Modifying gravity with the aether: An alternative to dark matter

Abstract

There is evidence that Newton and Einstein's theories of gravity cannot explain the dynamics of a universe made up solely of baryons and radiation. To be able to understand the properties of galaxies, clusters of galaxies and the universe on the whole it has become commonplace to invoke the presence of dark matter. An alternative approach is to modify the gravitational field equations to accommodate observations. We propose a new class of gravitational theories in which we add a new degree of freedom, the Aether, in the form of a vector field that is coupled covariantly, but non-minimally, with the space-time metric. We explore the Newtonian and non-Newtonian limits, discuss the conditions for these theories to be consistent and explore their effect on cosmology.

THINGS about MOND

“…Recent theoretical developments have also added plausibility to the case for MOND through the work of, e.g., Bekenstein (2004), Sanders (2005), Zlosnik et al (2007), Halle et al (2008), and Blanchet & Le Tiec (2008), who have all presented Lorentz-covariant theories yielding a MOND behaviour in the weak field limit. Although still fine-tuned and far from a fundamental theory explaining the MOND paradigm, these effective theories remarkably allow for new predictions regarding cosmology (e.g., Skordis et al 2006) and gravitational lensing (e.g., Angus et al 2007;Shan et al 2008).…”

Modifying gravity: you cannot always get what you want

“…(TeVeS is formally equivalent to a theory with an extended K, and a more exotic method of achieving a non-vanishing background value for A.) More details can be found in an earlier study [47]. TeVeS and GEA possess important advantages over MOND alone.…”

“…This enabled them [47] to broaden the class of covariant-modified gravity models that have properties similar to TeVeS: appropriate non-relativistic MOND (and Newtonian limits). They all share the existence of a time-like vector field A a , a so-called Einstein-Aether, and hence are referred to as generalized Einstein-Aether (GEA) theories.…”

“…A subclass of these models are the so-called GEA theories [47] that start with a covariant action and recover MOND (in its modified Poisson equation form) in the appropriate limits. In its simplest form, GEA contains a vector field, A, coupled to Einstein-Hilbert gravity but not to matter,…”

Reining in Alternative Gravity

“…with c i constants) and F ðxÞ is an arbitrary function (we have not included the "c 4 " term as it does not affect tensor modes) [46,47]. In this model α T ¼ −ðc 1 þ c 3 ÞF ;K =½1 þ ðc 1 þ c 3 ÞF ;K , so the constraint on α T implies c 1 ¼ −c 3 .…”