Cosmology of the Galileon extension of Bekenstein's theory of relativistic modified Newtonian dynamics

A generalization of Bekenstein's Tensor-Vector-Scalar (TeVeS) model of modified gravity has recently been proposed as an alternative to dark matter. This model-which we will refer to as g-TeVeS-utilizes a Galileon-induced Vainshtein mechanism to suppress modifications to General Relativity in strong gravity regimes and so avoids the need to introduce the baroque kinetic terms that typically exist in relativistic models of modified Newtonian dynamics (MOND). We explore the behavior of this model in spacetimes with exact Friedmann-Robertson-Walker (FRW) symmetry. The ability of the theory to recover MOND phenomenology places restrictions on the theory's parameter space and it is found that within an estimate of this area of parameter space the theory cannot successfully approximate the Friedmannian cosmological behavior of cold dark matter. It is found that much closer agreement may be recovered in other regions of the theory's parameter space and the reasons for this are discussed.