We examine the basic conservation laws for diffeomorphism symmetry in the context of spontaneous diffeomorphism and local Lorentz-symmetry breaking. The conservation laws are used as constraints on a generic series of terms in an expansion around a flat background. We find all such terms for a two-tensor coupling to cubic order in the metric and tensor field fluctuations. The results are presented in a form that can be used for phenomenological calculations. One key result is that if we preserve the underlying diffeomorphism symmetry in a spontaneous-symmetry breaking scenario, one cannot decouple the two-tensor fluctuations from the metric fluctuations at the level of the action, except in special cases of the quadratic actions.
We introduce the set of constraints the wave function of the Universe has to satisfy in order to describe an Universe undergoing through the process of spontaneous breaking of supersymmetry and discuss the way this may lead to the emergence of classical spacetime.
An overview is given of effective gravitational field theories with fixed background fields that break spacetime symmetry. The behavior of the background fields and the types of excitations that can occur depend on whether the symmetry breaking is explicit or spontaneous. For example, when the breaking is spontaneous, the background field is dynamical and massless Nambu--Goldstone and massive Higgs excitations can appear. However, if the breaking is explicit, the background is nondynamical, and in this case additional metric or vierbein excitations occur due to the loss of local symmetry, or t…
We study the effects of explicit spacetime-symmetry breaking on primordial tensor fluctuations using an effective-field theory for Lorentz/CPT violation. We find that the graviton is still massless, but that the propagation speed of tensor modes is modified, and we obtain a constraint on the coefficient determining the symmetry breaking on the order of $10^{-15}$ from the recent measurements of the speed of gravity. Due to the symmetry breaking, the de-Sitter phase is modified, and during this inflationary epoch, the power spectrum assumes a slow oscillation around the general-relativity limit…
When bosonic matter in the form of a complex scalar field is added to Ellis wormholes, the phenomenon of spontaneous symmetry breaking is observed. Symmetric solutions possess full reflection symmetry with respect to the radial coordinate of the two asymptotically flat spacetime regions connected by the wormhole, whereas asymmetric solutions do not possess this symmetry. Depending on the size of the throat, at bifurcation points pairs of asymmetric solutions arise from or merge with the symmetric solutions. These asymmetric solutions are energetically favoured. When the backreaction of the bos…
The Einstein-Gordon equations for Friedmann-Robertson-Walker (FRW) geometries in feedback reaction with the quartically self-interacting physical field, arisen from the "inner parity" spontaneous breaking, are explicitly formulated. The Hamiltonian density non-positive extrema would classically forbid both spatially closed and flat homogeneous and isotropic worlds if these were to allow the physical field to (repeatedly) go through and to (finally) settle down in a ground state. In this respect, the fixed point exact solutions of the spontaneous Z_2-symmetry breaking Einstein-Gordon equations …
We will discuss selected physical effects of spacetime geometry fluctuations, especially the operational signatures of geometry fluctuations and their effects on black hole horizons. The operational signatures which we discuss involve the effects of the fluctuations on images, and include luminosity variations, spectral line broadening and angular blurring. Our main interest will be in black hole horizon fluctuations, especially horizon fluctuations which have been enhanced above the vacuum level by gravitons or matter in squeezed states. We investigate whether these fluctuations can alter the…
A vector model with a hybrid form of spacetime symmetry breaking consisting of explicit diffeomorphism breaking but spontaneous local Lorentz violation is presented. The combined effects of these symmetry breakings give rise to a theory obeying the Einstein-Maxwell equations in a preferred spatially homogeneous and isotropic frame, with photons emerging as massless Nambu-Goldstone modes. Interpretations and possible generalizations of this model are discussed, and comparisons are made to previous models describing photons as Nambu-Goldstone modes.
Quantum fluctuations of the vacuum stress-energy tensor are highly non-Gaussian, and can have unexpectedly large effects on spacetime geometry. In this paper, we study a two-dimensional dilaton gravity model coupled to a conformal field, in which the distribution of vacuum fluctuations is well understood. In this model, the fluctuations of the matter field are responsible for the fluctuations of the geometry itself. By analyzing the geodesic deviation in this model, we show that a pencil of massive particles propagating on this fuzzy spacetime eventually converges and collapses. This is consis…
We consider the consequences of the presence of metric fluctuations upon the properties of a hydrogen atom. Particularly, we introduce these metric fluctuations in the corresponding effective Schroedinger equation and deduce the modifications that they entail upon the hyperfine structure related to a hydrogen atom. We will find the change that these effects imply for the ground state energy of the system and obtain a bound for its size comparing our theoretical predictions against the experimental uncertainty reported in the literature. In addition, we analyze the corresponding Lamb shift effe…
In this work, we study quantum fluctuations in the stress energy tensor of spinor fields evolving in general FRW spacetimes. We quantify these fluctuations by the noise kernel of spinor fields. For the particular case of de Sitter spacetime, we place the spinor field in what is called the fermionic Bunch Davies vacuum and study the variation of the noise kernel with the mass of the field. We then make use of the conformal invariance of massless spinor fields and employ an equivalence that relates a massless spinor field in any given FRW spacetime with a corresponding massless spinor field in d…
We investigate the Lorentz symmetry breaking effects (LSBE) on the deflection of light by a rotating cosmic string spacetime in the weak limit approximation. We first calculate the deflection angle by a static cosmic string for a fixed spacelike 4-vector case (FSL) with the corresponding effective-string optical metric using the Gauss-Bonnet theorem (GBT). Then, we focus on a more general scenario, namely we calculate the deflection angle by a rotating cosmic string applying the GBT to Randers effective-string metric. We obtain a significant modification in the deflection angle because of the …
A correspondence between fluctuations of conformally invariant quantum fields and that of classical fields finally reducing to perfect fluid matter content is shown to exist. Previously a similar correspondence between the stress tensors was known and well established in the 70's. Using recent results obtained in semiclassical stochastic gravity regarding exact definition and significance given to quantum fluctuations of the stress tensor, we obtain this correspondence, which is fundamental to statistical analysis of systems in curved spacetime. This is of immense importance, in that the fluct…
The one-loop effective potential for $ϕ^4$ theory on a Bianchi type-I universe is evaluated in the adiabatic approximation. It is used to see the quantum-field effects on symmetry breaking and restoration in anisotropic spacetimes. The results show that the fate of symmetry will not be changed in the cases of conformal coupling or a vanishing scale curvature, and only for some suitable values of scalar-gravitational coupling could the symmetry be radiatively broken or restored.
One of the deepest insights from the general theory of relativity is the relational nature of spacetime. While it is a generally agreed on that the nature of spacetime must be drastically different at the Planck scale, it has been a common practice to assume a full pseudo-Riemannian geometry of spacetime no matter what the physical fields present are, and to apply such geometry to cosmology. In the spirit of preserving the relational description of spacetime, we initiate a discussion on the applicability of general relativity all the way to Planck scale, and propose the possibility that the fu…
In the article we present explicit expressions for quantum fluctuations of spacetime in the case of $(4+n)$-dimensional spacetimes, and consider their holographic properties and some implications for clocks, black holes and computation. We also consider quantum fluctuations and their holographic properties in ADD model and estimate the typical size and mass of the clock to be used in precise measurements of spacetime fluctuations. Numerical estimations of phase incoherence of light from extra-galactic sources in ADD model are also presented.
We analyze the quantum fluctuations of vacuum stress tensors and spacetime curvatures, using the framework of linear response theory which connects these fluctuations to dissipation mechanisms arising when stress tensors and spacetime metric are coupled. Vacuum fluctuations of spacetime curvatures are shown to be a sum of two contributions at lowest orders; the first one corresponds to vacuum gravitational waves and is restricted to light-like wavevectors and vanishing Einstein curvature, while the second one arises from gravity of vacuum stress tensors. From these fluctuations, we deduce nois…
While it is generally agreed that the nature of spacetime must be drastically different at the Planck scale, it has been a common practice to assume that spacetime is endowed with a full pseudo-Riemannian geometry regardless of the physical fields present or the length scale at which the geometry is probed, and to adopt this assumption in theories of cosmology, particle physics, quantum gravity, etc. Following Einstein's view that the mathematical description of spacetime ought to be physically motivated, we initiate a discussion on the validity of this assumption, and propose that the full ps…
Mesoscopic effects associated with wave propagation in spacetime with metric stochasticity are studied. We show that the scalar and spinor waves in a stochastic spacetime behave similarly to the electrons in a disordered system. Viewing this as the quantum transport problem, mesoscopic fluctuations in such a spacetime are discussed. The conductance and its fluctuations are expressed in terms of a nonlinear sigma model in the closed time path formalism. We show that the conductance fluctuations are universal, independent of the volume of the stochastic region and the amount of stochasticity.
We argue that calculating vacuum energy requires quantum field theory whose axioms are adapted to curved spacetime. In this context, we suggest that non-zero vacuum energy is connected to dynamical breaking of electroweak symmetry. The observed meV scale can be understood in terms of electroweak physics via a naive estimate. The scenario requires all particle masses to have a dynamical origin. Any Higgs particle has to be a composite, and the origin of vacuum energy might be probed at the LHC.
The regime of exponentially fast expansion in 5D cosmological models was investigated. Many limit cases was also studied. It was shown that there is a possibility to particle creation in a static 4D spacetime if it embedded in an bulk with an expanding extra-dimension y. It was also shown that many physical quantities like the particle number density, vacuum pressure and energy density has its behavior governed by the expansion rate parameters (α,β) that control the inflation process. These parameters also limit the field modes that can be created in a given model. The case with modes with ky …
Any quantum system interacting with a complex environment undergoes decoherence. Empty space is filled with vacuum energy due to matter fields in their ground state and represents an underlying environment that any quantum particle has to cope with. In particular quantum gravity vacuum fluctuations should represent a universal source of decoherence. To study this problem we employ a stochastic approach that models spacetime fluctuations close to the Planck scale by means of a classical, randomly fluctuating metric (random gravity framework). We enrich the classical scheme for metric perturbati…
We compute fluctuations in the modular energy of the vacuum associated with a Rindler-wedge in AdS spacetime in the context of AdS/CFT. We discuss the possible effect of these energy fluctuations on the spacetime geometry, and on the traversal time of a light beam propagating from the boundary to the bulk and back.
Space--time can be understood as some kind of space--time foam of fluctuating bubbles or loops which are expected to be an outcome of a theory of quantum gravity. One recently discussed model for this kind of space--time fluctuations is the holographic principle which allows to deduce the structure of these fluctuations. We review and discuss two scenarios which rely on the holographic principle leading to holographic noise. One scenario leads to fluctuations of the space--time metric affecting the dynamics of quantum systems: (i) an apparent violation of the equivalence principle, (ii) a modi…
It has long been noticed that Laudau-Lifshitz theory can be used to study the fluctuation of a system that contains a black hole. Since the black string can be constructed by extending n-dimensional black hole into one extra dimension. We study the fluctuation of black string flow with a Schwarzschlid-like metric in D=n+1 dimensional spacetime and a charged solution in D=5 dimensional spacetime and get the second moments of the fluctuation of the mass flux and charge flux.
Quantum fluctuations of lightcone are examined in a 4-dimensional spacetime with two parallel planes. Both the Dirichlet and the Neumann boundary conditions are considered. In all the cases we have studied, quantum lightcone fluctuations are greater where the Neumann boundary conditions are imposed, suggesting that quantum lightcone fluctuations depend not only on the geometry and topology of the spacetime as has been argued elsewhere but also on boundary conditions. Our results also show that quantum lightcone fluctuations are larger here than that in the case of a single plane. Therefore, th…
We study the backreaction of superhorizon fluctuations of a light quantum scalar field on a classical de Sitter geometry by means of the Wilsonian renormalisation group. This allows us to treat the gravitationally amplified fluctuations in a nonperturbative manner and to analytically follow the induced renormalisation flow of the spacetime curvature as long wavelength modes are progressively integrated out. Unbounded loop corrections in the deep infrared are eventually screened by nonperturbative effects which stabilise the geometry.
The quantum fluctuations of the geodesic deviation equation in a flat background spacetime are discussed. We calculate the resulting mean squared fluctuations in the relative velocity and separation of test particles. The effect of these quantum fluctuations of the spacetime geometry is given in terms of the Riemann tensor correlation function. Three different sources of the Riemann tensor fluctuations are considered: a thermal bath of gravitons, gravitons in a squeezed state, and the graviton vacuum state.
For quantum fields on a curved spacetime with an Euclidean section, we derive a general expression for the stress energy tensor two-point function in terms of the effective action. The renormalized two-point function is given in terms of the second variation of the Mellin transform of the trace of the heat kernel for the quantum fields. For systems for which a spectral decomposition of the wave opearator is possible, we give an exact expression for this two-point function. Explicit examples of the variance to the mean ratio $Δ' = (<ρ^2>-<ρ>^2)/(<ρ>^2)$ of the vacuum energy density $ρ$ of a mas…
Using entanglement in dS/CFT correspondence, we show that a 4-dimensional de Sitter spacetime in the bulk fluctuates. We calculated the fluctuations of the entanglement entropy, which backreacts with the geometry of the bulk spacetime indicated by the fluctuations of the horizon radius. The variance of the fluctuations is suppressed by $G_N$ and multiplied by $H_{dS}^2$. Therefore, it will be more significant during the primordial era where it is also well described by de Sitter geometry. We also show that the distribution of the fluctuations is also skewed with the local non-linearity paramet…
In this work, we review the effective field theory framework to search for Lorentz and CPT symmetry breaking during the propagation of gravitational waves. The article is written so as to bridge the gap between the theory of spacetime-symmetry breaking and the analysis of gravitational-waves signals detected by ground-based interferometers. The primary physical effects beyond General Relativity that we explore here are dispersion and birefringence of gravitational waves. We discuss their implementation in the open-source LIGO-Virgo algorithm library suite, as well as the statistical method use…
We describe a model where breaking of W3 symmetry will lead to the emergence of time and subsequently of space. Surprisingly the simplest such models which lead to higher dimensional spacetimes are based on the four "magical" Jordan algebras of 3x3 Hermitian matrices with real, complex, quaternion and octonion entries, respectively. The simplest symmetry breaking leads to universes with spacetime dimensions 3, 4, 6, and 10.
The aim of this paper is to construct a quantum effective action for gravitational fields by the effective potential method in quantum field theory. The minimum of the quantum effective action gives an equation of quantum fluctuations. We discuss the quantum fluctuation in the flat spacetime and in the Schwarzschild spacetime. It is shown that a baby spacetime may be created from a classical vacuum through a quantum fluctuation.
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 possib…
Spontaneous Lorentz symmetry breaking can occur when the dynamics of a tensor field cause it to take on a non-zero expectation value in vacuo, thereby providing one or more "preferred directions" in spacetime. Couplings between such fields and spacetime curvature will then affect the dynamics of the metric, leading to interesting gravitational effects. Bailey & Kostelecky developed a post-Newtonian formalism that, under certain conditions concerning the field's couplings and stress-energy, allows for the analysis of gravitational effects in the presence of Lorentz symmetry breaking. We perform…
We study the vacuum polarization of a massive scalar field $ϕ$ with arbitrary coupling to gravity in pointlike global monopole spacetime. Using Schwinger-DeWitt proper time formalism, we calculate the vacuum expectation value $<ϕ^{2}>$, when the Compton length of the quantum field is much less than the characteristic radius of the curvature of the background geometry, and we can ignore nonlocal contributions. Explicit analytic expressions are obtained for a general curvature coupling parameter, and specified to the more physical cases of minimal and conformal coupling. Comparing the leading te…
We study the back reaction of a thermal field in a weak gravitational background depicting the far-field limit of a black hole enclosed in a box by the Close Time Path (CTP) effective action and the influence functional method. We derive the noise and dissipation kernels of this system in terms of quantities in quasi-equilibrium, and formally prove the existence of a Fluctuation-Dissipation Relation (FDR) at all temperatures between the quantum fluctuations of the thermal radiance and the dissipation of the gravitational field. This dynamical self-consistent interplay between the quantum field…
A non-Riemannian geometrical approach to the investigation of an acoustic black hole in irrotational mean flows, based on the Lighthill vortex sound theory is given. This additional example of analog gravity based on classical fluids is used to investigate the acoustic Lorentz violation. An example is given where the contortion vector is distributed along a ring inside the fluid which can be gravitational analog of the torsion thick string spacetime defect. It is found that the linear background flow velocity approximation, acoustic Lorentz symmetry is breaking by the acoustic Cartan contortio…
A correspondence between fluctuations of non-minimally coupled scalar fields and that of an effective fluid with heat flux and anisotropic stresses, is shown. Though the correspondence between respective stress tensors of scalar fields and fluids is known and widely used in literature, the fluctuations in the two cases still await a formal correspondence and are open to investigation in all details. Using results obtained in the newly established theory of semiclassical stochastic gravity which focuses on the fluctuations of the quantum stress tensor, we show new relations in this regard. This…
We argue that, in order to obtain decoherence of spacetime, we should consider quantum conformal metric fluctuations of spacetime. This could be the required environment in the problem of selfmeasurement of spacetime in quantum gravity.
It was recently proposed that deformations of the relativistic symmetry, as those considered in Deformed Special Relativity (DSR), can be seen as the outcome of a measurement theory in the presence of non-negligible (albeit small) quantum gravitational fluctuations [1,2]. In this paper we explicitly consider the case of a spacetime described by a flat metric endowed with stochastic fluctuations and, for a free particle, we show that DSR-like nonlinear relations between the spaces of the measured and classical momenta, can result from the average of the stochastic fluctuations over a scale set …
The quantum fluctuation of the stress tensor of a quantum field are discussed, as are the resulting spacetime metric fluctuations. Passive quantum gravity is an approximation in which gravity is not directly quantized, but fluctuations of the spacetime geometry are driven by stress tensor fluctuations. We discuss a decomposition of the stress tensor correlation function into three parts, and consider the physical implications of each part. The operational significance of metric fluctuations and the possible limits of validity of semiclassical gravity are discussed.
Spacetime geometry is treated as a fluctuating, stochastic quantum system allowing an effective quantum gravity solution to the cosmological constant problem. A Focker-Planck equation for the probability density of spacetime metric fluctuations is solved for an FRW universe and the most probable value for the metric scale factor R is for a very small cosmological constant.
Gravitational effective field theories with nondynamical backgrounds explicitly break diffeomorphism and local Lorentz invariance. At the same time, to maintain observer independence the action describing these theories is required to be mathematically invariant under general coordinate transformations and changes of local Lorentz bases. These opposing effects of having broken spacetime symmetries but invariance under mathematical observer transformations can result in theoretical inconsistency unless certain conditions hold. The consistency constraints that must hold originate from Noether id…
The operational meaning of spacetime fluctuations is discussed. Classical spacetime geometry can be viewed as encoding the relations between the motions of test particles in the geometry. By analogy, quantum fluctuations of spacetime geometry can be interpreted in terms of the fluctuations of these motions. Thus one can give meaning to spacetime fluctuations in terms of observables which describe the Brownian motion of test particles. We will first discuss some electromagnetic analogies, where quantum fluctuations of the electromagnetic field induce Brownian motion of test particles. We next d…
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…
In this paper we consider light-cone fluctuations arising as a consequence of the nontrivial topology of the locally flat cosmic string spacetime. By setting the light-cone along the z-direction we are able to develop a full analysis to calculate the renormalized graviton two-point function, as well as the mean square fluctuation in the geodesic interval function and the time delay (or advance) in the propagation of a light-pulse. We found that all these expressions depend upon the parameter characterizing the conical topology of the cosmic string spacetime and vanish in the absence of it. We …
With recent developments in high-precision quantum measurements, the question of whether observations of decoherence from spacetime fluctuations are accessible experimentally arises. Here we investigate the dynamics of bound states interacting with an environment of gravitons under the Markov approximation. The corresponding Lindblad master equation is presented that enables gravitational decoherence and dissipation due to zero-point spacetime fluctuations to be analyzed. Specifically, we consider a one-dimensional cavity of massless scalar particles that models a light beam with negligible sp…
