arXiv subjects

Marco Bruni

Publications and source records attributed to Marco Bruni.

77 records · Page 5Linked to original sources

arXiv1997

Gauge dependence in the theory of non-linear spacetime perturbations

Diffeomorphism freedom induces a gauge dependence in the theory of spacetime perturbations. We derive a compact formula for gauge transformations of perturbations of arbitrary order. To this end, we develop the theory of Taylor expansions for one-parameter families (not necessarily groups) of diffeomorphisms. First, we introduce the notion of knight diffeomorphism, that generalises the usual concept of flow, and prove a Taylor's formula for the action of a knight on a general tensor field. Then, we show that any one-parameter family of diffeomorphisms can be approximated by a family of suitable knights. Since in perturbation theory the gauge freedom is given by a one-parameter family of diffeomorphisms, the expansion of knights is used to derive our transformation formula. The problem of gauge dependence is a purely kinematical one, therefore our treatment is valid not only in general relativity, but in any spacetime theory.

gr-qc↗

arXiv1997

Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond

We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results concerning the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of diffeomorphisms. Second, we define gauge invariance to an arbitrary order $n$. Finally, we give a generating formula for the gauge transformation to an arbitrary order and explicit rules to second and third order. This formalism can be used in any field of applied general relativity, such as cosmological and black hole perturbations, as well as in other spacetime theories. As a specific example, we consider here second order perturbations in cosmology, assuming a flat Robertson-Walker background, giving explicit second order transformations between the synchronous and the Poisson (generalized longitudinal) gauges.

gr-qc↗

arXiv1994

Conserved Quantities in Perturbed Inflationary Universes

Given that observations seem to favour a \index{density parameter} $Ω_0<1$, corresponding to an open universe, we consider gauge\hs invariant perturbations of non\hs flat Robertson\hs Walker universes filled with a general imperfect fluid which can also be taken to represent a scalar field. Our aim is to set up the equations that govern the evolution of the density perturbations $Δ$ so that it can be determined through a {\it first order differential equation} with a quantity $\kk$ which is conserved at any length scale, even in non\hs flat universe models, acting as a source term. The quantity $\kk$ generalizes other variables that are conserved in specific cases (for example at large scales in a flat universe) and is useful to connect different epochs in the evolution of density perturbations via a transfer function. We show that the problem of finding a conserved $\kk$ can be reduced to determining two auxiliary variables $X$ and $Y$, and illustrate the method with two simple examples.

gr-qc↗

arXiv1993

Peculiar Velocity, Cosmic Perturbation Theory and the CMB Anisotropy

This is a somewhat extended version of the original July 93 report. It is proved that the cosmological density perturbation is associated with a peculiar velocity field. This allows a simple formulation of cosmological perturbation theory, which works entirely with quasi-Newtonian fluid flow equations. As an illustration, the large scale cosmic microwave background anisotropy (Sachs-Wolfe effect) is calculated without any reference to the metric perturbation. In addition, assuming the usual adiabatic initial condition on the density perturbation, we show that the dipole of the anisotropy measures our peculiar velocity relative to the average peculiar velocity within the last scattering surface of the microwave background, thus defining its frame of reference.

astro-ph↗

arXiv1993

Dust-Radiation Universes: Stability Analysis

Flat and open universe models are considered, containing a mixture of cold matter (dust) and radiation interacting only through gravity, with the aim of studying their stability with respect to linear scalar perturbations. To this end the perturbed universe is considered as a dynamical system, described by coupled differential equations for a gauge\hs invariant perturbation variable and a relevant background variable. The phase\hs space analysis of this dynamical system shows that flat dust\hs radiation models are unstable, and open models structurally unstable, with respect to adiabatic perturbations. It is shown that there are perturbations which decay even if their wavelength at equidensity is larger than the corresponding Jeans scale. Metric and curvature perturbations are also briefly discussed. We believe that this analysis gives a clearer idea of the stability properties of realistic universe models than the standard one based on the Jeans scale, despite our simplifying assumptions.

astro-ph↗