Post-Newtonian parameters in the tensor-vector-scalar theory

Abstract

We investigate post-Newtonian parameters in the tensor-vector-scalar (TeVeS) theory in a general setting while previous researches have been restricted to spherically symmetric cases. Based on the assumption that both the physical and Einstein metrics have Minkowski metric at the zeroth order, we show γ = 1 as in the previous researches. We find two remarkable things for other parameters. The first is the value β = 1 while it has been reported that β = 1 for the case when the vector field is not purely timelike. This discrepancy occurs from the above assumption which is natural as a starting point. The second is the result that the Newtonian potential must be static to be consistent with the vector equation. As a result, we cannot determine α1 and α2. We consider that it is related to the instability against linear perturbation and occurrence of caustic singularities for various initial perturbations which have been reported recently.

Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions

“…Although the above constraints on classical MOND models are useful guides, proper constraints can thus only truly be set on the various relativistic theories presented in Sect. 7, the first order constraints on these theories coming from their own post-newtonian parameters [66,100,174,373,391,451]. What is more, and makes all these tests perhaps unnecessary, it has recently been shown that it was possible to cancel any deviation from General Relativity at small distances in most of these relativistic theories, independently of the form of the µ-function [22].…”

“…The relations between this free function and Milgrom's µ can be found in [146,432] (see also Sect. 6.2), 49 Expressed in terms of Uµ and its congugate momenta P µ = ∂L/∂Uµ the detailed structure of null and timelike geodesics of the theory in [432], the analysis of the parametrized post-Newtonian coefficients (including the preferred-frame parameters quantifying the local breaking of Lorentz invariance) in [174,373,391,451], solutions for black holes and neutron stars in [245,246,248,247,375,439,440], and gravitational waves in [217,215,216,374]. It is important to remember that TeVeS is not equivalent to GR in the strong regime, which is why it can be tested there, e.g.…”

Interacting New Generalized Chaplygin Gas

“…In recent years, such options are carefully investigated in literature. Alternative gravity theories based on the modification of Einstein-Hilbert action include f (R) gravity [14][15][16][17], scalar-tensor gravity [18][19][20] and Lovelock gravity [21,22], to name a few. Similarly there are models in which only the matter term is modified, examples are Cardassian model [23][24][25], the bulk viscous stress [26][27][28] and the anisotropic stress [29].…”

Scalars, vectors and tensors from metric-affine gravity

“…Various astrophysical and cosmological phenomena exhibit observable signatures of TeVeS [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. TeVeS is essentially a bi-metrical gravitational theory where matter and gravity are distinguished by the metric fields they operate with.…”