Scalar–tensor–vector gravity (STVG) is a modified theory of gravity developed by John Moffat, a researcher at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario. The theory is also often referred to by the acronym MOG (MOdified Gravity).
Contents
Overview
Scalar–tensor–vector gravity theory, also known as MOdified Gravity (MOG), is based on an action principle and postulates the existence of a vector field, while elevating the three constants of the theory to scalar fields. In the weak-field approximation, STVG produces a Yukawa-like modification of the gravitational force due to a point source. Intuitively, this result can be described as follows: far from a source gravity is stronger than the Newtonian prediction, but at shorter distances, it is counteracted by a repulsive fifth force due to the vector field.
STVG has been used successfully to explain galaxy rotation curves, the mass profiles of galaxy clusters, gravitational lensing in the Bullet Cluster, and cosmological observations without the need for dark matter. On a smaller scale, in the Solar System, STVG predicts no observable deviation from general relativity. The theory may also offer an explanation for the origin of inertia.
Mathematical details
STVG is formulated using the action principle. In the following discussion, a metric signature of
We begin with the Einstein-Hilbert Lagrangian:
where
We introduce the Maxwell-Proca Lagrangian for the STVG vector field
where
The three constants of the theory,
where
The STVG action integral takes the form
where
Spherically symmetric, static vacuum solution
The field equations of STVG can be developed from the action integral using the variational principle. First a test particle Lagrangian is postulated in the form
where
where
where
where
Observations
STVG/MOG has been applied successfully to a range of astronomical, astrophysical, and cosmological phenomena.
On the scale of the Solar System, the theory predicts no deviation from the results of Newton and Einstein. This is also true for star clusters containing no more than a maximum of a few million solar masses.
The theory accounts for the rotation curves of spiral galaxies, correctly reproducing the Tully-Fisher law.
STVG is in good agreement with the mass profiles of galaxy clusters.
STVG can also account for key cosmological observations, including: