Synchronous coordinates and gauge-invariant observables in cosmological spacetimes

We consider the relational approach to construct gauge-invariant observables in cosmological perturbation theory using synchronous coordinates. We construct dynamical synchronous coordinates as non-local scalar functionals of the metric perturbation in the fully non-linear theory in an arbitrary gauge. We show that the observables defined in this dynamical coordinate system are gauge-independent, and that the full perturbed metric has the expected form in these coordinates. Our construction generalises the familiar synchronous gauge in linearised gravity, widely used in cosmological perturbation theory, to the non-linear theory. We also work out the expressions for the gauge-invariant Einstein equations, sourced either by an ideal fluid or a scalar field up to second order in perturbation theory, and give explicit expressions for the Hubble rate -- as measured by synchronous observers or by observers co-moving with the matter field -- up to that order. Finally, we consider quantised linear perturbations around Minkowski and de Sitter backgrounds, and compute the two-point function of the gauge-invariant metric perturbation in synchronous coordinates, starting with two-point function in a general linear covariant gauge. Although the gauge-fixed two-point function contains gauge modes, we show that the resulting gauge-invariant two-point function only contains the physical tensor modes and it is thus positive, i.e., it has a spectral representation.Comment: 52 pages. Comments are welcom

Awaking the vacuum with spheroidal shells

It has been shown that well-behaved spacetimes may induce the vacuum fluctuations of some nonminimally coupled free scalar fields to go through a phase of exponential growth. Here, we discuss this mechanism in the context of spheroidal thin shells emphasizing the consequences of deviations from spherical symmetry.Comment: 10 pages, 7 figures. Minor changes, version published on Phys. Rev.

From quantum to classical instability in relativistic stars

It has been shown that gravitational fields produced by realistic classical-matter distributions can force quantum vacuum fluctuations of some nonminimally coupled free scalar fields to undergo a phase of exponential growth. The consequences of this unstable phase to the background spacetime have not been addressed so far due to known difficulties concerning backreaction in semiclassical gravity. It seems reasonable to believe, however, that the quantum fluctuations will "classicalize" when they become large enough, after which backreaction can be treated in the general-relativistic context. Here we investigate the emergence of a classical regime out of the quantum field evolution during the unstable phase. By studying the appearance of classical correlations and loss of quantum coherence, we show that by the time backreaction becomes important the system already behaves classically. Consequently, the gravity-induced instability leads naturally to initial conditions for the eventual classical description of the backreaction. Our results give support to previous analyses which treat classically the instability of scalar fields in the spacetime of relativistic stars, regardless whether the instability is triggered by classical or quantum perturbations.Comment: 16 pages. Minor changes to match the published versio

L'immixtion et la trop grande expertise du propriétaire, cause d'exonération de responsabilité des architectes et des entrepreneurs sous l'article 1688 C.C.

In May 1977, the Supreme Court of Canada gave an authoritative judgment on the interpretation of article 1688 of the Civil Code dealing with the liability of the builder and the architect. In Davie Shipbuilding Ltd v. Cargill Grain Company Ltd and The Foundation Company of Canada Ltd, the court established a new method of rebutting the presumption of liability resulting from the article. Indeed, the Supreme Court found that where the owner intervened during the construction and was more qualified than the contractors in charge of the work to judge its quality, he could not invoke the presumption resulting from article 1688 C.C. and was responsible for any loss. The case is not an easy one — questions of law and facts are not simple in this dispute involving more than eleven million dollars

Graviton backreaction on the local cosmological expansion in slow-roll inflation

We compute the graviton one-loop correction to the expectation value of the local expansion rate in slow-roll inflation, with both slow-roll parameters finite. The calculation is based on a recent method to explicitly construct gauge-invariant observables in perturbative quantum gravity at all orders in perturbation theory, and it is particularly suited in cases of highly-symmetrical space-time backgrounds. Our analysis adds to recent calculations of that correction in de Sitter space-time and in single-field inflation with constant deceleration. In the former case a vanishing one-loop correction was found, while in the latter the quantum backreaction produces a secular effect that accelerates the expansion. The quantum correction we describe here produces a finite secular effect that can either accelerated or decelerate the background expansion, depending on the value of the slow-roll parameters

Non-commutative Geometry from Perturbative Quantum Gravity in de Sitter spacetime

We show that a non-commutative structure arises naturally from perturbative quantum gravity in a de Sitter background metric. Our work builds on recent advances in the construction of observables in highly symmetric background spacetimes [Brunetti et al., JHEP 08, 032 (2016); Fr\"ob and Lima, Class. Quant. Grav. 35, 095010 (2018)], where the dynamical coordinates that are needed in the relational approach were established for such backgrounds to all orders in perturbation theory. We show that these dynamical coordinates that describe events in the perturbed spacetime are naturally non-commuting, and determine their commutator to leading order in the Planck length. Our result generalizes the causal non-commutative structure that was found using the same approach in Minkowski space [Fr\"ob, Much and Papadopoulos, Phys. Rev. D 107, 064041 (2023)]

Product line architecture recovery with outlier filtering in software families: the Apo-Games case study

Software product line (SPL) approach has been widely adopted to achieve systematic reuse in families of software products. Despite its benefits, developing an SPL from scratch requires high up-front investment. Because of that, organizations commonly create product variants with opportunistic reuse approaches (e.g., copy-and-paste or clone-and-own). However, maintenance and evolution of a large number of product variants is a challenging task. In this context, a family of products developed opportunistically is a good starting point to adopt SPLs, known as extractive approach for SPL adoption. One of the initial phases of the extractive approach is the recovery and definition of a product line architecture (PLA) based on existing software variants, to support variant derivation and also to allow the customization according to customers’ needs. The problem of defining a PLA from existing system variants is that some variants can become highly unrelated to their predecessors, known as outlier variants. The inclusion of outlier variants in the PLA recovery leads to additional effort and noise in the common structure and complicates architectural decisions. In this work, we present an automatic approach to identify and filter outlier variants during the recovery and definition of PLAs. Our approach identifies the minimum subset of cross-product architectural information for an effective PLA recovery. To evaluate our approach, we focus on real-world variants of the Apo-Games family. We recover a PLA taking as input 34 Apo-Game variants developed by using opportunistic reuse. The results provided evidence that our automatic approach is able to identify and filter outlier variants, allowing to eliminate exclusive packages and classes without removing the whole variant. We consider that the recovered PLA can help domain experts to take informed decisions to support SPL adoption.This research was partially funded by INES 2.0; CNPq grants 465614/2014-0 and 408356/2018-9; and FAPESB grants JCB0060/2016 and BOL2443/201

Gravity-induced vacuum dominance

It has been widely believed that, except in very extreme situations, the influence of gravity on quantum fields should amount to just small, sub-dominant contributions. This view seemed to be endorsed by the seminal results obtained over the last decades in the context of renormalization of quantum fields in curved spacetimes. Here, however, we argue that this belief is false by showing that there exist well-behaved spacetime evolutions where the vacuum energy density of free quantum fields is forced, by the very same background spacetime, to become dominant over any classical energy-density component. This semiclassical gravity effect finds its roots in the infrared behavior of fields on curved spacetimes. By estimating the time scale for the vacuum energy density to become dominant, and therefore for backreaction on the background spacetime to become important, we argue that this vacuum dominance may bear unexpected astrophysical and cosmological implications.Comment: To appear in Phys. Rev. Lett