We construct a model of dark energy with a technically natural small contribution to cosmic acceleration, i.e. this contribution does not receive corrections from other scales in the theory. The proposed acceleration mechanism appears generically in the low-energy limit of gravity theories with violation of Lorentz invariance that contain a derivatively coupled scalar field Theta. The latter may be the Goldstone field of a broken global symmetry. The model, that we call Theta-CDM, is a valid effective field theory up to a high cutoff just a few orders of magnitude below the Planck scale. Furthermore, it can be ultraviolet-completed in the context of Horava gravity. We discuss the observational predictions of the model. Even in the absence of a cosmological constant term, the expansion history of the Universe is essentially indistinguishable from that of Lambda-CDM. The difference between the two theories appears at the level of cosmological perturbations. We find that in Theta-CDM the matter power spectrum is enhanced at subhorizon scales compared to Lambda-CDM. This property can be used to discriminate the model from Lambda-CDM with current cosmological data.
It is shown that a spontaneously-broken gauge theory of the Lorentz group contains Ashtekar's chiral formulation of General Relativity accompanied by dust. From this perspective, gravity is described entirely by a connection $ω$ valued in the Lie algebra of the complexified Lorentz group and a Lorentz-charged scalar field $τ$. The model is "pre-geometric" in the sense that the spacetime metric may be constructed only in the symmetry-broken regime. We speculate on the extent to which this dust may account for dark matter and on the behaviour of the theory in regimes where the symmetry is not br…
We continue the study of covariant power-counting renormalizable gravity constrained by scalar Lagrange multiplier. Lorentz symmetry breaking is investigated in such a theory in comparison with the one in ghost condensation model. Covariant power-counting renormalizable vector gravity which is invariant under $U(1)$ gauge symmetry is proposed. Several forms of vector Lagrange multiplier in this theory are discussed. It is shown that covariant scalar/vector gravity under consideration may have power-law or de Sitter accelerating cosmological solution corresponding to inflationary era. Simplest …
A scalar field can be inserted in Maxwell and/or Einstein theory to effect symmetry breaking. Consequences of such a modification are discussed. Possible dynamics for the scalar field are presented.
In this book, we review various aspects of the Lorentz symmetry breaking, both classical and quantum ones, with the special interest to perturbative generation of Lorentz-breaking terms. We present impacts of Lorentz symmetry breaking in noncommutative and supersymmetric theories. Also, we discuss the problem of Lorentz symmetry breaking in a curved space-time. The book is closed with a review of experimental studies of Lorentz symmetry breaking.
We obtain an exact Kerr-like black hole solution by solving the corresponding gravitational field equations in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking. In order to study the effects of this breaking, we consider the black hole shadow and find that the radial of the unstable spherical orbit on the equatorial plane $r_c$ decreases with the Lorentz breaking constant $\ell>0$, and increases with $\ell<0$. These shifts are similar to …
We investigate the possibility of the acoustic superresonance phenomenon (analog to the superradiance in black hole physics), i.e., the amplification of a sound wave by reflection from the ergoregion of a rotating acoustic black hole with Lorentz symmetry breaking. For rotating black holes the effect of superradiance corresponds to the situation where the incident waves has reflection coefficient greater than one, and energy is extracted from them. For an acoustic Kerr-like black hole its rate of loss of mass is affected by the Lorentz symmetry breaking. We also have shown that for suitable va…
In the context of modified teleparallel gravity, we study the generation of primordial density fluctuations in a general scalar-torsion theory whose Lagrangian density is an arbitrary function $f(T,ϕ)$ of the torsion scalar $T$ and a scalar field $ϕ$, plus the kinetic term of this latter. It is well known that generic modifications of teleparallel gravity are not invariant under six-parameter local Lorentz transformations. In order to restore the local Lorentz symmetry, we have incorporated six additional degrees of freedom in the form of Goldstone modes of the symmetry breaking through a Lore…
A systematic study of the different phases of Lorentz-breaking massive gravity in a curved background is performed. For tensor and vector modes, the analysis is very close to that of Minkowski space. The most interesting results are in the scalar sector where, generically, there are two propagating degrees of freedom (DOF). While in maximally symmetric spaces ghost-like instabilities are inevitable, they can be avoided in a FRW background. The phases with less than two DOF in the scalar sector are also studied. Curvature allows an interesting interplay with the mass parameters; in particular, …
Spontaneous breaking of Lorentz symmetry has been suggested as a possible mechanism that might occur in the context of a fundamental Planck-scale theory, such as string theory or a quantum theory of gravity. However, if Lorentz symmetry is spontaneously broken, two sets of questions immediately arise: what is the fate of the Nambu-Goldstone modes, and can a Higgs mechanism occur? A brief summary of some recent work looking at these questions is presented here.
In this paper, we consider the perturbative generation of the CPT-even aether-like Lorentz-breaking term in the extended Lorentz-breaking QED within different approaches and discuss its ambiguities.
In this paper, phase transition of AdS black holes in lorentz breaking massive gravity has been studied in the framework of holography. We find that there is a first order phase transition(FPT) and second order phase transition(SPT) both in Bekenstein-Hawking entropy(BHE)-temperature plane and holographic entanglement entropy(HEE)-temperature plane. Furthermore, for the FPT, the equal area law is checked and for the SPT, the critical exponent of the heat capacity is also computed. Our results confirm that the phase structure of HEE is similar to that of BHE in lorentz breaking massive gravity,…
This talk briefly explains how the breaking of a Lorentz-invariant description of nature at tiny space-time intervals might affect the non-Gaussian character of the primordial fluctuations left by inflation. For example, a model that contains irrelevant operators that only preserve the spatial symmetries along constant-time surfaces can generate a larger non-Gaussian component in the pattern of primordial fluctuations than is ordinarily predicted by inflation. This property can be useful for constraining models that allow some Lorentz violation at short distances, beyond the constraints possib…
Perturbative expansions of relativistic quantum field theories typically contain ultraviolet divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. We shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory, and discuss its impl…
In this paper, we consider the finite temperature behaviour of the CPT-even aether-like Lorentz-breaking term in the extended Lorentz-breaking QED and demonstrate that its ambiguities whose presence has been shown earlier in the zero temperature case stay also at the finite temperature.
Within the superfield approach, we formulate the superfield supersymmetric aether-like Lorentz-breaking models, both in three- and in four-dimensional cases.
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 …
In this paper, we use gauge embedding procedure and master action approach to establish the equivalence between the self-dual and Maxwell-Chern-Simons models with Lorentz symmetry breaking. As a result, new kinds of Lorentz-breaking terms arise.
The four dimensional Lorentz-breaking finite and determined Chern-Simons like action is generated as a one loop perturbative correction via an appropriate Lorentz-breaking coupling of the gauge field with the spinor field. Unlike the known schemes of calculations, within this scheme this term is found to be regularization independent.
We set up a covariant renormalisation group equation on a foliated spacetime which preserves background diffeomorphism symmetry. As a first application of the new formalism, we study the effect of quantum fluctuations in Lorentz symmetry breaking theories of quantum gravity. It is found that once a small breaking is introduced e.g. at the Planck scale, quantum fluctuations enhance this breaking at low energies. A numerical analysis shows that the magnification is of order unity for trajectories compatible with a small cosmological constant. The immediate consequence is that the stringent obser…
The lagrangian-based Standard-Model Extension framework offers a broad description of possible gravitational effects from local Lorentz violation. In this talk, I review the status of the theoretical and phenomenological work in this area. The extension of previous results in linearized gravity to the nonlinear regime is discussed.
In this paper we derive acoustic black hole metrics in the (3+1) and (2+1)-dimensional Abelian Higgs model with Lorentz symmetry breaking. In this set up the sound waves lose the Lorentz boost invariance and suffer a 'birefringence' effect. We have found acoustic black holes and respective Hawking temperatures depending on the Lorentz violating parameter. Furthermore, we obtain an acoustic Kerr-like black hole metric with the Lorentz violating term affecting its rate of loss of mass. We also have shown that for suitable values of the Lorentz violating parameter a wider spectrum of particle wav…
We study the vacuum solutions of a gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking (LSB), radial/temporal LSB and axial/temporal LSB. The purely radial LSB result corresponds to new black hole solutions. When possible, Parametrized Post-Newtonian (PPN) parameters are computed and observational boundaries used to constrain the Lorentz symmetry breaking scale.
We study the effect of spontaneous breaking of Lorentz invariance on black hole thermodynamics. We consider a scenario where Lorentz symmetry breaking manifests itself by the difference of maximal velocities attainable by particles of different species in a preferred reference frame. The Lorentz breaking sector is represented by the ghost condensate. We find that the notions of black hole entropy and temperature loose their universal meaning. In particular, the standard derivation of the Hawking radiation yields that a black hole does emit thermal radiation in any given particle species, but w…
We consider some aspects of spontaneous breaking of Lorentz Invariance in field theories, discussing the possibility that the certain tensor operators may condensate in the ground state in which case the tensor Goldstone particles would appear. We analyze their dynamics and discuss to which extent such a theory could imitate the gravity. We are also interested if the universality of coupling of such `gravitons' with other particles can be achieved in the infrared limit. Then we address the more complicated models when such tensor Goldstones coexist with the usual geometrical gravitons. At the …
This paper is devoted to investigating the interactions between stationary sources of the electromagnetic field, in a model which exhibits explicit Lorentz-symmetry breaking due to the presence of a single background vector. We focus on physical phenomena that emerge from this kind of breaking and which have no counterpart in Maxwell Electrodynamics.
In the Ashtekar-Barbero formulation of canonical general relativity based on an SU(2) connection, Lorentz covariance is a subtle issue which has been the focus of some debate. Here we present a Lorentz covariant formulation generalising the notion of a foliation of spacetime to a field of local observers which specify a time direction only locally. This field spontaneously breaks the local SO(3,1) symmetry down to a subgroup SO(3); we show that the apparent symmetry breaking to SO(3) is not in conflict with Lorentz covariance. We give a geometric picture of our construction as Cartan geometrod…
In Vaidya-Bonner de Sitter Black hole space-time, the tunneling radiation characteristics of fermions and bosons are corrected by taking Lorentz symmetry breaking theory into account. The corresponding gamma matrices and ether-like field vectors of the black hole are constructed, then the new modified form of Dirac equation for the fermion with spin 1/2 and the new modified form of Klein-Gordon equation for boson in the curved space-time of the black hole are obtained. Through solving the two equations, new and corrected expressions of surface gravity, Hawking temperature and tunneling rate of…
We propose UV complete (Partially) Composite Higgs models with compositeness scale up to the Planck scale assisted by a novel mechanism. This mechanism is based on softly breaking a global $ \mathbb{Z}_2 $ symmetry by technically natural small vacuum misalignment, dynamically triggering the electroweak symmetry breaking and Standard Model fermion mass generation. This mechanism can be present in various models based on vacuum misalignment. For concreteness, we demonstrate it in a minimal partially composite two-Higgs scheme, where the Higgs is a mixture of a composite and an elementary state, …
A four-dimensional Lorentz-breaking non-Abelian Chern-Simons like action is generated as a one-loop perturbative correction via an appropriate Lorentz-breaking coupling of the non-Abelian gauge field to the spinor field. This term is shown to be regularization dependent but nevertheless it can be found unambiguously in different regularization schemes at zero and finite temperature.
We consider new issues of duality in four-dimensional Lorentz-breaking field theories. In particular, we demonstrate that the arising of the aether-like Lorentz-breaking term is necessary in order for the 4D models to display the duality analog between the MCS and self-dual models in 3D. We further study the dispersion relations in both theories and discuss the physical contents of the models involved in this new dualilty.
It is shown the existence of a static self-dual semilocal vortex configuration for the Maxwell-Higgs system with a Lorentz-violating CPT-even term. The dependence of the vorticity upper limit on the Lorentz-break term is also investigated.
In this paper, we investigate the thermal effect on the Casimir energy associated with a massive scalar quantum field confined between two large parallel plates in a CPT-even, aether-like Lorentz-breaking scalar field theory. In order to do that we consider a nonzero chemical potential for the scalar field assumed to be in thermal equilibrium at some finite temperature. The calculations of the energies are developed by using the Abel-Plana summation formula, and the corresponding results are analyzed in several asymptotic regimes of the parameters of the system, like mass, separations between …
We demonstrate the generation of the CPT-even, aether-like Lorentz-breaking actions for the scalar and electromagnetic fields via their appropriate Lorentz-breaking coupling to spinor fields in three, four and five space-time dimensions. Besides, we show that the aether-like terms for the spinor field also can be generated as a consequence of the same couplings. Also we discuss the dispersion relations in the theories with aether-like Lorentz-breaking terms and find the tree-level effective (Breit) potential for fermion scattering and the one-loop effective potential corresponding to the actio…
We extend a result by Ojima on spontaneous symmetry breaking of Lorentz boosts in thermal (KMS) states and show that it is in fact a special case in a more general class of examples of spontaneous symmetry breaking of Lorentz symmetry in relativistic many-body systems. Furthermore we analyse the nature of the corresponding Goldstone phenomenon and the type of Goldstone excitations (provided they have particle character).
The first one-loop higher-derivative contribution to the effective action of the Lorentz-breaking spinor QED is obtained and shown to be finite and ambiguous.
We present a Lorentz-breaking supersymmetric algebra characterized by a critical exponent $z$. Such construction requires a non trivial modification of the supercharges and superderivatives. The improvement of renormalizability for supersymmetric scalar QED is shown and the Kählerian effective potentials are calculated in different cases. We also show how the theory flows naturally to the Lorentz symmetric case at low energies.
In this paper, we describe the perturbative generation of the higher-derivative Lorentz-breaking terms for the gauge field, that is, the Myers-Pospelov term and the higher-derivative Carroll-Field-Jackiw term. These terms are explicitly calculated in the one-loop approximation and shown to be finite and ambiguous.
In this paper, we study the spontaneous Lorentz symmetry breaking for a four-dimensional massless four-fermion model. Our methodology is based on use of the rationalized propagator. We show that a bumblebee potential arises as a result of one-loop calculations and displays nontrivial minima. Also we demonstrate that a phase transition restoring Lorentz invariance can occur at a finite temperature.
One kind of spontaneous (2+1)-dimensional Lorentz symmetry breaking is discussed. The symmetry breaking pattern is $SO(2,1)\rightarrow SO(1,1)$. Using the coset construction formalism, we derive the Goldstone covariant derivative and the associated covariant gauge field. Finally, the two-derivative low-energy effective action of the Nambu-Goldstone bosons is obtained.
In this work, we discuss the relativistic Landau-He-McKellar-Wilkens quantization and relativistic bound states solutions for a Dirac neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present new possible scenarios of studying Lorentz symmetry breaking effects by fixing the space-like vector field background in special configurations. It is worth mentioning that we use the criterion for studying the violation of Lorentz symmetry is that the gauge symmetry should be preserved.
The propagation of electromagnetic waves in a Lorentz-symmetry violating scenario where there is a region of polarized vacuum is studied. It turns out that the photon field acquires an interesting polarization state, possibly useful to set up upper bounds in Lorentz-violating models at laboratory scales.
In this paper we deal with the issue of Lorentz symmetry breaking in quantum field theories formulated in a non-commutative space-time. We show that, unlike in some recente analysis of quantum gravity effects, supersymmetry does not protect the theory from the large Lorentz violating effects arising from the loop corrections. We take advantage of the non-commutative Wess-Zumino model to illustrate this point.
A scenario is presented on how to shift the predicted cutoff in the cosmic ray spectrum at 10**20 eV, called the Greisen-Zatsepin-Kuzmin limit (GKZ), to larger energies without breaking the Lorentz invariance. The formulation is based on a pseudo-complex extension of standard field theory. The dispersion relation of particles can be changed, leading to a modification of the GKZ limit. Maximal shifts are determined.
Some traces of a specific Lorentz symmetry breaking scenario in the ground state of the Hydrogen atom are investigated. It is used standard Rayleigh-Schrödinger perturbation theory in order to obtain the corrections to the the ground state energy and wave function. It is shown that an induced four-pole moment arises, due to the Lorentz symmetry breaking. The model considered is the one studied in reference Eur. Phys. J. C {\bf 74}, 2937 (2014), where the Lorentz symmetry is broken in the electromagnetic sector.
In this work, we present two possible venues to accomodate the $K_{F}$-type Lorentz-symmetry violating Electrodynamics in an $N=1$-supersymmetric framework. A chiral and a vector superfield are chosen to describe the background that signals Lorentz-symmetry breaking. In each case, the $\ K_{μνκλ}$-tensor is expressed in terms of the components of the background superfield that we choose to describe the breaking. We also present in detail the actions with all fermionic partners of the background that determine $\ K_{μνκλ}$.
A method is presented for deducing classical point-particle Lagrange functions corresponding to a class of quartic dispersion relations. Applying this to particles violating Lorentz symmetry in the minimal Standard-Model Extension leads to a variety of novel lagrangians in flat spacetime. Morphisms in these classical systems are studied that echo invariance under field redefinitions in the quantized theory. The Lagrange functions found offer new possibilities for understanding Lorentz-breaking effects by exploring parallels with Finsler-like geometries.
We construct an action which is invariant under the foliation preserving diffeomorphism from the Einstein Hilbert action. Starting from the Einstein Hilbert action, we introduce the gauge invariance under the anisotropic rescaling by using the Stückelberg method. We then introduce the gauge field corresponds to the anisotropic rescaling, and the Stückelberg field turns out to be the Nambu-Goldstone boson. The Nambu-Goldstone boson, however, is not completely eaten by the massive gauge field and the Nambu-Goldstone boson can be integrated out from the action. Then the resultant action is a Hora…
We consider the two-point function of the gauge field in Lorentz-breaking theories with higher-derivative extension of the Dirac Lagrangian. We show that the Carroll-Field-Jackiw term naturally arises in this theory as a quantum correction being perfectly finite and thus displaying no ambiguities. Also, the finiteness of this term at low energy limit and the absence of large Lorentz violating corrections allows to avoid the fine-tuning problem.
In this paper, we study a CPT-even Lorentz-breaking extension of the scalar QED. For this theory, we calculate the one-loop lower-order contributions in the Lorentz-violating parameters to the two-point functions of scalar and gauge fields. We found that the two background tensors, coming from the two sectors (scalar and gauge) are mixed in the one-loop corrections both in finite and divergent parts. This shows that these two Lorentz-breaking terms cannot be studied in an isolated form. Besides, the results in the gauge sector are confirmed to be transversal.
We calculate explicitly the one-loop effective potential in different Lorentz-breaking field theory models. First, we consider a Yukawa-like theory and, then, some examples of Lorentz-violating extensions of scalar QED. We observed, for the extended QED models, that the resulting effective potential converges to the known result in the limit in which Lorentz-symmetry is restored. Besides, the one-loop corrections to the effective potential in all the cases we studied depend on the background tensors responsible for the Lorentz symmetry violation. This have consequences in physical quantities l…
In a 4D four-fermion model we study the dynamical restoration of Lorentz and CPT symmetries at finite temperature. We evaluate the gap equation both at zero and at finite temperature and observe that, depending on the parameters of the theory, there is a critical temperature at which the Lorentz and CPT symmetries are restored.
