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Register a new userGravitational waves in Einstein-{ae}ther and generalized TeVeS theory after GW170817
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In this work, we discuss the polarization contents of Einstein-ae ther theory and the generalized tensor-vector-scalar (TeVeS) theory, as both theories have a normalized timelike vector field. We derive the linearized equations of motion around the flat spacetime background using the gauge-invariant variables to easily separate physical degrees of freedom. We find the plane wave solutions are then found, and identify the polarizations by examining the geodesic deviation equations. We find that there are five polarizations in Einstein-ae ther theory and six polarizations in the generalized TeVeS theory. In particular, the transverse breathing mode is mixed with the pure longitudinal mode. We also discuss the experimental tests of the extra polarizations in Einstein-ae ther theory using pulsar timing arrays combined with the gravitational-wave speed bound derived from the observations on GW 170817 and GRB 170817A. It turns out that it might be difficult to use pulsar timing arrays to distinguish different polarizations in Einstein-ae ther theory. The same speed bound also forces one of the propagating modes in the generalized TeVeS theory to travel much faster than the speed of light. Since the strong coupling problem does not exist in some parameter subspaces, the generalized TeVeS theory is excluded in these parameter subspaces.
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The timing of millisecond pulsars has long been used as an exquisitely precise tool for testing the building blocks of general relativity, including the strong equivalence principle and Lorentz symmetry. Observations of binary systems involving at least one millisecond pulsar have been used to place bounds on the parameters of Einstein-{ae}ther theory, a gravitational theory that violates Lorentz symmetry at low energies via a preferred and dynamical time threading of the spacetime manifold. However, these studies did not cover the region of parameter space that is still viable after the recent bounds on the speed of gravitational waves from GW170817/GRB170817A. The restricted coverage was due to limitations in the methods used to compute the pulsar sensitivities, which parameterize violations of the strong-equivalence principle in these systems. We extend here the calculation of pulsar sensitivities to the parameter space of Einstein-{ae}ther theory that remains viable after GW170817/GRB170817A. We show that observations of the damping of the period of quasi-circular binary pulsars and of the triple system PSR J0337+1715 further constrain the viable parameter space by about an order of magnitude over previous constraints.
We present the solution space of the field equations in the Einstein-ae ther theory for the case of a $FLRW$ and a LRS Bianchi Type $III$ space-time. We also find that there are portions of the initial parameters space for which no solution is admitted by the reduced equations. The reduced Lagrangians deduced from the full action are, in general, correctly describing the dynamics whenever solutions do exist
We investigate Kantowski-Sachs models in Einstein-{ae}ther theory with a perfect fluid source using the singularity analysis to prove the integrability of the field equations and dynamical system tools to study the evolution. We find an inflationary source at early times, and an inflationary sink at late times, for a wide region in the parameter space. The results by A. A. Coley, G. Leon, P. Sandin and J. Latta (JCAP 12, 010, 2015), are then re-obtained as particular cases. Additionally, we select other values for the non-GR parameters which are consistent with current constraints, getting a very rich phenomenology. In particular, we find solutions with infinite shear, zero curvature, and infinite matter energy density in comparison with the Hubble scalar. We also have stiff-like future attractors, anisotropic late-time attractors, or both, in some special cases. Such results are developed analytically, and then verified by numerics. Finally, the physical interpretation of the new critical points is discussed.
We revisit the status of scalar-tensor theories with applications to dark energy in the aftermath of the gravitational wave signal GW170817 and its optical counterpart GRB170817A. At the level of the cosmological background, we identify a class of theories, previously declared unviable in this context, whose anomalous gravitational wave speed is proportional to the scalar equation of motion. As long as the scalar field is assumed not to couple directly to matter, this raises the possibility of compatibility with the gravitational wave data, for any cosmological sources, thanks to the scalar dynamics. This newly rescued class of theories includes examples of generalised quintic galileons from Horndeski theories. Despite the promise of this leading order result, we show that the loophole ultimately fails when we include the effect of large scale inhomogeneities.
By use of the gauge-invariant variables proposed by Kodama and Ishibashi, we obtain the most general perturbation equations in the $(m+n)$-dimensional spacetime with a warped product metric. These equations do not depend on the spectral expansions of the Laplace-type operators on the $n$-dimensional Einstein manifold. These equations enable us to have a complete gauge-invariant perturbation theory and a well-defined spectral expansion for all modes and the gauge invariance is kept for each mode. By studying perturbations of some projections of Weyl tensor in the case of $m=2$, we define three Teukolsky-like gauge-invariant variables and obtain the perturbation equations of these variables by considering perturbations of the Penrose wave equations in the $(2+n)$-dimensional Einstein spectime. In particular, we find the relations between the Teukolsky-like gauge-invariant variables and the Kodama-Ishibashi gauge-invariant variables. These relations imply that the Kodama-Ishibashi gauge-invariant variables all come from the perturbations of Weyl tensor of the spacetime.
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