Lorentz violation is motivated by quantum gravity and it is generically described by nondynamical tensors. In this work a Lorentz violating extension of general relativity is studied where a nondynamical tensor couples to the Weyl tensor. A family of static and spherically symmetric solutions in vacuum is found, confirming that there are consistent solutions with explicit Lorentz violation in dynamical spacetimes. These solutions produce an unconventional dependence of the gravitational redshift, which, in turn, leads to the first bounds on such nondynamical tensor that do not rely on the physics of the early universe. Moreover, the bounds obtained in this work are competitive with respect to limits on similar nondynamical tensors.
Matter collineations of spherically Symmetric Lorentzian Manifolds are considered. These are investigated when the energy-momentum tensor is non-degenerate and also when it is degenerate. We have classified spacetimes admitting higher symmetries and spacetimes admitting SO(3) as the maximal isometry group. For the non-degenerate case, we obtain either {\it four}, {\it six}, {\it seven} or {\it ten} independent matter collineations in which {\it four} are isometries and the rest are proper. The results of the previous paper [1] are recovered as a special case. It is worth noting that we have al…
We show that a static spherically symmetric black hole, in a generic theory of gravity with generic matter fields, has a two-dimensional Lorentz symmetry.
In the context of threshold investigations of Lorentz violation, we discuss the fundamental principle of coordinate invariance, the role of an effective dynamical framework, and the conditions of positivity and causality. Our analysis excludes a variety of previously considered Lorentz-breaking parameters and opens an avenue for viable dispersion-relation investigations of Lorentz violation.
A brief summary is presented of recent work examining the fate of the Nambu-Goldstone modes in gravitational theories with spontaneous Lorentz violation.
In the last decade, a variety of high-precision experiments have searched for miniscule violations of Lorentz symmetry. These searches are largely motivated by the possibility of uncovering experimental signatures from a fundamental unified theory. Experimental results are reported in the framework called the Standard-Model Extension (SME), which describes general Lorentz violation for each particle species in terms of its coefficients for Lorentz violation. Recently, the role of gravitational experiments in probing the SME has been explored in the literature. In this talk, I will summarize th…
In general relativity, the masslessness of gravitons can be traced to symmetry under diffeomorphisms. Here we consider another possibility, whereby the masslessness arises from spontaneous violation of Lorentz symmetry.
We show that the families of effective actions considered by Jacobson et al. to study Lorentz invariance violations contain a class of models that represent pure General Relativity with Euclidean signature. We also point out that some members of this family of actions preserve Lorentz invariance in a generalized sense.
In this proceedings, similarities between the structure of theories with Lorentz violation and theories with constant torsion in flat spacetime are exploited to place bounds on torsion components. An example is given showing the analysis leading to bounds on the axial-vector and mixed-symmetry components of torsion, based on a dual-maser experiment.
We discuss spherically symmetric solutions for point-like sources in Lorentz-breaking massive gravity theories. This analysis is valid for Stückelberg's effective field theory formulation, for Lorentz Breaking Massive Bigravity and general extensions of gravity leading to an extra term $-Sr^γ$ added to the Newtonian potential. The approach consists in analyzing the stability of the geodesic equations, at the first order (deviation equation). The main result is a strong constrain in the space of parameters of the theories. This motivates higher order analysis of geodesic perturbations in order …
The f(T) gravity is nowadays being widely used for cosmological model building, as well as for constructing spherically symmetric solutions. In its classical pure tetrad formulation it violates the local Lorentz symmetry in the space of tetrads. By using an appropriate spin connection it can be brought to a formally Lorentz invariant shape. However, despite some mathematical elegance obtained and new options of looking for non-standard couplings to matter probably made possible, it is fully equivalent in itself to the initial formulation. It seems that this fact, that the covariantisation does…
Lorentz violations in gravitational waves are investigated. Plane-wave solutions for arbitrary gauge-invariant violations in linearized gravity are constructed. Signatures of Lorentz violation include dispersion, birefringence, and anisotropies. Modifications to waves from coalescing compact binaries and to strain signals in gravitational-wave detectors are derived.
General Relativity predicts two modes for plane gravitational waves. When a tiny violation of Lorentz invariance occurs, the two gravitational wave modes are modified. We use perturbation theory to study the detailed form of the modifications to the two gravitational wave modes from the minimal Lorentz-violation coupling. The perturbation solution for the metric fluctuation up to the first order in Lorentz violation is discussed. Then, we investigate the motions of test particles under the influence of the plane gravitational waves with Lorentz violation. First-order deviations from the usual …
General violations of Lorentz symmetry can be described by the Standard-Model Extension (SME) framework. The SME predicts modifications to existing physics and can be tested in high-precision experiments. By looking for small deviations from Newton gravity, short-range gravity experiments are expected to be sensitive to possible gravitational Lorentz-violation signals. With two group's short-range gravity data analyzed recently, no nonminimal Lorentz violation signal is found at the micron distance scale, which gives stringent constraints on nonminimal Lorentz-violation coefficients in the SME…
This contribution to the CPT'19 meeting provides a brief overview of recent theoretical studies of nonminimal Lorentz violation in linearized gravity. Signatures in gravitational waves from coalescing compact binaries are discussed.
Spacetime nonmetricity can be studied experimentally through its couplings to fermions and photons. We use recent high-precision searches for Lorentz violation to deduce first constraints involving the 40 independent nonmetricity components down to levels of order $10^{-43}$ GeV.
Recently, a state of the art experiment shows evidence for Lorentz violation in the gravitational sector. To explain this experiment, we investigate a spontaneous Lorentz violation scenario with a generalized scalar field. We find that when the scalar field is nonminimally coupled to gravity, the Lorentz violation induces a deformation in the Newtonian potential along the direction of Lorentz violation.
Classical point-particle relativistic lagrangians are constructed that generate the momentum-velocity and dispersion relations for quantum wave packets in Lorentz-violating effective field theory.
Violations of local Lorentz invariance in the gravitationally coupled matter sector have yet to be sought in strong-gravity systems. We present the implications of matter-sector Lorentz violation for orbital perturbations in pulsar systems and show that the analysis of pulsar data can provide sensitivities to these effects that exceed the current reach of solar system and laboratory tests by several orders of magnitude.
We employ techniques from quantum estimation theory (QET) to estimate the Lorentz violation parameters in the 1+3-dimensional flat spacetime. We obtain and discuss the expression of the quantum Fisher information (QFI) in terms of the Lorentz violation parameter $σ_0$ and the momentum k of the created particles. We show that the maximum QFI is achieved for a specific momentum $k_{\mathrm{max}}$. We also find that the optimal precision of estimation of the Lorentz violation parameter is obtained near the Planck scale.
Many new linearized coefficients for Lorentz violation are discovered in our recent work on the construction of a generic Lorentz-violating effective field theory in curved spacetime. The new coefficients can be constrained by experiments in weak gravity fields. In this work, we compare experiments in different gravitational potentials and study three types of gravity-related experiments: free-fall, gravitational interferometer, and gravitational bound-state experiments. First constraints on the new coefficients for Lorentz violation are extracted from those experiments.
We present a detailed study of the spherically symmetric solutions in Lorentz breaking massive gravity. There is an undetermined function $\mathcal{F}(X, w_1, w_2, w_3)$ in the action of Stückelberg fields $S_ϕ=Λ^4\int{d^4x\sqrt{-g}\mathcal{F}}$, which should be resolved through physical means. In the general relativity, the spherically symmetric solution to the Einstein equation is a benchmark and its massive deformation also play a crucial role in Lorentz breaking massive gravity. $\mathcal{F}$ will satisfy the constraint equation $T_0^1=0$ from the spherically symmetric Einstein tensor $G_0…
An optical ring cavity is used to place the first laboratory constraints on parity-odd nonrenormalizable Lorentz violation. Variations in resonant frequencies are limited to parts in $10^{15}$. Absolute sensitivity to Lorentz-violating operators of mass dimension 6 is improved by a factor of a million over existing parity-even microwave-cavity bounds. Sensitivity to dimension-8 violations is improved by fourteen orders of magnitude.
In this contribution to the CPT'19 proceedings, we summarize efforts that use data from the MICROSCOPE space mission to search for Lorentz violation in the Standard-Model Extension.
A brief summary of some of the main consequences of spontaneous Lorentz violation in gravity is presented, including evasion of a no-go theorem, concomitant spontaneous diffeomorphism breaking, the appearance of massless Nambu-Goldstone modes and massive Higgs modes, and the possibility of a Higgs mechanism in gravity.
We study the quantization of a simple model of antisymmetric tensor field with spontaneous Lorentz violation in curved spacetime. We evaluate the 1-loop corrections at first order of metric perturbation, using a general covariant effective action approach. We revisit the issue of quantum equivalence, and find that it holds for non-Lorentz-violating modes but breaks down for Lorentz violating modes.
An experimental test of the Newtonian inverse square law at short range has been used to set limits on Lorentz violation in the pure gravity sector of the Standard-Model Extension. On account of the planar test mass geometry, nominally null with respect to inverse square forces, the limits derived for the SME coefficients of Lorentz violation are on the order s ~ 10000.
Many quantum theories of gravity propose Lorentz violating dispersion relations of the form $ω= |k|\, f(|k|/M)$, with recovery of approximate Lorentz invariance at energy scales much below $M$. We show that a quantum field with this dispersion predicts drastic low energy Lorentz violation in atoms modelled as Unruh-DeWitt detectors, for any $f$ that dips below unity somewhere. As an example, we show that polymer quantization motivated by loop quantum gravity predicts such Lorentz violation below current ion collider rapidities.
A more complete theoretical model of testing Lorentz violation by the comparison of atomic clocks is developed in the Robertson-Mansouri-Sexl kinematic framework. As this frame postulates the deviation of the coordinate transformation from the Lorentz transformation, from the viewpoint of the transformation violations on time and space, the LI violating effect in the atomic clock comparison can be explained as two parts: time-delay effect $α\frac {v^2}{c^2}$ and structure effect $-\frac {β+2δ}{3} \frac {v^2}{c^2}$. Standard model extension is a widely used dynamic frame to characterize the Lor…
In this paper, we discuss the tunneling of scalar particles near the event horizon of stationary and nonstationary Kerr-de Sitter black hole using Lorentz violation theory in curved space time. The modified form of Hamilton-Jacobi equation is derived from the Klein-Gordon equation by applying Lorentz violation theory. The Hawking temperatures derived from stationary and nonstationary Kerr-de Sitter black holes are modified due to Lorentz violation theory. It is noted that the change in Bekenstein-Hawking entropy and modified Hawking temperatures of stationary and nonstationary Kerr-de Sitter b…
We present constraints on violations of Lorentz Invariance based on Lunar Laser Ranging (LLR) data. LLR measures the Earth-Moon separation by timing the round-trip travel of light between the two bodies, and is currently accurate to a few centimeters (parts in $10^{11}$ of the total distance). By analyzing archival LLR data under the Standard-Model Extension (SME) framework, we derived six observational constraints on dimensionless SME parameters that describe potential Lorentz-violation. We found no evidence for Lorentz violation at the $10^{-6}$ to $10^{-11}$ level in these parameters.
Comparatively few searches have been performed for violations of local Lorentz invariance in the pure-gravity sector. We show that tests of short-range gravity are sensitive to a broad class of unconstrained and novel signals that depend on the experimental geometry and on sidereal time.
Spontaneous Lorentz violation is a viable mechanism to look for Planck scale physics. In this work, we study spontaneous Lorentz violation models, in flat spacetime, where a vector field produces such a violation and matter is modeled by a complex scalar field. We show that it is possible to construct a Hamilton density for which the evolution respects the dynamical constraints. However, we also find that the initial data, as required by standard field theory, does not determine the fields evolution in a unique way. In addition, we present some examples where the physical effects of such ambig…
Lorentz violation in a brane-world scenario is presented and used to obtain a relationship between the speed of gravitational waves in the bulk and that on the brane. Lorentz violating effects would manifest themselves in gravitational waves travelling with a greater speed in the bulk than on the brane and this effect is independent of the signature of the extra dimension.
We discuss the impact of Lorentz violation on the cosmology. Firstly, we show that the Lorentz violation affects the dynamics of the chaotic inflationary model and gives rise to an interesting feature. Secondly, we propose the Lorentz violating DGP brane models where the Lorentz violating terms on the brane accelerate the current universe. We conjecture that the ghost disappears in the Lorentz violating DGP models.
This talk given at the CPT'10 meeting provides a brief introduction to Lorentz and CPT violation and outlines a few recent developments in the subject.
We construct supersymmetric Lorentz violating operators for matter and gauge fields. We show that in the supersymmetric Standard Model the lowest possible dimension for such operators is five, and therefore they are suppressed by at least one power of an ultra--violet energy scale, providing a possible explanation for the smallness of Lorentz violation and its stability against radiative corrections. Supersymmetric Lorentz noninvariant operators do not lead to modifications of dispersion relations at high energies thereby escaping constraints from astrophysical searches for Lorentz violation.
In this note, we derive an ordinary differential equation for outgoing light rays in the spacetime of a spherically symmetric contracting dust cloud. The violation of strong cosmic censorship is equivalent to the existence of a solution blowing up at the centre of the symmetry. As an application, we reprove the generic violation of strong cosmic censorship for a dust cloud first proved by Christodoulou. We also derive a similar equation for a spherically symmetric dust cloud in the case of positive cosmological constant and show the generic violation of strong cosmic censorship in this case.
We consider bulk fields coupled to the graviton in a Lorentz violating fashion. We expect that the overly tested Lorentz symmetry might set constraints on the induced Lorentz violation in the brane, and hence on the dynamics of the interaction of bulk fields on the brane. We also use the requirement for Lorentz symmetry to constrain the cosmological constant observed on the brane.
Lorentz and diffeomorphism violations are studied in linearized gravity using effective field theory. A classification of all gauge-invariant and gauge-violating terms is given. The exact covariant dispersion relation for gravitational modes involving operators of arbitrary mass dimension is constructed, and various special limits are discussed.
A search for sidereal variations in the force between two planar tungsten oscillators separated by about 80 microns sets the first experimental limits on Lorentz violation involving quadratic couplings of the Riemann curvature, consistent with no effect at the level of $10^{-7}$ m$^2$.
A general framework for tests of Lorentz invariance with electromagnetic waves is presented, allowing for operators of arbitrary mass dimension. Signatures of Lorentz violations include vacuum birefringence, vacuum dispersion, and anisotropies. Sensitive searches for violations using sources such as active galaxies, gamma-ray bursts, and the cosmic microwave background are discussed. Direction-dependent dispersion constraints are obtained on operators of dimension 6 and 8 using gamma-ray bursts and the blazar Markarian 501. Stringent constraints on operators of dimension 3 are found using 5-ye…
Bipartite Riemann-Finsler geometries with complementary Finsler structures are constructed. Calculable examples are presented based on a bilinear-form coefficient for explicit Lorentz violation.
Exceptional sensitivity to spacetime torsion can be achieved by searching for its couplings to fermions. Recent experimental searches for Lorentz violation are exploited to extract new constraints involving 19 of the 24 independent torsion components down to levels of order 10^{-31} GeV.
In this paper, the tunneling of scalar particles near the event horizons of Riemann space time, BTZ black hole and Schwarzschild-de Sitter black hole are investigated by applying Hamilton-Jacobi equation with Lorentz violation theory in curved space time. The modified Hamilton-Jacobi equation is derived from Klein-Gordon equation of scalar particles induced by Lorentz violation theory in curved space time. The Hawking temperatures of Riemann space time and the BTZ black hole are modified due to the effect of Lorentz violation theory. Moreover, the Bekenstein-Hawking entropy near the event hori…
The physics of classical particles in a Lorentz-breaking spacetime has numerous features resembling the properties of Finsler geometry. In particular, the Lagrange function plays a role similar to that of a Finsler structure function. A summary is presented of recent results, including new calculable Finsler structures based on Lagrange functions appearing in the Lorentz-violation framework known as the Standard-Model Extension.
We present an explicit proof that a minimal model of rank-2 antisymmetric field with spontaneous Lorentz violation and a classically equivalent vector field model are also quantum equivalent, by calculating quantum effective actions of both theories. We comment on the issues encountered while checking quantum equivalence in curved spacetime.
We correct the fitting formula used in refs. [1,2] to obtain a robust limit on a violation of Lorentz invariance that depends linearly on the photon energy. The correction leads to a slight increase of the limit on the scale of the violation, to M > 1.4 x 10^{16} GeV.
