Gauge Artifact Research Articles

Influence of Gauge Artifact on Adiabatic and Entropy Perturbations during Inflation

In recent publications we proposed one way to calculate gauge-invariant variables in a local observable universe which is limited to a portion of the whole universe. To provide a theoretical prediction of the observable fluctuations, we need to preserve the gauge-invariance in the local universe, which is referred to the genuine gauge-invariance. The importance of the genuine gauge invariance is highlighted in the study of primordial fluctuations in the infrared (IR) limit. The stability against IR loop corrections to primordial fluctuations is guaranteed in requesting the genuine gauge invariance. The genuine gauge-invariance also gives impacts on the detectable fluctuations. We showed that at observable scales the bi-spectrum calculated in the conventional perturbation theory vanishes in the squeezed limit, if we request the genuine gauge invariance. This indicates that the conventional bi-spectrum is, in this limit, dominated by a gauge artifact, which cannot be observed. These studies have been elaborated in single-field models of inflation. In this paper we generalize our argument to multi-field models of inflation, where, in addition to the adiabatic field, the entropy field can participate in the generation of primordial fluctuations. We will find that the entropy field can generate the observable fluctuations, which cannot be eliminated by gauge transformations in the local universe.

Gravity waves from a cosmological phase transition: Gauge artifacts and daisy resummations

The finite-temperature effective potential customarily employed to describe the physics of cosmological phase transitions often relies on specific gauge choices, and is manifestly not gauge invariant at finite order in its perturbative expansion. As a result, quantities relevant for the calculation of the spectrum of stochastic gravity waves resulting from bubble collisions in first-order phase transitions are also not gauge invariant. We assess the quantitative impact of this gauge dependence on key quantities entering predictions for gravity waves from first-order cosmological phase transitions. We resort to a simple Abelian Higgs model, and discuss the case of ${R}_{\ensuremath{\xi}}$ gauges. By comparing with results obtained using a gauge-invariant Hamiltonian formalism, we show that the choice of gauge can have a dramatic effect on theoretical predictions for the normalization and shape of the expected gravity wave spectrum. We also analyze the impact of resumming higher-order contributions as needed to maintain the validity of the perturbative expansion, and show that doing so can suppress the amplitude of the spectrum by an order of magnitude or more. We comment on open issues and possible strategies for carrying out ``daisy resummed'' gauge-invariant computations in non-Abelian models for which a gauge-invariant Hamiltonian formalism is not presently available.

Infrared Behavior and Gauge Artifacts in de Sitter Spacetime: The Photon Field

We study the infrared (long-distance) behavior of the free photon field in de Sitter spacetime. Using a two-parameter family of gauge-fixing terms, we show that the infrared (IR) behavior of the two-point function is highly gauge-dependent and ranges from vanishing to growing. This situation is in disagreement with its counterpart in flat spacetime, where the two-point function vanishes in the IR region for any choice of the gauge-fixing parameters. A criterion to isolate the physical part of the two-point function is given and is shown to lead to a well-behaved two-point function in the IR region.

Dominance of gauge artifact in the consistency relation for the primordial bispectrum

The conventional cosmological perturbation theory has been performed under the assumption that we know the whole spatial region of the universe with infinite volume. This is, however, not the case in the actual observations because observable portion of the universe is limited. To give a theoretical prediction to the observablefluctuations, gauge-invariant observables should be composed of the information in our local observable universe with finite volume. From this point of view, we reexamine the primordial non-Gaussianity in singlefield models, focusing on the bispectrum in the squeezed limit. A conventional prediction states that the bispectrum in this limit is related to the power spectrum through the so-called consistencyrelation. However, it turns out that, if we adopt a genuine gauge invariant variable which is naturally composed purely of the information in our local universe, the leading term for the bispectrum in the squeezed limit predicted by the consistency relation vanishes.

Comment on ‘Hawking radiation from fluctuating black holes’

Takahashi and Soda (2010 Class. Quantum Grav. 27 175008) have recently considered the effect (at lowest non-trivial order) of dynamical, quantized gravitational fluctuations on the spectrum of scalar Hawking radiation from a collapsing Schwarzschild black hole. However, due to an unfortunate choice of gauge, the dominant (even divergent) contribution to the coefficient of the spectrum correction that they identify is a pure gauge artifact. I summarize the logic of their calculation, comment on the divergences encountered in its course and on how they could be eliminated, and thus the calculation be completed.

Infrared divergence does not affect the gauge-invariant curvature perturbation

We address the infrared(IR) divergence problem during inflation that appears in the loop corrections to the primordial perturbations. In our previous paper, we claimed that, at least in single field models, the IR divergence is originating from the gauge artifact. Namely, diverging IR corrections should not appear in genuine gauge-invariant observables. We propose here one simple but explicit example of such gauge-invariant quantities. Then, we explicitly calculate such a quantity to find that the IR divergence is absent at the leading order in the slow-roll approximation for the usual scale invariant vacuum state. At the same time we notice that there is a subtle issue on the gauge-invariance in how to specify the initial vacuum state.

On the perturbative S-matrix of generalized sine-Gordon models

Motivated by its relation to the Pohlmeyer reduction of AdS_5 x S^5 superstring theory we continue the investigation of the generalized sine-Gordon model defined by SO(N+1)/SO(N) gauged WZW theory with an integrable potential. Extending our previous work (arXiv:0912.2958) we compute the one-loop two-particle S-matrix for the elementary massive excitations. In the N = 2 case corresponding to the complex sine-Gordon theory it agrees with the charge-one sector of the quantum soliton S-matrix proposed in hep-th/9410140. In the case of N > 2 when the gauge group SO(N) is non-abelian we find a curious anomaly in the Yang-Baxter equation which we interpret as a gauge artifact related to the fact that the scattered particles are not singlets under the residual global subgroup of the gauge group.

Double field theory

The zero modes of closed strings on a torus — the torus coordinates plus dual coordinates conjugate to winding number — parameterize a doubled torus. In closed string field theory, the string field depends on all zero-modes and so can be expanded to give an infinite set of fields on the doubled torus. We use string field theory to construct a theory of massless fields on the doubled torus. Key to the consistency is a constraint on fields and gauge parameters that arises from the L0−0 = 0 condition in closed string theory. The symmetry of this double field theory includes usual and `dual diffeomorphisms', together with a T-duality acting on fields that have explicit dependence on the torus coordinates and the dual coordinates. We find that, along with gravity, a Kalb-Ramond field and a dilaton must be added to support both usual and dual diffeomorphisms. We construct a fully consistent and gauge invariant action on the doubled torus to cubic order in the fields. We discuss the challenges involved in the construction of the full nonlinear theory. We emphasize that the doubled geometry is physical and the dual dimensions should not be viewed as an auxiliary structure or a gauge artifact.

Bödeker’s effective theory: From Langevin dynamics to Dyson–Schwinger equations

The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order | k | ∼ g 2 T . Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Bödeker has derived an effective theory that describes the dynamics of the soft field modes by means of a Langevin equation. This effective theory has been used for lattice calculations so far [G.D. Moore, Nucl. Phys. B568 (2000) 367. Available from: <hep-ph/9810313>; G.D. Moore, Phys. Rev. D62 (2000) 085011. Available from: <hep-ph/0001216>]. In this work we provide a complementary, more analytic approach based on Dyson–Schwinger equations. Using methods known from stochastic quantitation, we recast Bödeker’s Langevin equation in the form of a field theoretic path integral. We introduce gauge ghosts in order to help control possible gauge artefacts that might appear after truncation, and which leads to a BRST symmetric formulation and to corresponding Ward identities. A second set of Ward identities, reflecting the origin of the theory in a stochastic differential equation, is also obtained. Finally, Dyson–Schwinger equations are derived.

Calibration-based thermal error model for articulated arm coordinate measuring machines

Abstract The influence of thermal changes in the accuracy of articulated arm coordinate measuring machines (AACMMs) is one of their main error sources. Usually, the effects of this problem are minimized by using low thermal-expansion materials in the arm design or by implementing an empirical error correction model based on the outputs of several temperature sensors placed inside the arm. These models, inherited from temperature correction models for robot arms, are based on the empirical arm positioning error characterization of several temperatures inside its measuring range and by posterior corrections implemented using an average error approximation. Considering this approximation as a correction valid for all the temperature range violates the AACMM calibration conditions, which are defined by a kinematic parameter identification procedure at 20 °C. This implies that, by applying these models, the AACMM will work outside of calibration conditions and will not meet the nominal accuracy values obtained from the identification procedure. In this work a new empirical correction model for thermal errors is presented. This model keeps the calibration conditions established in the parameters identification procedure unaltered. This fact makes it possible to apply other correction models for geometric and non-geometric errors obtained at the calibration temperature after having applied the temperature correction. The algorithm and objective functions used, which are based on a new approach including terms regarding measurement accuracy and repeatability and using the measurements of a ball-beam gauge artifact are shown. The empirical correction model and the arm accuracy and repeatability results before and after correction are also explained, showing an important accuracy improvement in the arm performance for typical arm operation at temperatures different from 20 °C.

A COVARIANT ROAD TO SPATIAL AVERAGING IN COSMOLOGY: SCALAR CORRECTIONS TO THE COSMOLOGICAL EQUATIONS

A consistent approach to cosmology requires an explicit averaging of the Einstein equations, to describe a homogeneous and isotropic geometry. Such an averaging will in general modify the Einstein equations. The averaging procedure due to Buchert has attracted considerable attention recently since it offers the tantalizing hope of explaining the phenomenon of dark energy through such corrections. This approach has been criticized, however, on the grounds that its effects may be gauge artifacts. We apply the fully covariant formalism of Zalaletdinov's macroscopic gravity and show that, after making some essential gauge choices, the cosmological equations receive space–time scalar corrections which are therefore observable in principle, and further, that the broad structure of these corrections is identical to those derived by Buchert.

ANALYSIS OF THE TRANSVERSE EFFECT OF EINSTEIN'S GRAVITATIONAL WAVES

The investigation of the transverse effect of gravitational waves (GW's) could constitute a further tool to discriminate among several relativistic theories of gravity on the ground. After a review of the TT gauge, the transverse effect of GW's arising by standard general relativity (called Einstein's GW's in this paper) is reanalyzed with a different choice of coordinates. In the chosen gauge, test masses have an apparent motion in the direction of propagation of the wave, while in the transverse direction they appear at rest. Of course, this is only a gauge artefact. In fact, from careful investigation of this particular gauge, it is shown that the tidal forces associated with GW's act along the directions orthogonal to the direction of propagation of waves. In the analysis it is also shown, in a heuristic way, that the transverse effect of Einstein's GW's arises from the propagation of the waves at the speed of the light, thus only massless GW's are purely transverse. But, because the physics of gravitational waves has to be investigated by studying the tidal forces as appearing in the geodesic deviation equation and directly in a laboratory environment on Earth, an analysis of these tidal forces and of the transverse effect in the frame of the local observer is also performed. After this, for a further better understanding of the transverse effect, an example of a wave, which arises from scalar tensor gravity, with both transverse and genuinely longitudinal modes is given and discussed. In the example the connection between the longitudinal component and the velocity of the wave is mathematically shown. At the end of this paper, the review of the TT gauge is completed, recovering the gauge invariance between the presented gauge and the TT gauge.

Spatial averaging limit of covariant macroscopic gravity: Scalar corrections to the cosmological equations

It is known that any explicit averaging scheme of the type essential for describing the large scale behavior of the Universe must necessarily yield corrections to the Einstein equations applied in the cosmological setting. The question of whether or not the resulting corrections to the Einstein equations are significant is still a subject of debate, partly due to possible ambiguities in the averaging schemes available. In particular, it has been argued in the literature that the effects of averaging could be gauge artifacts. We apply the formalism of Zalaletdinov's macroscopic gravity (MG), which is a fully covariant and nonperturbative averaging scheme, in an attempt to construct gauge independent corrections to the standard Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) equations. We find that whereas one cannot escape the problem of dependence on one gauge choice\char22{}which is inherent in the assumption of large scale homogeneity and isotropy\char22{}it is however possible to construct space-time scalar corrections to the standard FLRW equations. This partially removes the criticism concerning the corrections being gauge artifacts. For a particular initial choice of gauge which simplifies the formalism, we explicitly construct these scalars in terms of the underlying inhomogeneous geometry, and incidentally demonstrate that the formal structure of the corrections with this gauge choice is identical to that of analogous corrections derived by Buchert in the context of spatial averaging of scalars.

Gravity of cosmological perturbations in the CMB

First, we establish which measures of large-scale perturbations are least afflicted by gauge artifacts and directly map the apparent evolution of inhomogeneities to local interactions of cosmological species. Considering nonlinear and linear perturbations of phase-space distribution, radiation intensity and arbitrary species' density, we require that: (i) the dynamics of perturbations defined by these measures is determined by observables within the local Hubble volume; (ii) the measures are practically applicable on microscopic scales and in an unperturbed geometry retain their microscopic meaning on all scales. We prove that all measures of linear overdensity that satisfy (i) and (ii) coincide in the superhorizon limit. Their dynamical equations are simpler than the traditional ones, have a nonsingular superhorizon limit and explicit Cauchy form. Then we show that, contrary to the popular view, the perturbations of the cosmic microwave background (CMB) in the radiation era are not resonantly boosted self-gravitationally during horizon entry. (Consequently, the CMB signatures of uncoupled species which may be abundant in the radiation era, e.g. neutrinos or early quintessence, are mild; albeit non-degenerate and robust to cosmic variance.) On the other hand, dark matter perturbations in the matter era gravitationally suppress large-angle CMB anisotropy by an order of magnitude stronger than presently believed. If cold dark matter were the only dominant component then, for adiabatic perturbations, the CMB temperature power spectrum C_l would be suppressed 25-fold.

Gauge dependence of the infrared behaviour of massless QED3

Using the Zumino identities it is shown that in a class of non-local gauges, massless QED3 has an infrared behaviour of a conformal field theory with a continuously varying anomalous dimension of the fermion. In the usual Lorentz gauge, the fermion propagator falls off exponentially for a large separation, but this apparent fermion mass is a gauge artifact.

Vector perturbations in a contracting Universe

In this note we show that vector perturbations exhibit growing mode solutions in a contracting Universe, such as the contracting phase of the pre big bang or the cyclic/ekpyrotic models of the Universe. This is not a gauge artifact and will in general lead to the breakdown of perturbation theory--a severe problem that has to be addressed in any bouncing model. We also comment on the possibility of explaining, by means of primordial vector perturbations, the existence of the observed large-scale magnetic fields. This is possible since they can be seeded by vorticity.

Energy-momentum tensor of cosmological fluctuations during inflation

We study the renormalized energy-momentum tensor (EMT) of cosmological scalar fluctuations during the slow-rollover regime for chaotic inflation with a quadratic potential and find that it is characterized by a negative energy density which grows during slow rollover. We also approach the back-reaction problem as a second-order calculation in perturbation theory, finding no evidence that the back reaction of cosmological fluctuations is a gauge artifact. In agreement with the results for the EMT, the average expansion rate is decreased by the back reaction of cosmological fluctuations.

Linearly-realised worldsheet supersymmetry in pp-wave backgrounds

We study the linearly-realised worldsheet supersymmetries in the “massive” type II light-cone actions for pp-wave backgrounds. The pp-waves have 16+ N sup Killing spinors, comprising 16 “standard” Killing spinors that occur in any wave background, plus N sup “supernumerary” Killing spinors (0⩽ N sup⩽16) that occur only for special backgrounds. We show that only the supernumerary Killing spinors give rise to linearly-realised worldsheet supersymmetries after light-cone gauge fixing, while the 16 standard Killing spinors describe only non-linearly realised inhomogeneous symmetries. We also study the type II actions in the physical gauge, and we show that although in this case the actions are not free, there are now linearly-realised supersymmetries coming both from the standard and the supernumerary Killing spinors. In the physical gauge, there are no mass terms for any worldsheet degrees of freedom, so the masses appearing in the light-cone gauge may be viewed as gauge artefacts. We obtain type IIA and IIB supergravity solutions describing solitonic strings in pp-wave backgrounds, and show how these are related to the physical-gauge fundamental string actions. We study the supersymmetries of these solutions, and find examples with various numbers of Killing spinors, including total numbers that are odd.

Structure functions are not parton probabilities

The common view that structure functions measured in deep inelastic lepton scattering are determined by the probability of finding quarks and gluons in the target is not correct in gauge theory. We show that gluon exchange between the fast, outgoing partons and target spectators, which is usually assumed to be an irrelevant gauge artifact, affects the leading twist structure functions in a profound way. This observation removes the apparent contradiction between the projectile (eikonal) and target (parton model) views of diffractive and small x_{Bjorken} phenomena. The diffractive scattering of the fast outgoing quarks on spectators in the target causes shadowing in the DIS cross section. Thus the depletion of the nuclear structure functions is not intrinsic to the wave function of the nucleus, but is a coherent effect arising from the destructive interference of diffractive channels induced by final state interactions. This is consistent with the Glauber-Gribov interpretation of shadowing as a rescattering effect.

Large-distance behaviour of the gravitontwo-point function in de Sitter spacetime

It is known that the graviton two-point function for the de Sitterinvariant `Euclidean' vacuum in a physical gauge grows logarithmicallywith distance in spatially flat de Sitter spacetime. We show that thislogarithmic behaviour is a gauge artefact by explicitly demonstrating thatthe same behaviour can be reproduced by a pure-gauge two-point function.