The solar system test for the general modified gravity theories

Abstract

In the past few decades, various versions of modified gravity theories were proposed to mimic the effect of dark matter. Compared with the conventional Newtonian or relativistic dynamics, these theories contain some extra apparent force terms in the dynamical equations to replace the role of dark matter. Generally speaking, the extra apparent force terms usually scale with radius so that the effect would be significant only on large scale to explain the missing mass in galaxies or galaxy clusters. Nevertheless, the apparent effect may still be observable in small structures like the solar system. In this article, we derive analytic general formulae to represent the contribution of the precession angle of the planets in the solar system due to the general modified gravity theories, in which the extra apparent force terms can be written in a power law of radius $r$ or an exponential function in $r$. We have tested three popular modified gravity theories, the Modified Newtonian Dynamics (MOND), the Emergent Gravity (EG), and the Modified Gravity (MOG). In particular, based on the solar system data, we have constrained the parameters involved for two popular general interpolating functions used in MOND. Our results can be generally applied to both of the modified inertia and modified gravity versions of MOND.

arXiv commentAccepted in MNRAS

References in corpus (51)

• On the Origin of Gravity and the Laws of Newton
• Dark Matter Search Results from a One Tonne$\times$Year Exposure of XENON1T
• Searching for Dark Matter Annihilation from Milky Way Dwarf Spheroidal Galaxies with Six Years of Fermi-LAT Data
• Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions
• Modified Newtonian Dynamics as an Alternative to Dark Matter
• The Radial Acceleration Relation in Rotationally Supported Galaxies
• Emergent Gravity and the Dark Universe
• A New Era in the Quest for Dark Matter
• Dark Matter Benchmark Models for Early LHC Run-2 Searches: Report of the ATLAS/CMS Dark Matter Forum
• One Law To Rule Them All: The Radial Acceleration Relation of Galaxies
• Modified Newtonian Dynamics in the Milky Way
• The MOG weak field approximation and observational test of galaxy rotation curves
• Fitting the radial acceleration relation to individual SPARC galaxies
• Improved dark matter search results from PICO-2L Run 2
• Milky Way Mass Models and MOND
• Confrontation of MOND with the rotation curves of early-type disc galaxies
• Testing modified gravity with globular cluster velocity dispersions
• The MOND limit from space-time scale invariance
• Gravitational waves in Einstein-æther and generalized TeVeS theory after GW170817
• MOND effects in the inner solar system
• Combined Solar System and rotation curve constraints on MOND
• Absence of a fundamental acceleration scale in galaxies
• Solar system constraints on multi-field theories of modified dynamics
• Semi-Analytical Models for the Formation of Disk Galaxies II. Dark Matter versus Modified Newtonian Dynamics
• Predictions and Outcomes for the Dynamics of Rotating Galaxies
• External field effect of modified Newtonian dynamics in the Solar system
• Nonlocal Modification of Newtonian Gravity
• The Weak Lensing Radial Acceleration Relation: Constraining Modified Gravity and Cold Dark Matter theories with KiDS-1000
• Universal MOND relation between the baryonic and `dynamical' central surface densities of disc galaxies
• A general class of gravitational theories as alternatives to dark matter where the speed of gravity always equals the speed of light
• Equilibrium configurations of 11eV sterile neutrinos in MONDian galaxy clusters
• Azimuthally Symmetric Theory of Gravitation (I)
• NIHAO XVIII: Origin of the MOND phenomenology of galactic rotation curves in a LCDM universe
• The radial acceleration relation in galaxy clusters
• Modified Gravity (MOG) fits to observed radial acceleration of SPARC galaxies
• Models of modified-inertia formulation of MOND
• On the Presence of a Universal Acceleration Scale in Elliptical Galaxies
• On the universality of MOG weak field approximation at galaxy cluster scale
• Testing Verlinde's emergent gravity in early-type galaxies
• Emergent gravity in galaxies and in the Solar System
• Testing MOdified Gravity (MOG) theory and dark matter model in Milky Way using the local observables
• Testing Emergent Gravity on Galaxy Cluster Scales
• Constraining annihilating dark matter mass by the radio continuum spectral data of NGC4214 galaxy
• Applying Modified Gravity (MOG) to the Lensing and Einstein Ring in Abell 3827
• There is no universal acceleration scale in galaxies
• The 1/c expansion of nonminimally coupled curvature-matter gravity model and constraints from planetary precession
• Modeling Nearly Spherical Pure-Bulge Galaxies with a Stellar Mass-to-Light Ratio Gradient under the $\Lambda$CDM and MOND Paradigms: II. The Orbital Anisotropy of Slow Rotators within the Effective Radius
• Constraints on annihilating dark matter in the Omega Centauri cluster
• Putting Yukawa-like Modified Gravity (MOG) on the test in the Solar System
• Constraining dark matter-nucleon scattering cross section by the background electron anti-neutrino flux data
• The analytic radial acceleration relation for galaxy clusters

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