We study a generally covariant model in which local Lorentz invariance is broken by a dynamical unit timelike vector field u a -the "aether". Such a model makes it possible to study the gravitational and cosmological consequences of preferred frame effects, such as "variable speed of light" or high frequency dispersion, while preserving a generally covariant metric theory of gravity. In this paper we restrict attention to an action for an effective theory of the aether which involves only the antisymmetrized derivative ∇ [a u b] . Without matter this theory is equivalent to a sector of the EinsteinMaxwell-charged dust system. The aether has two massless transverse excitations, and the solutions of the model include all vacuum solutions of general relativity (as well as other solutions). However, the aether generally develops gradient singularities which signal a breakdown of this effective theory. Including the symmetrized derivative in the action for the aether field may cure this problem.

Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.

We consider here the possibility of quantum gravity induced violation of Lorentz symmetry (LV). Even if suppressed by the inverse Planck mass such LV can be tested by current experiments and astrophysical observations. We review the effective field theory approach to describing LV, the issue of naturalness, and many phenomena characteristic of LV. We discuss some of the current observational bounds on LV, focusing mostly on those from high energy astrophysics in the QED sector at order E/M Planck . In this context, we present a number of new results which include the explicit computation of rates of the most relevant LV processes, the derivation of a new photon decay constraint, and modification of previous constraints taking proper account of the helicity dependence of the LV parameters implied by effective field theory.

Local Lorentz invariance violation can be realized by introducing extra tensor fields in the action that couple to matter. If the Lorentz violation is rotationally invariant in some frame, then it is characterized by an "aether", i.e. a unit timelike vector field. General covariance requires that the aether field be dynamical. In this paper we study the linearized theory of such an aether coupled to gravity and find the speeds and polarizations of all the wave modes in terms of the four constants appearing in the most general action at second order in derivatives. We find that in addition to the usual two transverse traceless metric modes, there are three coupled aether-metric modes.

Special relativity asserts that physical phenomena appear the same for all inertially moving observers. This symmetry, called Lorentz symmetry, relates long wavelengths to short ones: if the symmetry is exact it implies that spacetime must look the same at all length scales. Several approaches to quantum gravity, however, suggest that there may be a Lorentz violating microscopic structure of spacetime, for example discreteness [1], non-commutativity [2], or extra dimensions [3]. Here we determine a very strong constraint on a type of Lorentz violation that produces a maximum electron speed less than the speed of light. We use the observation of 100 MeV synchrotron radiation from the Crab nebula to improve the previous limits by a factor of 40 million, ruling out this type of Lorentz violation, and thereby providing an important constraint on theories of quantum gravity.To characterize Lorentz violation we adopt the simple framework of deformed dispersion relations. A dispersion relation is the relation between energy E and momentum p for a particle. In relativity, these quantities change under a Lorentz transformation, but the particle dispersion relation E 2 = m 2 c 2 + p 2 c 4 is invariant (where m is the particle mass and c is the * Previous title: Lorentz violation and Crab synchrotron emission: a new constraint far beyond the Planck scale 1