A Modified Scalar-Tensor-Vector Gravity Theory and the Constraint on its Parameters

Abstract

A gravity theory called scalar-tensor-vector gravity (STVG) has been recently developed and succeeded in solar system, astrophysical and cosmological scales without dark matter [J. W. Moffat, J. Cosmol. Astropart. Phys. 03, 004 (2006)]. However, two assumptions have been used: (i) $B(r)=A^{-1}(r)$, where $B(r)$ and $A(r)$ are $g_{00}$ and $g_{rr}$ in the Schwarzschild coordinates (static and spherically symmetric); (ii) scalar field $G=Const.$ in the solar system. These two assumptions actually imply that the standard parametrized post-Newtonian parameter $\gamma =1$. In this paper, we relax these two assumptions and study STVG further by using the post-Newtonian (PN) approximation approach. With abandoning the assumptions, we find $\gamma \ne 1$ in general cases of STVG. Then, a version of modified STVG (MSTVG) is proposed through introducing a coupling function of scalar field G: $\theta (G)$. We have derived the metric and equations of motion (EOM) in 1PN for general matter without specific equation of state and $N$ point masses firstly. Subsequently, the secular periastron precession $\dot{\omega }$ of binary pulsars in harmonic coordinates is given. After discussing two PPN parameters ($\gamma$ and $\beta$) and two Yukawa parameters ($\alpha$ and $\lambda$), we use $\dot{\omega }$ of four binary pulsars data (PSR B1913+16, PSR B1534+12, PSR J0737-3039 and PSR B2127+11C) to constrain the Yukawa parameters for MSTVG: $\lambda =(3.97\pm 0.01)\times 10^8$m and $\alpha =(2.40\pm 0.02)\times 10^{-8}$ if we fix $|2\gamma -\beta -1|=0$.

39 pages, 4 figures, accepted by PRD

References in corpus (32)

• The Confrontation between General Relativity and Experiment
• Relativistic gravitation theory for the MOND paradigm
• The fundamental constants and their variation: observational status and theoretical motivations
• Tests of general relativity from timing the double pulsar
• An increased estimate of the merger rate of double neutron stars from observations of a highly relativistic system
• Gravity with a dynamical preferred frame
• Tests of the Gravitational Inverse-Square Law
• Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects
• Binary and Millisecond Pulsars
• Study of the anomalous acceleration of Pioneer 10 and 11
• Scalar-Tensor-Vector Gravity Theory
• Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration
• Einstein-Aether Waves
• Galaxy Rotation Curves Without Non-Baryonic Dark Matter
• Testing gravity to second post-Newtonian order: a field-theory approach
• Studies of the Relativistic Binary Pulsar PSR B1534+12: I. Timing Analysis
• Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order
• The Bullet Cluster 1E0657-558 evidence shows Modified Gravity in the absence of Dark Matter
• Galaxy Cluster Masses Without Non-Baryonic Dark Matter
• Testing modified gravity with globular cluster velocity dispersions
• Parametrized Post-Newtonian Theory of Reference Frames, Multipolar Expansions and Equations of Motion in the N-body Problem
• Constraint on the Post-Newtonian Parameter gamma on Galactic Size Scales
• Gravitational solution to the Pioneer 10/11 anomaly
• Limits on deviations from the inverse-square law on megaparsec scales
• Using Pulsars to Detect Massive Black Hole Binaries via Gravitational Radiation: Sagittarius A* and Nearby Galaxies
• Testing the Newton law at long distances
• A Tighter Test of Local Lorentz Invariance using PSR J2317+1439
• First preliminary tests of the general relativistic gravitomagnetic field of the Sun and new constraints on a Yukawa-like fifth force from planetary data
• Constraints on the range lambda of Yukawa-like modifications to the Newtonian inverse-square law of gravitation from Solar System planetary motions
• Second post-Newtonian approximation of Einstein-aether theory
• Post-Newtonian parameters in the tensor-vector-scalar theory
• Constraint on intermediate-range gravity from earth-satellite and lunar orbiter measurements, and lunar laser ranging

Cited by in corpus (16)

• Particle Dynamics Near Kerr-MOG Black Hole
• On the (im)possibility of testing new physics in exoplanets using transit timing variations: deviation from inverse-square law of gravity
• Dark energy interactions near the galactic centre
• Testing scalar-tensor theories and PPN parameters in Earth orbit
• Testing modified gravity via Yukawa potential in two body problem: Analytical solution and observational constraints
• Post-Newtonian limitations on measurement of the PPN parameters caused by motion of gravitating bodies
• Yukawa effects on the clock onboard a drag-free satellite
• Chaos in a Magnetized Modified Gravity Schwarzschild Spacetime
• Testing Lorentz violation with binary pulsars: constraints on standard model extension
• Comparison of light-time formulations in the post-Newtonian framework for the BepiColombo MORE experiment
• Dynamical system approach to scalar-vector-tensor cosmology
• Modified Jordan-Brans-Dicke theory with scalar current and the Eddington-Robertson gamma-parameter
• Dark Energy as a Critical Period in Binary Motion: Bounds from Multi-scale Binaries
• Exact cosmological black hole solutions in Scalar Tensor Vector Gravity
• Leading-order gravitational time delay of massive particles by a moving Schwarzschild lens
• Relativistic Thermal Emission from Accretion Disks in Kerr-MOG Spacetimes