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

Abstract

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 Galileoninduced 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. A. IntroductionMilgrom's observation [1] that a wide variety of the astrophysical phenomena usually attributed to the effects of dark matter can instead be accounted for by a modification to the dynamics of visible matter has provided an intriguing hint that something may be missing in our understanding of gravity and/or inertia. In its original formulation, Milgrom's Modified Newtonian Dynamics (MOND) was non-relativistic in the same sense that Newton's theory of gravity is. If Newtonian gravity is a limiting form of General Relativity, what is MOND a limiting form of? One formulation of MOND is as a modified Poisson equation:where Φ is the gravitational potential felt by non-relativistic test particles, x = | ∇Φ|/a 0 , ρ b is the density of baryonic matter, G N is the locally measured value of Newton's gravitational constant, a 0 is a constant with the dimensions of acceleration and µ m (x) is a function subject to the limiting forms µ m → 1 as x 1 and µ m → x as x 1 but is otherwise unspecified; an explicit form such as µ m (x) = x/(1 + x) has usually been chosen but such forms lack theoretical motivation 1 .A significant amount of research has gone into studying the consequences of (1) in astrophysical systems [5][6][7][8][9][10][11][12][13][14][15][16]; however, the lack of a fully-relativistic formulation of the theory makes it difficult to know the realm of the equation's validity. It was also attempted to derive the MOND formula from fundamental theory [17]. A number of relativistic theories that recover MOND-like phenomenology have been proposed [18][19][20][21][22][23][24][25][26][27][28]. All of these examples possess a similar ambiguity to (1) in that all possess a function in the Lagrangian that must be chosen by hand. This makes it difficult to know exactly what a given theory predicts. Each of the examples involve the introduction of new degrees of freedom into physics and it can be that the line between their interpretation as an additional 'dark force' in nature or simply a type of dark matter becomes blurred. Indeed, ...

Parity violating Friedmann universes

“…Similar 'catastrophic complexification' of fields has also been observed in other modified theories of gravity[25].…”

“…From the definition of torsion we see that this degree of freedom in both quantities is the same. This degree of freedom propagates to the curvature (a set of 2-forms dependent on 2 tetrad indices) in the form of the Weyl tensor components (24) and (25). It is absent in the metric, and also in the matter content, since the stressenergy τ a forms a set of 3-forms with a single tetrad index.…”

“…We notice that indeed they have non-vanishing Weyl tensor, even though they are homogeneous and isotropic (but not parity invariant). From (24) and (25) we see that W ij = 0 for these solutions, but W 01 = 0. Because the Weyl tensor is non-zero, Einstein's equations in vacuum no longer reduce to Eq.…”

Testing general relativity in cosmology

“…Also, the theory has been combined with a Galilean scalar field (Babichev et al. 2011 ), although with some continuing but less stringent challenges (Złośnik and Skordis 2017 ).…”

Gravitational alternatives to dark matter with tensor mode speed equaling the speed of light

“…Due to the algebraic relation between the two metrics, there is only one tensor mode propagating gravitational wave perturbation (2 polarizations) in this theory just as in GR. The cosmology of TeVeS theory has been extensively investigated in [37][38][39][40]. The speed of the tensor mode GW in TeVeS theory is in general different than the speed of light, and it is then natural to ask what is the status of the TeVeS paradigm after GW170817.…”