Gauge invariant averages for the cosmological backreaction

Gasperini, M.; Marozzi, Giovanni; Veneziano, G.

doi:10.1088/1475-7516/2009/03/011

Cited by 60 publications

(140 citation statements)

References 43 publications

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“…Yet in a different approach using a gauge invariant formalism, the averaged geometry on the past null cone has been introduced [28,29]. This allows to average the luminosity-redshift relation [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Investigation of Frequency Characteristics in Cutting of Soft Tissue Using Prototype Ultrasonic Knives

Ebina

Hasegawa

Kanai

2007

jjap

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Cosmic structures determine how light propagates through the Universe and consequently must be taken into account in the interpretation of observations. In the standard cosmological model at the largest scales, such structures are either ignored or treated as small perturbations to an isotropic and homogeneous Universe. This isotropic and homogeneous model is commonly assumed to emerge from some averaging process at the largest scales. We assume that there exists an averaging procedure that preserves the causal structure of space-time. Based on that assumption, we study the effects of averaging the geometry of space-time and derive an averaged version of the null geodesic equation of motion. For the averaged geometry we then assume a flat Friedmann-Lemaître (FL) model and find that light propagation in this averaged FL model is not given by null geodesics of that model, but rather by a modified light propagation equation that contains an effective Hubble expansion rate, which differs from the Hubble rate of the averaged space-time.

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Section: Introductionmentioning

confidence: 99%

Investigation of Frequency Characteristics in Cutting of Soft Tissue Using Prototype Ultrasonic Knives

Ebina

Hasegawa

Kanai

2007

jjap

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“…These lead toφ = 0,ᾱ = 0 andψ = Ḣ φ ϕ where the last term, which we insert in (11), is constant in such a limit.…”

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confidence: 99%

“…The basic fact that the averaging procedure does not commute with the non linear evolution of Einstein equations [8] was first exploited to study the effective dynamics of the averaged geometry for a dust universe [9] (see [10] for a recent application in the context of inhomogeneity driven inflation). Gauge invariance of averaged quantities has recently been addressed in a novel context which introduces a GI but observer dependent averaging prescription [11] (see [12] for a recent application of such a prescription to the analysis of the present Hubble rate) whereas the effective equations for the averaged geometry [9] have been generalized in a covariant and GI form in [13]. Taking advantage of these recent results and having in mind the backreaction of quantum fluctuations during inflation, we devote this Letter to describing, for the first time in this context, an analysis of the GI effective equations which nevertheless depend on the different observers intrinsically used in the GI construction.…”

mentioning

confidence: 99%

“…Following the results of [11,13] one can consider an effective scale factor a ef f which describes the dynamics of a perfect fluid-dominated early universe as a ef f = |γ| 1/3 (where we have chosen A (0) (t) = t to have standard results at the homogeneous level [14]), and obtain a quantum gauge invariant version of the effective cosmological equations for the averaged geometry:…”

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confidence: 99%

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Backreaction during Inflation: A Physical Gauge Invariant Formulation

et al. 2011

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Within a genuinely gauge invariant approach recently developed for the computation of the cosmological backreaction, we study, in a cosmological inflationary context and with respect to various observers, the impact of scalar fluctuations on the space-time dynamics in the long wavelength limit. We stress that such a quantum backreaction effect is evaluated in a truly gauge independent way using a set of effective equations which describe the dynamics of the averaged geometry. In particular we show under what conditions the free falling (geodetic) observers do not experience any scalar-induced backreaction in the effective Hubble rate and fluid equation of state.PACS numbers: 98.80. Cq, 04.62.+v Introduction. The computation of backreaction effects induced by cosmological fluctuations in an inflationary era [1,2], has been the subject of controversial analysis [3][4][5][6][7]. Such a task has been plagued by fundamental ambiguities in constructing perturbatively gauge invariant (GI) observables [3] and average quantities. The basic fact that the averaging procedure does not commute with the non linear evolution of Einstein equations [8] was first exploited to study the effective dynamics of the averaged geometry for a dust universe [9] (see [10] for a recent application in the context of inhomogeneity driven inflation). Gauge invariance of averaged quantities has recently been addressed in a novel context which introduces a GI but observer dependent averaging prescription [11] (see [12] for a recent application of such a prescription to the analysis of the present Hubble rate) whereas the effective equations for the averaged geometry [9] have been generalized in a covariant and GI form in [13]. Taking advantage of these recent results and having in mind the backreaction of quantum fluctuations during inflation, we devote this Letter to describing, for the first time in this context, an analysis of the GI effective equations which nevertheless depend on the different observers intrinsically used in the GI construction.Gauge Invariant Backreaction. We start by illustrating how, following a recent proposal [11,13], one may define observables, of a non local nature and constructed with quantum averages, which obey GI dynamical equations. Specifically what has been investigated is how to give a classical or quantum GI average of a scalar S(x), for a classical field or a composite quantum operator, assumed to be renormalized, respectively. In such an approach the fundamental point is the choice of a hypersurface, which defines a class of observers, with respect to which the average is done. In particular a hypersurface Σ A0 is defined, using another scalar field A(x) with a timelike gradient, through the constraint A(x) = A 0 , where A 0 is a con-

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“…First of all, it is the first exact non-perturbative expression for the area distance and once again we stress that it has been possible to find it thanks to the properties of the GLC gauge. 4 GLC gauge also provides a gauge invariant averaging procedure for spacelike domains [16,17] and on the light-cone [3,4,6]. 5 More generally, k μ = ωΥ −1 δ μ τ where ω is an arbitrarily normalization constant.…”

Section: The Jacobi Map and The Glc Gaugementioning

confidence: 99%

Jacobi map and geodesic light-cone gauge: an exact solution

Fanizza

2014

EPJ Web of Conferences

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Abstract. An exact expression for the Jacobi map is furnished. This result has been achieved thanks to the properties of the recently proposed geodesic light-cone gauge. From here, a non-perturbative expression for the area distance is given. It is remarkable that the expression we get nicely appears as the product of a pure source term times a pure observer one. This is true only in the particular gauge we adopt, as shown by transforming the area distance in the synchronous gauge and in the longitudinal one. The consistency among the two expressions is finally checked.

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Gauge invariant averages for the cosmological backreaction

Cited by 60 publications

References 43 publications

Investigation of Frequency Characteristics in Cutting of Soft Tissue Using Prototype Ultrasonic Knives

Investigation of Frequency Characteristics in Cutting of Soft Tissue Using Prototype Ultrasonic Knives

Backreaction during Inflation: A Physical Gauge Invariant Formulation

Jacobi map and geodesic light-cone gauge: an exact solution

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