful guide for gravitational wave observers to test modified gravity models
• The Volume of the Past Light-Cone and the Paneitz Operator
• Cosmological extrapolation of MOND
• From dark matter to MOND

Cited by in corpus (20)

• A new relativistic theory for Modified Newtonian Dynamics
• A general class of gravitational theories as alternatives to dark matter where the speed of gravity always equals the speed of light
• MOND as a regime of quantum gravity
• Galactic dynamics and long-range quantum gravity
• Revival of the Deser-Woodard nonlocal gravity model: Comparison of the original nonlocal form and a localized formulation
• Determining Cosmology for a Nonlocal Realization of MOND
• Aether scalar tensor theory: Linear stability on Minkowski space
• Primordial bouncing cosmology in the Deser-Woodard nonlocal gravity
• Dynamical system analysis of cosmological evolution in the Aether scalar tensor theory
• Relativistic Khronon Theory in agreement with Modified Newtonian Dynamics and Large-Scale Cosmology
• Cosmology of the Galileon extension of Bekenstein's theory of relativistic Modified Newtonian Dynamics
• Structure Formation in Nonlocal MOND
• Aether scalar tensor theory: Hamiltonian Formalism
• Coincident Massless, Minimally Coupled Scalar Correlators on General Cosmological Backgrounds
• Electrovacuum solutions in non-local gravity
• Quantum Cosmology in Four Dimensions
• Sudden cosmological singularities in Aether scalar-tensor theories
• The Case for Nonlocal Modifications of Gravity
• Is MOND necessarily nonlinear?
• A test of MOND and Emergent Gravity with SMACS J0723.3-7327 using eROSITA observations