Bimetric gravity and “dark matter”

Abstract

We present a bimetric theory of gravity containing a length scale of galactic size. For distances less than this scale the theory satisfies the standard tests of general relativity. For distances greater than this scale the theory yields an effective gravitational constant much larger than the locally observed value of Newton's constant. The transition from one regime to the other through the galactic scale can explain the observed rotation curves of galaxies and hence the effects normally attributed to the presence of dark matter. Phenomena on an extragalactic scale such as galactic clusters and the expansion of the universe are controlled by the enhanced gravitational coupling. This provides an explanation of the missing matter normally invoked to account for the observed value of Hubble's constant in relation to observed matter.

Geometry of manifolds with area metric: Multi-metric backgrounds

“…Existing proposals for modifications of general relativity, such as bimetric [11,12,13,14] and non-symmetric [21,22] theories of gravity, but also generalized string geometries including the antisymmetric Neveu-Schwarz two form [2,3,4], may be fruitfully reinterpreted from the point of view of area metric geometry. Rather than the individual metrics or two-forms in such approaches, it is then only the induced area metric that carries physical significance.…”

“…There might be a number of further potential applications of area geometry in connection to other ideas of recent interest, such as bimetric gravity theories [11,12,13,14] or Regge triangulations of spacetime with area variables [15,16,17]. We will present some more speculation in that direction in our conclusion.…”

Quantum field theory in a multimetric background

“…This metric provides a lightcone structure that determines causal relationships between events in the manifold. Modified gravity theories involving more than one metric have been proposed as potential explanations of dark matter and dark energy effects in cosmology [1,2,3,4]. They are also relevant to models of massive gravity [5,6].…”

A scalar-tensor cosmological model with dynamical light velocity

“…It is the combination of the gravitational metric and the biscalar field that we consider as being the gravitational fields of our theory. This type of model has attracted some interest in the field [7,8,9], and similar models that introduce the prior-geometric structure in a different way have also appeared [10,11]. Since a varying light velocity (in 3+1 spacetime) is a fairly generic feature of higher-dimensional models [12,13,14], they are also of interest as effective or toy models that may result from such a theory.…”