Signals for Lorentz violation in post-Newtonian gravity

Abstract

The pure-gravity sector of the minimal standard-model extension is studied in the limit of Riemann spacetime. A method is developed to extract the modified Einstein field equations in the limit of small metric fluctuations about the Minkowski vacuum, while allowing for the dynamics of the 20 independent coefficients for Lorentz violation. The linearized effective equations are solved to obtain the postNewtonian metric. The corresponding post-Newtonian behavior of a perfect fluid is studied and applied to the gravitating many-body system. Illustrative examples of the methodology are provided using bumblebee models. The implications of the general theoretical results are studied for a variety of existing and proposed gravitational experiments, including lunar and satellite laser-ranging, laboratory experiments with gravimeters and torsion pendula, measurements of the spin precession of orbiting gyroscopes, timing studies of signals from binary pulsars, and the classic tests involving the perihelion precession and the time delay of light. For each type of experiment considered, estimates of the attainable sensitivities are provided. Numerous effects of local Lorentz violation can be studied in existing or near-future experiments at sensitivities ranging from parts in 10 4 down to parts in 10 15 .

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

“…3. In some of the alternative theories of gravity the hypersurfaces of the light and gravity null cones do not coincide as the speed of propagation of gravity and light are different [25,[71][72][73][74]. We have discussed the gravitational deflection of light caused by moving bodies, in such theories in a number of other papers [22,64,72] which can be used as references.…”

One-loop renormalization of Lorentz and CPT -violating scalar field theory in curved spacetime

“…Also, the minimal form of the gravitational action requested by the renormalization of the violating scalar field theory in curved spacetime was established based on the previous one-loop calculations. In particular, the effect of some Lorentz violating gravitational terms, which are necessary at a semiclassical quantum level, were already discussed in the short range gravity limit [42,43] and in the quantum gravity [44]. At the next stage, a similar analysis for the other missing new terms in Eq.…”

“…From the technical side, this is not a trivial task since the expression (48) is quite complicated; then we are going to expose some details concerning the needed conformal transformation rules. Since the conformal group is a one-parameter Lie group, one can restrict our considerations to the infinitesimal version of transformation (42). Disregarding the higher orders in σ and superficial terms, after some tedious algebra, we arrive at the following transformation rules for each term present in (48):…”

“…The investigation of the possible phenomenological manifestations of terms linear in curvature was performed in Ref. [42] on the basis of PPN formalism, and recently, an extensive systematic analysis of the Lorentz violating higher derivatives terms has been started in [43], also in the weak gravitational field approximation. According to [43], the presence of higher derivative violating terms leads to a modified Poisson equation for the gravitational potential φ g ðrÞ in the form…”

Global three-parameter model for neutrino oscillations using Lorentz violation

“…In obtaining Eq. (4), possible gravitational couplings [5,41] have been disregarded, and the coefficients a L ab and c L ab are assumed to be spacetime constants. If these coefficients originate in spontaneous Lorentz violation, they have companion NambuGoldstone fluctuations that could be interpreted as the photon [42], the graviton [43], or additional neutrino interactions [44], but these effects are secondary in the present context and are disregarded in this work.…”