Breaking Of Space-time Symmetry Research Articles

Dynamical dark energy from spacetime-symmetry breaking — Late-time behaviour and phantom crossing

We investigate the late-time cosmological dynamics in a simple case of explicit spacetime-symmetry breaking. By expanding in a small symmetry-breaking coefficient we are able to write the Friedmann equations as ΛCDM + dynamical dark energy, which we show contains logarithmic dependence of the scale factor. We find that the dark energy equation of state displays divergencies and phantom behaviour for certain values of the symmetry-breaking coefficient, where the NEC is also broken. We discuss the adiabatic sound speed of dark energy and compare the model to current constraints using the Chevallier–Polarski–Linder parametrisation. Remarkably, although the constraints on the same symmetry-breaking coefficient from e.g. gravitational-wave propagation are orders of magnitude stronger than what we obtain in this paper, we are able to cut those constraints, which are more or less symmetric around zero, in half by showing that same coefficient must be negative (or zero) if one wishes to keep the NEC intact.

Spacetime symmetry breaking effects in gravitational-wave generation at the first post-Newtonian order

Spacetime symmetry breaking effects in gravitational-wave generation at the first post-Newtonian order

Spontaneous and Explicit Spacetime Symmetry Breaking in Einstein–Cartan Theory with Background Fields

Explicit and spontaneous breaking of spacetime symmetry under diffeomorphisms, local translations, and local Lorentz transformations due to the presence of fixed background fields is examined in Einstein–Cartan theory. In particular, the roles of torsion and violation of local translation invariance are highlighted. The nature of the types of background fields that can arise and how they cause spacetime symmetry breaking is discussed. With explicit breaking, potential no-go results are known to exist, which if not evaded lead to inconsistencies between the Bianchi identities, Noether identities, and the equations of motion. These are examined in detail, and the effects of nondynamical backgrounds and explicit breaking on the energy–momentum tensor when torsion is present are discussed as well. Examples illustrating various features of both explicit and spontaneous breaking of local translations are presented and compared to the case of diffeomorphism breaking.

Space-time symmetry breaking in nonequilibrium frustrated magnetism

Spontaneous symmetry breaking is responsible for rich phenomena in equilibrium physics. Driving a system out-of-equilibrium can significantly enrich the possibility of spontaneous symmetry breaking, which occurs not only in space, but also in the time domain. This study investigates a driven-dissipative frustrated magnetic system with alternate ferromagnetic and antiferromagnetic coupling. Results show that frustration in such a far-from-equilibrium system could lead to nonequilibrium phases with intriguing space-time symmetry breaking, e.g., a discrete time crystal accompanied by a time-dependent magnetism with alternating tripartite stripe and ferromagnetic orders.

Search for anisotropic, birefringent spacetime-symmetry breaking in gravitational wave propagation from GWTC-3

An effective field theory framework, the Standard-Model Extension, is used to investigate the existence of Lorentz and CPT-violating effects during gravitational wave propagation. We implement a modified equation for the dispersion of gravitational waves, that includes isotropic, anisotropic and birefringent dispersion. Using the LIGO-Virgo-KAGRA algorithm library suite, we perform a joint Bayesian inference of the source parameters and coefficients for spacetime symmetry breaking. From a sample of 45 high confidence events selected in the GWTC-3 catalog, we obtain a maximal bound of $3.19 \times 10^{-15}$~m at 90\% CI for the isotropic coefficient $k_{(V)00}^{(5)}$ when assuming the anisotropic coefficients to be zero. The combined measurement of all the dispersion parameters yields limits on the order of $10^{-13}$~m for the 16 $k_{(V)ij}^{(5)}$ coefficients. We study the robustness of our inference by comparing the constraints obtained with different waveform models, and find that a lack of physics in the simulated waveform may appear as spacetime symmetry breaking-induced dispersion for a subset of events.

Short-range forces due to Lorentz-symmetry violation

Complementing previous theoretical and experimental work, we explore new types of short-range modifications to Newtonian gravity arising from spacetime-symmetry breaking. The first non-perturbative, i.e. to all orders in coefficients for Lorentz-symmetry breaking, are constructed in the Newtonian limit. We make use of the generic symmetry-breaking terms modifying the gravity sector and examine the isotropic coefficient limit. The results show new kinds of force law corrections, going beyond the standard Yukawa parameterization. Further, there are ranges of the values of the coefficients that could make the resulting forces large compared to the Newtonian prediction at short distances. Experimental signals are discussed for typical test mass arrangements.

Time gel and origin of matter

Standard model and/or QCD broadly envisage operation of a symmetry breaking in creation of mass [1]. Likewise, any phase transition brought about by a critical transition refer to operation of a symmetry breaking [2,3]. Such aspects of symmetry breaking directly follows from Noether's theorem and further implies that in principle, non-equlibrium self-assembly could emulate under correct electrochemical conditions creation of ‘matter’. In this work, we test this earlier conjecture of ours and show with experimental evidence how space-time symmetry breaking emulated by electrochemical realization of a ‘Time-Gel’ in the lab brought about by a critical phenomenon can be explored to demonstrate, at least in principle, origin of matter. The ‘Time-Gel’ is realized by electrochemical induction of a critical phenomenon of ‘gelation’ of discrete molecular precursors, where upon with temporally controlled charge injection/abstraction Q (as an indicator of temporal information) we evidence direct creation of ‘Time-Gel's (a polymer-colloid mixture) ‘mass’ (volume fraction, Φg) from a mass ‘null’ state. ‘Time-Gel's volume fraction (Φg) acts as a descriptor of spatio-temporal information. We observe further the descriptor of temporal information (Q) varies with volume fraction of gel formed (Φg) manifest as spatio-temporal fluctuation with a relation Q∝ Φgn. The order of n, is 5, and is obtained experimentally. Such an exponent in the power law, implies divergence in creation of matter. The above observation implicit in our finding is consistent to existing knowledge of divergent creation of matter as a direct consequence of breaking of symmetry under conditions following directly from Noether's theorem. In short, the present proposition prompted by experimental findings centers around the idea of symmetry breaking, where an experimental realization of a ‘time-gel’ model shows how space-time and charge might have led to the formation of matter under conditions away from equilibrium. ‘Time-Gel’ may thus act as an alternative model based on Chemical Science to explain and envisage the emergence of matter as a direct consequence of Noether's theorem.

Time-Gel

Can creation of matter be modelled? This communication proposes the idea of Time-Gel to address this question. Using existing framework of temporal dynamics of gelation, crystallization, criticality, time-crystal, and the idea of space-time symmetry breaking, with appropriate approximations, it is proposed Time-Gel concept can be used to this end.

Gravity with Explicit Diffeomorphism Breaking

Modified theories of gravity that explicitly break diffeomorphism invariance have been used for over a decade to explore open issues related to quantum gravity, dark energy, and dark matter. At the same time, the Standard-Model Extension (SME) has been widely used as a phenomenological framework in investigations of spacetime symmetry breaking. Until recently, it was thought that the SME was suitable only for theories with spontaneous spacetime symmetry breaking due to consistency conditions stemming from the Bianchi identities. However, it has recently been shown that, particularly with matter couplings included, the consistency conditions can also be satisfied in theories with explicit breaking. An overview of how this is achieved is presented, and two examples are examined. The first is massive gravity, which includes a nondynamical background tensor. The second is a model based on a low-energy limit of Hořava gravity, where spacetime has a physically preferred foliation. In both cases, bounds on matter–gravity interactions that explicitly break diffeomorphisms are obtained using the SME.

Image of the Electron Suggested by Nonlinear Electrodynamics Coupled to Gravity

We present a systematic review of the basic features that were adopted for different electron models and show, in a brief overview, that, for electromagnetic spinning solitons in nonlinear electrodynamics minimally coupled to gravity (NED-GR), all of these features follow directly from NED-GR dynamical equations as model-independent generic features. Regular spherically symmetric solutions of NED-GR equations that describe electrically charged objects have obligatory de Sitter center due to the algebraic structure of stress–energy tensors for electromagnetic fields. By the Gürses-Gürsey formalism, which includes the Newman–Janis algorithm, they are transformed to axially symmetric solutions that describe regular spinning objects asymptotically Kerr–Newman for a distant observer, with the gyromagnetic ratio g=2. Their masses are determined by the electromagnetic density, related to the interior de Sitter vacuum and to the breaking of spacetime symmetry from the de Sitter group. De Sitter center transforms to the de Sitter vacuum disk, which has properties of a perfect conductor and ideal diamagnetic. The ring singularity of the Kerr–Newman geometry is replaced with the superconducting current, which serves as the non-dissipative source for exterior fields and source of the intrinsic magnetic momentum for any electrically charged spinning NED-GR object. Electromagnetic spinning soliton with the electron parameters can shed some light on appearance of a minimal length scale in the annihilation reaction e+e−→γγ(γ).

Supersymmetric space-time symmetry breaking sources

We construct new families of deformed supersymmetric field theories which break space-time symmetries but preserve half of the original supersymmetry. We do this by writing deformations as couplings to background multiplets. In many cases it is important to use the off-shell representation as auxiliary fields of the non-dynamical fields must be turned on to preserve supersymmetry. We also consider backgrounds which preserve some superconformal symmetry, finding scale-invariant field profiles, as well as mathcal{N} = 2 theories on S3. We discuss how this is related to previous work on interface SCFTs and other holographic calculations.

Boosting GWs in supersolid inflation

Inflation driven by a generic self-gravitating medium is an interesting alternative to study the impact of spontaneous spacetime symmetry breaking during a quasi de-Sitter phase, in particular the 4-dimensional diffeomorphism invariance of GR is spontaneously broken down to I SO(3). The effective description is based on four scalar fields that describe the excitations of a supersolid. There are two phonon-like propagating scalar degrees of freedom that mix non-trivially both at early and late times and, after exiting the horizon, give rise to non-trivial correlations among the different scalar power spectra. The non-linear structure of the theory allows a secondary gravitational waves production during inflation, efficient enough to saturate the present experimental bound and with a blue-tilted spectral index.

Regular black holes and self-gravitating solitons replacing naked singularities

We present a systematic review of the basic properties of regular black holes (RBH) and self-gravitating solitons replacing naked singularities including electrically charged RBHs and electromagnetic spinning solitons, predicted by analysis of regular solutions to dynamical equations with metrics of the Kerr-Schild class governing their behavior. We briefly outline observational cases which display and verify their fundamental generic features which are the de Sitter vacuum interiors and relation of their masses to spacetime symmetry breaking.

Effective field theory for acoustic and pseudoacoustic phonons in solids

We present a relativistic effective field theory for the interaction between acoustic and gapped phonons in the limit of a small gap. We show that, while the former are the Goldstone modes associated with the spontaneous breaking of spacetime symmetries, the latter are pseudo-Goldstones associated with some (small) explicit breaking. We hence dub them "pseudo-acoustic" phonons. In this first investigation, we build our effective theory for the cases of one and two spatial dimensions, two atomic species, and assuming large distance isotropy. As an illustrative example, we show how the theory can be applied to compute the total lifetime of both acoustic and pseudo-acoustic phonons. This construction can find applications that range from the physics of bilayer graphene to sub-GeV dark matter detectors.

Nonreciprocal directional dichroism in multiferroics

Nonreciprocal directional dichroism in multiferroics, namely magnetoelectric coupling in the dynamic regime, is endowed with rich physics and promising applications, which are entangled with fundamental physical components, such as spin, orbital, lattice, charge, and topology. Such a linear nonreciprocal response behavior in the GHz-THz frequency range, represented by optical magnetoelectric effect and magnetochiral dichroism, occurs ubiquitously in material systems with the spontaneous breaking of space-time symmetry, and is subject to Onsager’s reciprocal theorem in the thermodynamic limit. Microscopically, these nonreciprocal responses are usually encoded by toroidization (chirality) and electromagnon (quasiparticle), thus establishing a comprehensive understanding of magnetoelectric coupling and irreversible dynamics. Herein, the basic mechanisms and emergent nonreciprocal directional dichroism in single-phase multiferroics are summarized. We expect that the present review will stimulate diverse possibilities toward nonreciprocal directional dichroism within and beyond multiferroics.

The Fundamental Roles of the de Sitter Vacuum

We overview the fundamental roles of the de Sitter vacuum in cosmology where it is responsible for powering the early inflationary stage(s) and the present accelerated expansion, in black hole physics where it provides the existence of a wide class of regular black holes and self-gravitating solitons replacing naked singularities, and in particle physics where it ensures the intrinsic relation of the Higgs mechanism with gravity and spacetime symmetry breaking.

Gravity with explicit spacetime symmetry breaking and the standard model extension

The Standard-Model Extension (SME) is the general phenomenological framework used to investigate Lorentz violation at the level of effective field theory. It has been used to obtain stringent experimental bounds on Lorentz violation in a wide range of tests. In the gravity sector of the SME, it is typically assumed that the spacetime symmetry breaking occurs spontaneously in order to avoid potential conflicts with the Bianchi identities. A post-Newtonian limit as well as matter-gravity couplings in the SME have been developed and investigated based on this assumption. In this paper, the possibility of using the SME to also describe gravity theories with explicit spacetime symmetry breaking is investigated. It is found that in a wide range of cases, particularly when matter-gravity couplings are included, consistency with the Bianchi identities can be maintained, and therefore the SME can be used to search for signals of the symmetry breaking. Two examples with explicit breaking are considered. The first is ghost-free massive gravity with an effective metric that couples to matter. The second is Horava gravity coupled with matter in an infrared limit.

Counting Rules of Nambu–Goldstone Modes

When global continuous symmetries are spontaneously broken, there appear gapless collective excitations called Nambu–Goldstone modes (NGMs) that govern the low-energy property of the system. The application of this famous theorem ranges from high-energy particle physics to condensed matter and atomic physics. When a symmetry breaking occurs in systems that lack the Lorentz invariance to start with, as is usually the case in condensed matter systems, the number of resulting NGMs can be lower than that of broken symmetry generators, and the dispersion of NGMs is not necessarily linear. In this article, we review recently established formulae for NGMs associated with broken internal symmetries that work equally for relativistic and nonrelativistic systems. We also discuss complexities of NGMs originating from space-time symmetry breaking. Along the way we cover many illuminating examples from various context. We also present a complementary point of view from the Lieb–Schultz–Mattis theorem.

Solving puzzles of spontaneously broken spacetime symmetries

We establish a classical analog of the Nambu-Goldstone theorem for spontaneous breaking of spacetime symmetries. It provides a counting rule for independent Nambu-Goldstone fields and states which of them are gapped. We demonstrate that only those symmetry group generators give rise to independent Nambu-Goldstone fields that act non-trivially on a vacuum at the origin of coordinates. Other generators give rise to auxiliary fields that must be excluded from a theory by the means of inverse Higgs constraints. The physical meaning of the inverse Higgs phenomenon and an application of our results to theories of massive gravity are discussed.

Generic Features of Thermodynamics of Horizons in Regular Spherical Space-Times of the Kerr-Schild Class

We present a systematic review of thermodynamics of horizons in regular spherically symmetric spacetimes of the Kerr-Schild class, d s 2 = g ( r ) d t 2 − g − 1 ( r ) d r 2 − r 2 d Ω 2 , both asymptotically flat and with a positive background cosmological constant λ . Regular solutions of this class have obligatory de Sitter center. A source term in the Einstein equations satisfies T t t = T r r and represents an anisotropic vacuum dark fluid ( p r = − ρ ), defined by the algebraic structure of its stress-energy tensor, which describes a time-evolving and spatially inhomogeneous, distributed or clustering, vacuum dark energy intrinsically related to space-time symmetry. In the case of two vacuum scales it connects smoothly two de Sitter vacua, 8 π G T ν μ = Λ δ ν μ as r → 0 , 8 π G T ν μ = λ δ ν μ as r → ∞ with λ < Λ . In the range of the mass parameter M c r 1 ≤ M ≤ M c r 2 it describes a regular cosmological black hole directly related to a vacuum dark energy. Space-time has at most three horizons: a cosmological horizon r c , a black hole horizon r b < r c , and an internal horizon r a < r b , which is the cosmological horizon for an observer in the internal R-region asymptotically de Sitter as r → 0 . Asymptotically flat regular black holes ( λ = 0 ) can have at most two horizons, r b and r a . We present the basic generic features of thermodynamics of horizons revealed with using the Padmanabhan approach relevant for a multi-horizon space-time with a non-zero pressure. Quantum evaporation of a regular black hole involves a phase transition in which the specific heat capacity is broken and changes sign while a temperature achieves its maximal value, and leaves behind the thermodynamically stable double-horizon ( r a = r b ) remnant with zero temperature and positive specific heat. The mass of objects with the de Sitter center is generically related to vacuum dark energy and to breaking of space-time symmetry. In the cosmological context space-time symmetry provides a mechanism for relaxing cosmological constant to a certain non-zero value. We discuss also observational applications of the presented results.