Modified Gravity

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Ever since it has been established in the 1930s that Newton's or Einstein's theory cannot account for the orbital velocities stars in the outer regions of a spiral galaxy, there has been an interest in modifying gravity theory.

If successful, a modified gravity theory would do away with the need for dark matter. Instead, the anomalous velocities of stars far from a galactic center would be accounted for by a deviation from Newton's or Einstein's predictions at large distances.

A successful modified gravity theory has to clear many hurdles, among them:

Yes, Einstein had it easy a hundred years ago. Today, with all the observational data at hand, the bar is set much higher. Why, we might ask, would one even bother with a modified gravity theory then, if the standard model of cosmology works so well? Simple: in the standard model, 96% of the universe is invisible, undetectable, or both. Surely that is a good enough reason.

Without further ado, there is a modified gravity theory that successfully meets these challenges (at least as far as we know.) It is called MOG, and it grew out of research by Moffat into nonsymmetric gravitational theory. MOG is a field theory. Its basic postulate is a field theory Lagrangian that, in addition to the standard Einstein-Hilbert term, incorporates a massive vector field. This massive vector field results in a repulsive gravitational force that cancels out gravity at short range. In other words, rather than making gravity stronger at large distances, MOG does the opposite: it assumes that gravity was stronger all along, but at shorter distances (galactic, subgalactic, or smaller scales) much of that strength is canceled out by the repulsive force.

The mass of the MOG vector field and its strength are governed by two constants. In MOG, these two constants, as well as Newton's gravitational constant G are running; they are promoted to scalar fields. Thus the full MOG Lagrangian consists of the Einstein-Hilbert tensor term describing ordinary gravity; the massive vector term describing the repulsive force; three massless scalar fields; and potentials associated with the vector field and the three scalar fields. (For this reason, MOG has also been known by the acronym STVG, which stands for Scalar-Tensor-Vector Gravity theory.)

The result is a theory that is in good agreement with observation at scales ranging from the laboratory all the way to cosmology. In the solar system, and up to the scale of star clusters, MOG predicts no observable deviation from Einstein gravity. On the scale of galaxies, MOG correctly predicts the Tully Fisher law of galaxy rotation curves. On even larger scales, MOG is consistent with the lensing and mass distribution of galaxy clusters. MOG is fitted to the precision acoustic power spectrum of the cosmic microwave background, it is consistent with the luminosity-distance relationship of Type Ia supernovae, and it correctly reproduces the matter power spectrum of galaxy distributions. The latter provides an especially notable possible test of the theory: at soon-to-be-achieved data resolutions, the presence or absence of baryonic oscillations in the matter power spectrum can once and for all determine whether or not collisionless dark matter dominates the universe.

MOG and its physical consequences are worked out in a series of papers by Moffat and others, dating back to 1979. Some of the more important and current papers are: