FRW cosmology in Milgrom's bimetric theory of gravity

We consider spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) solutions of Milgrom's recently proposed class of bimetric theories of gravity. These theories have two different regimes, corresponding to high and low acceleration. We find simple power-law matter dominated solutions in both, as well as solutions with spatial curvature, and exponentially expanding solutions. In the high acceleration limit these solutions behave like the FRW solutions of General Relativity, with a cosmological constant term that is of the correct order of magnitude to explain the observed accelerating expansion of the Universe. We find that solutions that remain in the high acceleration regime for their entire history, however, require non-baryonic dark matter fields, or extra interaction terms in their gravitational Lagrangian, in order to be observationally viable. The low acceleration regime also provides some scope to account for this deficit, with solutions that differ considerably from their general relativistic counterparts.Comment: 12 page

Exploring Cartan gravity with dynamical symmetry breaking

24 pags.; 2 figs.; 3 app. PACS number: 04.50.+hIt has been known for some time that General Relativity can be regarded as a Yang-Mills-type gauge theory in a symmetry broken phase. In this picture the gravity sector is described by an SO(1, 4) or SO(2, 3) gauge field and Higgs field Va which acts to break the symmetry down to that of the Lorentz group SO(1, 3). This symmetry breaking mirrors that of electroweak theory. However, a notable difference is that while the Higgs field Φ of electroweak theory is taken as a genuine dynamical field satisfying a Klein-Gordon equation, the gauge independent norm V2 ≡ ηabV aVb of the Higgs-type field Va is typically regarded as non-dynamical. Instead, in many treatments Va does not appear explicitly in the formalism or is required to satisfy V2 = const. ≠ 0 by means of a Lagrangian constraint. As an alternative to this we propose a class of polynomial actions that treat both the gauge connection and Higgs field Va as genuine dynamical fields with no ad hoc constraints imposed. The resultant equations of motion consist of a set of first-order partial differential equations. We show that for certain actions these equations may be cast in a second-order form, corresponding to a scalar-tensor model of gravity. One simple choice leads to the extensively studied Peebles-Ratra rolling quintessence model. Another choice yields a scalar-tensor symmetry broken phase of the theory with positive cosmological constant and an effective mass M of the gravitational Higgs field ensuring the constancy of V2 at low energies and agreement with empirical data if M is sufficiently large. More general cases are discussed corresponding to variants of Chern-Simons modified gravity and scalar-Euler form gravity, each of which yield propagating torsion. © 2014 IOP Publishing Ltd.HW was supported by the Spanish MICINN/MINECO Project FIS2011-29287, the CAM research consortium QUITEMAD S2009/ESP-1594, and the CSIC JAE-DOC 2011 program. TZ was supported by STFC grant ST/J000353/1.Peer Reviewe

The Geometry Of Modified Newtonian Dynamics

Modified Newtonian Dynamics is an empirical modification to Poisson's equation which has had success in accounting for the `gravitational field' $\Phi$ in a variety of astrophysical systems. The field $\Phi$ may be interpreted in terms of the weak field limit of a variety of spacetime geometries. Here we consider three of these geometries in a more comprehensive manner and look at the effect on timelike and null geodesics. In particular we consider the Aquadratic Lagrangian (AQUAL) theory, Tensor-Vector-Scalar (TeVeS) theory and Generalized Einstein-{\AE}ther (GEA) theory. We uncover a number of novel features, some of which are specific to the theory considered while others are generic. In the case of AQUAL and TeVeS theories, the spacetime exhibits an excess (AQUAL) or deficit (TeVeS) solid angle akin to the case of a Barriola-Vilenkin global monopole. In the case of GEA, a disformal symmetry of the action emerges in the limit of \grad\Phi\rightarrow 0. Finally, in all theories studied, massive particles can never reach spatial infinity while photons can do so only after experiencing infinite redshift.Comment: 18 page