Lorentz Invariance Research Articles

Constraining Lorentz invariance violation with next-generation long-baseline experiments

Unified theories such as string theory and loop quantum gravity allow the Lorentz Invariance Violation (LIV) at the Planck Scale (MP ~ 1019 GeV). Using an effective field theory, this effect can be observed at low energies in terms of new interactions with a strength of ~ 1/MP. These new interactions contain operators with LIV coefficients which can be CPT-violating or CPT-conserving. In this work, we study in detail how these LIV parameters modify the transition probabilities in the next-generation long-baseline experiments, DUNE and Hyper-K. We evaluate the sensitivities of these experiments in isolation and combination to constrain the off-diagonal CPT-violating (aeμ, aeτ, aμτ) and CPT-conserving (ceμ, ceτ, cμτ) LIV parameters. We derive approximate compact analytical expressions of appearance (νμ → νe) and disappearance (νμ → νμ) probabilities in the presence of these LIV parameters to explain our numerical results. We explore the possible correlations and degeneracies between these LIV parameters and the most uncertain 3ν oscillation parameters, namely, θ23 and δCP. We find that for non-maximal values of θ23 (θ23 ≠ 45°), there exist degenerate solutions in its opposite octant for standalone DUNE and Hyper-K. These degeneracies disappear when we combine the data from DUNE and Hyper-K. In case of no-show, we place the expected upper bounds on these CPT-violating and CPT-conserving LIV parameters at 95% C.L. using the standalone DUNE, Hyper-K, and their combination. We observe that due to its access to a longer baseline and multi-GeV neutrinos, DUNE has a better reach in probing all these LIV parameters as compared to Hyper-K. Since the terms containing the CPT-conserving LIV parameters are proportional to neutrino energy in oscillation probabilities, Hyper-K is almost insensitive to the CPT-conserving LIV parameters because it mostly deals with sub-GeV neutrinos.

Some observable physical properties of the higher dimensional dS/AdS black holes in Einstein-bumblebee gravity theory

We study the greybody factors, quasinormal modes, and shadow of the higher dimensional de-Sitter (dS)/anti de-Sitter (AdS) black hole spacetimes derived from the Einstein-bumblebee gravity theory within the Lorentz symmetry breaking (LSB) framework. We specifically apply the semi-analytical WKB method and the time domain approach to study the scalar and Dirac perturbations of the black hole. In-depth researches are done on the effects of the LSB and dimensionality on the bosonic/fermionic greybody factors, quasinormal modes, and shadow of the higher dimensional bumblebee black hole. The results obtained are discussed, tabulated, and illustrated graphically.

Accretion of the Vlasov gas onto a Schwarzschild-like black hole

We consider spherical steady accretion of the relativistic Vlasov gas onto a Schwarzschild-like black hole. We determine the expressions for the particle current density and accretion rate and present the limiting expressions for the mass accretion rate at high and low temperature. The results show that the parameter characterizing the breaking of Lorentz symmetry can affects the radial component of the particle current density and the mass accretion rate.

Lorentz symmetry and IR structure of the BFSS matrix model

The BFSS matrix model relates flat space M-theory to a large N limit of matrix quantum mechanics describing N non-relativistic D0-branes. M-theory, being a theory of gravity in flat space, has a rich infrared structure that includes various soft theorems and an infinite set of conserved charges associated to asymptotic symmetries. In this work, we ask: to what extent is this infrared structure present in BFSS? We find that all the salient features concerning the infrared structure of M-theory carry over naturally to the quantum mechanics dual. Moreover, we demonstrate that the dual statement of the soft graviton theorem in the matrix model implies that D0-brane scattering amplitudes in BFSS enjoy the full 11d Lorentz symmetry of M-theory, a claim which has been long anticipated. We also offer several first-principle consistency checks for our findings, including a computation of the soft theorem which does not presuppose the BFSS duality and a non-trivial match between several known symmetries of M-theory and BFSS that appear naturally in this formalism. These calculations give non-perturbative evidence in support of the BFSS duality as a model of flat space holography.

Investigating the effects of Lorentz Invariance Violation on the CP-sensitivities of the Deep Underground Neutrino Experiment

The phenomena of neutrino oscillations offer a great potential for probing new-physics beyond the Standard Model. Any additional effects on neutrino oscillations can help understand the nature of the non-standard effects. The violation of fundamental symmetries may appear as a probe for new-physics in various neutrino experiments. Lorentz symmetry is one such fundamental symmetry in nature and the breakdown of spacetime is a possible motivation for a departure from the standard Lorentz symmetry picture. The Lorentz invariance violation (LIV) is intrinsic in nature and its effects exist even in a vacuum. Neutrinos can be an intriguing probe for exploring such violations of Lorentz symmetry. The effect of violation of Lorentz invariance can be explored through its impact on the neutrino oscillation probabilities. The effect of LIV is treated as a perturbation to the standard neutrino Hamiltonian considering the Standard Model Extension (SME) framework. In this work, we have probed the effects of LIV on the measurement of neutrino oscillation parameters considering Deep Underground Neutrino Experiment (DUNE) as a case study. The inclusion of LIV affects the measurements of various neutrino oscillation parameters as it modifies the standard neutrino oscillation probabilities. We looked into the capability of DUNE in constraining the LIV parameters and then explored the impact of CPT-violating LIV terms on the mass-induced neutrino oscillation probabilities. We have also probed the impact of LIV parameters on the CP-measurement sensitivities at DUNE.

Lorentz and gauge invariance of quantum space

Motivated by the generalized uncertainty principle, we derive a discrete picture of the space that respects Lorentz symmetry as well as gauge symmetry by setting an equivalency between the linear Generalized Uncertainty Principle (GUP) correction term and electromagnetic interaction term in the Dirac equation. We derived a wave function solution that satisfies this equivalency. This discreteness may explain the crystal and quasicrystal structures observed in nature at different energy scales.

Prospects for the detection rate of very-high-energy γ-ray emissions from short γ-ray bursts with the HADAR experiment* *Supported by the National Natural Science Foundation of China (12263004, 12263005, 12275279).

The observation of short gamma ray bursts (SGRBs) in the TeV energy range plays an important role in understanding the radiation mechanism and probing potential new physics, such as Lorentz invariance violation (LIV). However, no SGRBs have been observed in this energy range owing to the short duration of SGRBs and the weakness of current experiments. New experiments with new technology are required to detect the very high energy (VHE) emission of SGRBs. In this study, we simulate the VHE γ-ray emissions from SGRBs and calculate the annual detection rate with the High Altitude Detection of Astronomical Radiation (HADAR) experiment. First, a set of pseudo-SGRB samples is generated and checked using the observations of the Fermi-GBM, Fermi-LAT, and Swift-BAT measurements. The annual detection rate is calculated from these SGRB samples based on the performance of the HADAR instrument. As a result, the HADAR experiment can detect 0.5 SGRBs per year if the spectral break-off of γ-rays caused by the internal absorption and Klein-Nishina (KN) effect is larger than 100 GeV. For a GRB090510-like GRB in HADAR's view, it should be possible to detect approximately 2000 photons considering the internal absorption and KN effect. With a time delay assumption due to LIV effects, a simulated light curve of GRB090510 has evident energy dependence. We hope that the HADAR experiment can perform SGRB observations and test our calculations in the future.

Rotating BTZ-like black hole and central charges in Einstein-bumblebee gravity

We obtain an exact rotating BTZ-like black hole solution by solving the corresponding gravitational field equations and the bumblebee motion equations in Einstein-bumblebee gravity theory. Result is presented for the purely radial Lorentz symmetry violating and can only exist with a linear functional potential of the bumblebee field. This black hole has two horizons and an ergosphere which are dependent on the bumblebee coupling constant ell . The concepts of the area and volume of the horizon should be renewed in this LV spacetime due to the nontrivial contribution of coupling between the bumblebee field and the Ricci tensor. Only in this way, the entropy-area relation, first law of thermodynamics and the Smarr formula can still be constructed. We also study the AdS/CFT correspondence of this black hole, find that the entropy product of its inner and outer horizons is universal. So the central charges of the dual CFT on the boundary can be obtained via the thermodynamic method, and they can reappear black hole mass and angular momentum in the bulk.

The geometrical meaning of the Weitzenböck connection

In the literature, there are many discussions about the local Lorentz invariance of modified teleparallel gravity. This symmetry is obviously violated in the classical “pure tetrad” formulation of the theory, while it gets restored in the “fully covariant” approach. My claim is that, despite many heated discussions, the two formulations are just equivalent. The purpose of this note is to argue that the local Lorentz invariance is not natural for the modified teleparallel theories at all, making the pure tetrad approach more fundamentally justified.

Comprehensive study of Lorentz invariance violation in atmospheric and long-baseline experiments

Comprehensive study of Lorentz invariance violation in atmospheric and long-baseline experiments

A Lorentz-violating low-energy model for the bilayer graphene

In this work, we propose a model with Lorentz symmetry violation which describes the electronic low energy limit of the AA-bilayer graphene (BLG) system. The AA-type bilayer is known to preserve the linear dispersion relation of the graphene layer in the low energy limit. The theoretical model shows that in the BLG system, a time-like vector can be associated with the layer separation and contributes to the energy eigenstates. Based on these properties, we can describe in a $(2+1)$-dimensional space-time the fermionic quasi-particles that emerge in the low-energy limit with the introduction of a Lorentz-violating parameter, in analogy with the $(3 + 1)$-dimensional Standard Model Extension (SME). Moreover, we study the consequences of the coupling of these fermionic quasi-particles with the electromagnetic field, and we show via effective action that the low-energy photon acquires a massive spectrum. Finally, using the hydrodynamic approach in the collisionless limit, one finds that the LSV generates a new kind of anomalous thermal current to the vortexes of the system via coupling of the LSV vector.

Born reciprocity and relativistic generalized uncertainty principle in Finsler structure: Fundamental tensor in discretized curved spacetime

The main findings of the generalized uncertainty principle (GUP), the phenomenological approach, for instance, the emergence of a minimal measurable length uncertainty, are obtained in various versions from theories of quantum gravity, such as string theory, loop quantum gravity, doubly special relativity and black hole physics. GUP counts for impacts of relativistic energies and finite gravitational fields on the fundamental theories of quantum mechanics (QM), the noncommutation and measurement uncertainty. Utilizing GUP in reconciling principles of general relativity (GR) and QM, thereby enables to draw convincing conclusions about quantum gravity. To resolve the shortcuts reported with the nonrelativistic three-dimensional GUP, namely, violation of Lorentz covariance, dependence on frame of reference, and violation of the linear additional law of momenta, we introduce relativistic four-dimensional generalized uncertainty principle (RGUP) to curved spacetime. To unify GR and QM, we apply the Born reciprocity principle (BRP), distance-momentum duality symmetry and RGUP to estimate the fundamental tensor in discretized curved spacetime. To this end, we generalize Riemann geometry. The Finsler geometry, which is characterized by manifold and Finsler structure, allows to directly apply RGUP to the Finsler structure of a free particle so that [Formula: see text] can be expressed as [Formula: see text], from which the metric tensor in discretized Riemann spacetime could be deduced. We conclude that [Formula: see text] is homogeneous with degree [Formula: see text] in [Formula: see text], while [Formula: see text] is [Formula: see text]-homogeneous resulting in [Formula: see text]. Despite, the astonishing similarity with the conformal transformation, know as Weyl tensor, this study suggests that principles of QMs could be unambiguously imposed on the resulting fundamental tensor. Also, we conclude that the features of Finsler geometry assumed in this study are likely the ones of the duel Hamilton geometry.

Quasinormal modes and bounding greybody factors of GUP-corrected black holes in Kalb–Ramond gravity

The vacuum expectation value of the non-minimally coupled Kalb–Ramond (KR) field leads to spontaneous local Lorentz symmetry violation, and static spherically symmetric solutions exist. In this study, we study the quasinormal modes (QNMs) of modified black holes in non-minimally coupled KR gravity. We employ a higher-order Padé averaged WKB method to compute the QNMs for scalar, electromagnetic, and gravitational perturbations. In order to account for quantum corrections, we examine the geometric characteristics of the horizon and QNMs by introducing the generalized uncertainty principle (GUP). Additionally, we shed light on the impact of the Lorentz violating parameters on our findings and estimate QNMs for different perturbations. Further, we estimate bounds on the greybody factors for the modified and GUP-corrected black holes. Our findings reveal the influence of the Lorentz violating parameters in the model on the QNM frequencies and their reliance on the GUP parameters.

Balancing act: Multivariate rational reconstruction for IBP

We address the problem of unambiguous reconstruction of rational functions of many variables. This is particularly relevant for recovery of exact expansion coefficients in integration-by-parts identites (IBPs) based on modular arithmetic. These IBPs are indispensable in modern approaches to evaluation of multiloop Feynman integrals by means of differential equations. Modular arithmetic is far more superior to algebraic implementations when one deals with high-multiplicity situations involving a large number of Lorentz invariants. We introduce a new method based on balanced relations which allows one to achieve the goal of a robust functional restoration with minimal data input. The technique is implemented as a Mathematica package Reconstruction.m in the FIRE6 environment and thus successfully demonstrates a proof of concept.

Constraining quantum fluctuations of spacetime foam from BBN

A possibility to describe quantum gravitational fluctuations of the spacetime background is provided by virtual $D$-branes. These effects may induce a tiny violation of the Lorentz invariance (as well as a possible violation of the equivalence principle). In this framework, we study the formation of light elements in the early Universe (Big Bang Nucleosynthesis). By using the Big Bang Nucleosynthesis observations, We infer an upper bound on the topological fluctuations in the spacetime foam vacuum $\sigma^2$, given by $\sigma^2 \lesssim 10^{-22}$.

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.

Paths to gravitation via the gauging of parametrized field theories

In special-relativistic physics, spacetime is imbued with a fixed, non-dynamical metric tensor. A path to gravitational theory is to promote this tensor to a genuine dynamical field. An alternative description of special-relativistic physics involves no fixed geometry but instead the inclusion of scalar fields $X^{I}(x^{\mu})$ which dynamically may take the form of inertial coordinates in spacetime. This suggests an alternative approach to gravity where the invariance of actions under global Poincar\'{e} transformations of $X^{I}$ is promoted to either a local Poincar\'{e} or local Lorentz symmetry via the introduction of gauge fields. Points of commonality and departure of the resulting gravitational theories as compared to General Relativity are discussed. It is shown that the model based on local Lorentz symmetry is an extension of General Relativity that can introduce a standard of time into the dynamics of the gravitational field and allows for spacetimes described by a Minkowski metric or flat Euclidean signature metric despite the gravitational gauge field possessing non-zero curvature.

Groups of Coordinate Transformations between Accelerated Frames

The analysis of the present paper reveals that, besides the relativistic symmetry expressed by the Lorentz group of coordinate transformations which leave invariant the Minkowski metric of space-time of inertial frames, there exists one more relativistic symmetry expressed by a group of coordinate transformations leaving invariant the space-time metric of the frames with a constant proper-acceleration. It is remarkable that, in the flat space-time, only those two relativistic symmetries, corresponding to groups of continuous transformations leaving invariant the metric of space-time of extended rigid reference frames, exist. Therefore, the new relativistic symmetry should be considered on an equal footing with the Lorentz symmetry. The groups of transformations leaving invariant the metric of the space-time of constant proper-acceleration are determined using the Lie group analysis, supplemented by the requirement that the group include transformations to or from an inertial to an accelerated frame. Two-parameter groups of two-dimensional (1 + 1), three-dimensional (2 + 1), and four-dimensional (3 + 1) transformations, with the group parameters related to the ratio of accelerations of the frames and the relative velocity of the frame space origins at the initial moment, can be considered as counterparts of the Lorentz group of corresponding dimensions. Defining the form of the interval and the groups of coordinate transformations satisfying the relativity principle paves the way to defining the invariant forms of the laws of dynamics and electrodynamics in accelerated frames. Thus, the problem of extending the relativity principle from inertial to uniformly accelerated frames has been resolved without use of the equivalence principle and/or the general relativity equations. As an application of the transformations to purely kinematic phenomena, the problem of differential aging between accelerated twins is treated.

Cellular automaton for spinor gravity in four dimensions

Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four dimensions. Local Lorentz symmetry is exact on the discrete level and diffeomorphism symmetry emerges in the naive continuum limit. Our setting could serve as a model for quantum gravity if diffeomorphism symmetry is realized in the true continuum limit and suitable collective fields for vierbein and metric acquire non-vanishing expectation values. The discussion of this interesting specific model reveals may key qualitative features of the continuum limit for probabilistic cellular automata. This limit obtains for a very large number of cells if the probabilistic information is sufficiently smooth. It is associated to coarse graining. The automaton property that every bit configuration is updated at every discrete time step to precisely one new bit configuration does no longer hold on the coarse grained level. A coarse grained configuration of occupation numbers can evolve into many different configurations with certain probabilities. This characteristic feature of quantum field theories can come along with the emergence of continuous space-time symmetries.

Effects of the Lorentz Symmetry Violation Caused by the Coupling Between the Vector Field $$f^{\mu }\gamma ^{5}$$ and the Derivative of the Fermionic Field on the Modified Pöschl-Teller, Woods-Saxon and Harmonic Oscillator Potentials

Effects of the Lorentz Symmetry Violation Caused by the Coupling Between the Vector Field $$f^{\mu }\gamma ^{5}$$ and the Derivative of the Fermionic Field on the Modified Pöschl-Teller, Woods-Saxon and Harmonic Oscillator Potentials