Lorentz-violating Effects Research Articles

Power spectra and circular polarization of primordial gravitational waves with parity and Lorentz violations

The violations of parity and Lorentz symmetries in gravity can change the propagating properties of gravitational waves (GWs) in the cosmological background, which can arise from a large number of parity- and Lorentz-violating theories. In this paper, through a systematic parametrization for characterizing possible derivations from the standard GW propagation in general relativity, we study both the parity- and Lorentz-violating effects on the power spectra and the polarization of the primordial gravitational waves (PGWs) during the slow-roll inflation. To this end, we calculate explicitly the power spectrum and the corresponding circular polarization of the PGWs analytically by using the uniform asymptotic approximation. It is shown that the new contributions to power spectra contain two parts, one from the parity-violating terms and the other from the Lorentz-violating terms. While the Lorentz-violating terms can only affect the overall amplitudes of PGWs, the parity-violating terms induce nonzero circular polarization of PGWs, i.e., the left-hand and right-hand polarization modes of GWs have different amplitudes.

Classical radiation fields for scalar, electromagnetic, and gravitational waves with spacetime-symmetry breaking

An effective field theory framework is used to investigate some Lorentz-violating effects on the generation of electromagnetic and gravitational waves, complementing previous work on propagation. Specifically we find solutions to a modified, anisotropic wave equation, sourced by charge or fluid matter. We derive the radiation fields for scalars, classical electromagnetic radiation, and partial results for gravitational radiation. For gravitational waves, the results show longitudinal and breathing polarizations proportional to coefficients for spacetime-symmetry breaking.

Gaussian beam propagation in a Lorentz-violating vacuum in the presence of a semi-transparent mirror

In this paper we study the propagation of structured optical scalar beams in a Lorentz-violating (LV) vacuum parametrized by a constant 4-vector u μ and in the presence of a semi-transparent mirror. The two bosonic degrees of freedom of the electromagnetic field can be described by a LV extension of the massless scalar field theory, whose LV part is characterized by the term (u · ∂ϕ)2. The mirror at a surface Σ is modelled by a delta-type potential in the Lagrange density for the LV scalar field, i.e. λ δ(Σ)ϕ 2, where the parameter λ controls the degree of transparency of the mirror. Using Green’s function techniques, we investigate the propagation of a Gaussian beam in the presence of a mirror which is perpendicular to the propagation direction and for two particular choices of the background 4-vector: parallel and perpendicular to the propagation direction. To quantify the Lorentz-violating effects we introduce the fidelity as a measurement of the closeness of the propagated field distribution with respect to that in the conventional vacuum. In the absence of the mirror (λ = 0) the fidelity is found to be close to one, and hence LV effects are quite small. However in the presence of the mirror, there are regions where the fidelity drops to zero, thus implying that LV effects could be clearly differentiated from the propagation in vacuum. Within the paraxial approximation we determine analytically the LV effects upon the Rayleigh range, the radius of the beam, the Gouy phase and the radius of curvature of the wavefronts. We discuss possible scenarios where our results could apply, by using optically transparent multiferroic materials, which offer unprecedented opportunities to tailor structured beam propagation, as well as to simulate an LV vacuum.

Gravitational wave constraints on nonbirefringent dispersions of gravitational waves due to Lorentz violations with GWTC-3 events

The standard model extension (SME) is an effective field theory framework that can be used to study the possible violations of Lorentz symmetry in the gravitational interaction. In the SME's gauge invariant linearized gravity sector, the dispersion relation of GWs is modified, resulting in anisotropy, birefringence, and dispersion effects in the propagation of GWs. In this paper, we mainly focus on the non-birefringent and anisotropic dispersion relation in the propagation of GWs due to the violation of Lorentz symmetry. With the modified dispersion relation, we calculate the corresponding modified waveform of GWs generated by the coalescence of compact binaries. We consider the effects from the operators with the lowest mass dimension $d=6$ in the gauge invariant linearized gravity sector of the SME which are expected to have the dominant Lorentz-violating effect on the propagation of GWs. For this case, the Lorentz-violating effects are presented by 25 coefficients and we constrain them independently by the ``maximal-reach" approach. We use 90 high-confidence GW events in the GWTC-3 catalog and use {\tt Bilby}, an open source software, and {\tt Dynest}, a nested sampling package, to perform parameter estimation with the modified waveform. We do not find any evidence of Lorentz violation in the GWs data and give a $90\%$ confidence interval for each Lorentz violating coefficient.

Odd-parity perturbations of the wormhole-like geometries and quasi-normal modes in Einstein-Æther theory

The Einstein-Æther theory has drawn a lot of attentions in recent years. As a representative case of gravitational theories that break the Lorentz symmetry, it plays an important role in testing the Lorentz-violating effects and shedding light on the attempts to construct quantum gravity. Since the first detection to the gravitational wave, the event GW150914, a brand new window has been opened to testing the theory of gravity with gravitational wave observations. At the same time, the study of gravitational waves itself also provides us a serendipity of accessing the nature of a theory. In this paper, we focus on the odd-parity gravitational perturbations to a background that describes a wormhole-like geometry under the Einstein-Æther theory. Taking advantage of this set of analytic background solutions, we are able to simplify the Lagrangian and construct a set of coupled single-parameter dependent master equations, from which we solve for the quasi-normal modes that carry the physical information of the emitted gravitational waves. Basically, the results reflect a consistency between Einstein-Æther theory and general relativity. More importantly, as long as the no-ghost condition and the latest observational constraints are concerned, we notice that the resultant quasi-normal mode solutions intimate a kind of dynamical instability. Thus, the solutions are ruled out based on their stability against small linear perturbations.

The Boltzmann equation and equilibrium thermodynamics in Lorentz-violating theories

In this work, we adapt the foundations of relativistic kinetic theory and the Boltzmann equation to particles with Lorentz-violating dispersion relations. The latter are taken to be those associated to two commonly considered sets of coefficients in the minimal Standard-Model Extension. We treat both the cases of classical (Maxwell–Boltzmann) and quantum (Fermi–Dirac and Bose–Einstein) statistics. It is shown that with the appropriate definition of the entropy current, Boltzmann’s H-theorem continues to hold. We derive the equilibrium solutions and then identify the Lorentz-violating effects for various thermodynamic variables, as well as for Bose–Einstein condensation. Finally, a scenario with nonelastic collisions between multiple species of particles corresponding to chemical or nuclear reactions is considered.

Effects of Lorentz symmetry breaking environment on generalized relativistic quantum oscillator field

In this paper, we study the generalized Klein–Gordon oscillator under the effects of the violation of Lorentz symmetry defined by a tensor field ( KF) μναβ out of the standard model extension. We consider a possible scenario of Lorentz-violating with a Cornell-type potential form electric field and a linear magnetic field that contributes a harmonic-type central potential effects in the quantum motions of oscillator fields. The bound-state solutions of the wave equation using the parametric Nikiforov–Uvarov method by considering Coulomb- and Cornell-type potential form functions are obtained. We see that the eigenvalue solutions get modified by the Lorentz symmetry breaking effects in comparison to the Landau levels (without Lorentz-violation effects in flat space).

Impact of Lorentz violation on anomalous magnetic moments of charged leptons

We address the question whether a violation of Lorentz symmetry can explain the tension between the measurement and the Standard-Model prediction of the anomalous magnetic moment of the muon, (g − 2)μ, and whether it can significantly impact the one of the electron, (g — 2)e. While anisotropic Lorentz-violating effects are, in general, expected to produce sidereal oscillations in observables, isotropic Lorentz violation (LV) in the charged-lepton sector could also feed into (g — 2)e,μ. However, we find that this type of Lorentz violation, parametrised via a dim-4 field operator of the Standard-Model Extension (SME), is already strongly constrained by the absence of vacuum Čerenkov radiation and photon decay. In particular, the observations of very-high-energetic astrophysical photons at LHAASO and of high-energetic electrons (muons) by the LHC (IceCube) place the most stringent two-sided bounds on the relevant SME coefficients overset{circ }{c} (e) ( overset{circ }{c} (μ)). Therefore, any explanation of the tension in (g − 2)μ via isotropic Lorentz violation of the minimal spin-degenerate SME is excluded, and the possible size of its impact on (g − 2)e is very limited.

Tree-level unitarity, causality, and higher-order Lorentz and CPT violation

Higher-order effects of CPT and Lorentz violation within the SME effective framework including Myers-Pospelov dimension-five operator terms are studied. The model is canonically quantized by giving special attention to the arising of indefinite-metric states or ghosts in an indefinite Fock space. As is well-known, without a perturbative treatment that avoids the propagation of ghost modes or any other approximation, one has to face the question of whether unitarity and microcausality are preserved. In this work, we study both possible issues. We found that microcausality is preserved due to the cancellation of residues occurring in pairs or conjugate pairs when they become complex. Also, by using the Lee-Wick prescription, we prove that the $S$ matrix can be defined as perturbatively unitary for tree-level $2\to 2$ processes with an internal fermion line.

Holographic complexity of LST and single trace Toverline{T} , Joverline{T} and Toverline{J} deformations

This work is an extension of our previous work [1] where we exploited holography to compute the complexity characteristics of Little String Theory (LST), a nonlocal, nongravitational field theory which flows to a local 2d CFT in the IR under RG via an integrable irrelevant left(Toverline{T}right) deformation. Here we look at the more general LST obtained by UV deforming the 2d CFT by incorporating Lorentz violating irrelevant Joverline{T} and Toverline{J} deformations on top of Toverline{T} deformation, in an effort to capture the novel signatures of Lorentz violation (on top of nonlocality) on quantum complexity. In anticipation of the fact that the dual field theory is Lorentz violating, we compute the volume complexity in two different Lorentz frames and the comparison is drawn between the results. It turns out that for this system the nonlocality and Lorentz violation effects are inextricably intertwined in the UV divergence structure of the quantum complexity. The coefficients of the divergences carry the signature of Lorentz boost violation. We also compute the subregion complexity which displays a (Hagedorn) phase transition with the transition point being the same as that for the phase transition of entanglement entropy [2]. These new results are consistent with our previous work [1]. Null warped AdS3 is treated as special case of interest.

Exploring Anisotropic Lorentz Invariance Violation from the Spectral-Lag Transitions of Gamma-Ray Bursts

The observed spectral lags of gamma-ray bursts (GRBs) have been widely used to explore possible violations of Lorentz invariance. However, these studies were generally performed by concentrating on the rough time lag of a single highest-energy photon and ignoring the intrinsic time lag at the source. A new way to test nonbirefringent Lorentz-violating effects has been proposed by analyzing the multi-photon spectral-lag behavior of a GRB that displays a positive-to-negative transition. This method gives both a plausible description of the intrinsic energy-dependent time lag and comparatively robust constraints on Lorentz-violating effects. In this work, we conduct a systematic search for Lorentz-violating photon dispersion from the spectral-lag transition features of 32 GRBs. By fitting the spectral-lag data of these 32 GRBs, we place constraints on a variety of isotropic and anisotropic Lorentz-violating coefficients with mass dimension d=6 and 8. While our dispersion constraints are not competitive with existing bounds, they have the promise to complement the full coefficient space.

Overcoming 1 part in 10^9 of earth angular rotation rate measurement with the G Wettzell data

The absolute measurement of the Earth angular rotation rate with ground-based instruments becomes challenging if the 1 part in 10^9 of precision has to be obtained. This threshold is important for fundamental physics and for geodesy, to investigate effects of General Relativity and Lorentz violation in the gravity sector and to provide the fast variation of the Earth rotation rate. High sensitivity Ring Laser Gyroscopes (RLG) are currently the only promising technique to achieve this task in the near future, but their precision has been so far limited by systematics related to the laser operation. In this paper we analyze two different sets of observations, each of them three days long. They were obtained from the G ring laser at the Geodetic Observatory Wettzell. The applied method has been developed for the GINGERINO ring laser in order to identify and extract the laser systematics. For the available data sets the residuals show mostly white noise behavior and the Allan deviation drops below 1 part in 10^9 after an integration time of about 10^4 s.

Effects of lorentz violation in the higgs sector of the minimal standard model extension

A bound on the CPT-odd four-vector coefficient [Formula: see text] that appears in Higgs sector of the minimal Standard Model Extended (mSME) is presented. The analysis is based on the contributions arising from the sector in question to the anomalous magnetic dipole moment (AMDM) for leptons calculated at the one-loop level, for which an analytical expression is obtained. The largest contribution of this Lorentz violating coefficient is on the lightest lepton, which results as a consequence of a strong nondecoupling effect. By using the experimental uncertainty of the electron AMDM we predict that [Formula: see text].

Exact solution of generalized KG-oscillator under Lorentz-violating effects by a fixed vector field subject to interaction potential

In this work, the relativistic quantum oscillator under the Lorentz symmetry violation environment defined by an arbitrary constant vector field [Formula: see text] is analyzed. We solve the generalized Klein–Gordon oscillator with different vector field configurations and obtained the bound-states solutions. After that, we insert a static Coulomb-type scalar potential in the wave equation and solve the generalized Klein–Gordon oscillator analytically. We discuss the effects of Lorentz symmetry violation and the Coulomb-type potential on the energy spectrum of these oscillator fields.

Effects of Lorentz symmetry breaking by a tensor field subject to Coulomb-type potential on relativistic quantum oscillator

In this paper, we solve the Klein–Gordon oscillator analytically under Lorentz-violating effects defined by a tensor field subject to a Coulomb-type scalar potential. We obtain the bound-state solutions of the quantum system by choosing various electromagnetic field configurations and discuss the effects on the energy profiles and the wave function of these oscillator fields.

Effects of Lorentz violation in superconductivity

This paper presents the effects of Lorentz violation in superconductivity. Constructing a Lorentz-violating Ginzburg-Landau theory of superconductivity we discuss the influence of the Lorentz-violating tensors and in London's penetration depth, in the coherence length and critical magnetic field.

Applications of the Schwarzschild\u2013Finsler\u2013Randers model

In this article, we study further applications of the Schwarzschild–Finsler–Randers (SFR) model which was introduced in a previous work Triantafyllopoulos et al. (Eur Phys J C 80(12):1200, 2020). In this model, we investigate curvatures and the generalized Kretschmann invariant which plays a crucial role for singularities. In addition, the derived path equations are used for the gravitational redshift of the SFR-model and these are compared with the GR model. Finally, we get some results for different values of parameters of the generalized photonsphere of the SFR-model and we find small deviations from the classical results of general relativity (GR) which may be ought to the possible Lorentz violation effects.

The Lorentz-violating real scalar field at thermal equilibrium

In this paper we study Lorentz-violation (LV) effects on the thermodynamics properties of a real scalar field theory due to the presence of a constant background tensor field. In particular, we analyse and compute explicitly the deviations of the internal energy, pressure, and entropy of the system at thermal equilibrium due to the LV contributions. For the free massless scalar field we obtain exact results, whereas for the massive case we perform approximated calculations. Finally, we consider the self interacting phi ^4 theory, and perform perturbative expansions in the coupling constant for obtaining relevant thermodynamics quantities.

Bounds on Lorentz-violating Yukawa couplings via lepton electromagnetic moments

The effective-Lagrangian description of Lorentz-invariance violation provided by the so-called Standard-Model Extension covers all the sectors of the Standard Model, allowing for model-independent studies of high-energy phenomena that might leave traces at relatively-low energies. In this context, the quantification of the large set of parameters characterizing Lorentz-violating effects is well motivated. In the present work, effects from the Lorentz-nonconserving Yukawa sector on the electromagnetic moments of charged leptons are calculated, estimated, and discussed. Following a perturbative approach, explicit expressions of leading contributions are derived and upper bounds on Lorentz violation are estimated from current data on electromagnetic moments. Scenarios regarding the coefficients of Lorentz violation are considered. In a scenario of two-point insertions preserving lepton flavor, the bound on the electron electric dipole moment yields limits as stringent as $10^{-28}$, whereas muon and tau-lepton electromagnetic moments determine bounds as restrictive as $10^{-14}$ and $10^{-6}$, respectively. Another scenario, defined by the assumption that Lorentz-violating Yukawa couplings are Hermitian, leads to less stringent bounds, provided by the muon anomalous magnetic moment, which turn out to be as restrictive as $10^{-14}$.

A field theory in Randers-Finsler spacetime

Finsler geometry is a natural arena to investigate the physics of spacetimes with local Lorentz violation. The directional dependence of the Finsler metric provides a way to encode the Lorentz-violating effects into the geometric structure of the spacetime. Here, a classical field theory is proposed in a special Finsler geometry, the so-called Randers-Finsler spacetime, where the Lorentz violation is produced by a background vector field. By promoting the Randers-Finsler metric to a differential operator, a Finsler-invariant action for the scalar, gauge and fermions are proposed. The theory contains nonlocal terms, as in the Very Special Relativity based theories. By expanding the Lagrangian, minimal and nonminimal Standard Model Extension terms arise, revealing a perturbative Lorentz violation. For a CPT-even term, the Carrol-Field-Jackiw and derivative extensions are obtained.