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.Comment: paper accepted for publication in Communications of Mathematical Physics; SISSA preprint 105/97/A. 10 pages and 2 figures, standard late

Quasi-isotropic cycles and non-singular bounces in a Mixmaster cosmology

A Bianchi IX Mixmaster spacetime is the most general spatially homogeneous solution of Einstein's equations and it can represent the space-averaged Universe. We introduce two novel mechanisms resulting in a Mixmaster Universe with non-singular bounces which are quasi-isotropic. A fluid with a non-linear equation of state allows non-singular bounces. Using negative anisotropic stresses successfully isotropises this Universe and mitigates the well known Mixmaster chaotic behaviour. Thus the Universe can be an eternal Mixmaster, going through an infinite series of different cycles separated by bounces, with a sizable fraction of cycles isotropic enough to be well approximated by a standard Friedmann-Lema\^itre-Robertson-Walker model from the radiation era onward.Comment: 5 pages, 4 figure

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.Comment: 21 pages + 4 figures (available as hard copies from K.P.), LaTeX, SISSA 126/93/

fNL - gNL mixing in the matter density field at higher orders

In this paper we examine how primordial non-Gaussianity contributes to nonlinear perturbative orders in the expansion of the density field at large scales in the matter dominated era. General Relativity is an intrinsically nonlinear theory, establishing a nonlinear relation between the metric and the density field. Representing the metric perturbations with the curvature perturbation zeta, it is known that nonlinearity produces effective non-Gaussian terms in the nonlinear perturbations of the matter density field, even if the primordial zeta is Gaussian. Here we generalise these results to the case of a non-Gaussian primordial zeta. Using a standard parametrization of primordial non-Gaussianity in zeta in terms of fNL, gNL, hNL..., we show how at higher order (from third and higher) nonlinearity also produces a mixing of these contributions to the density field at large scales, e.g. both fNL and gNL contribute to the third order in the density contrast. This is the main result of this paper. Our analysis is based on the synergy between a gradient expansion (aka long-wavelength approximation) and standard perturbation theory at higher order. In essence, mathematically the equations for the gradient expansion are equivalent to those of first order perturbation theory, thus first-order results convert into gradient expansion results and, vice versa, the gradient expansion can be used to derive results in perturbation theory at higher order and large scales

Newman-Penrose quantities as valuable tools in astrophysical relativity

In this talk I will briefly outline work in progress in two different contexts in astrophysical relativity, i.e. the study of rotating star spacetimes and the problem of reliably extracting gravitational wave templates in numerical relativity. In both cases the use of Weyl scalars and curvature invariants helps to clarify important issues.Comment: 3 pages. Proceedings of 16th SIGRAV conference, Vietri, Italy, September 200

Non-linear relativistic perturbation theory with two parameters

An underlying fundamental assumption in relativistic perturbation theory is the existence of a parametric family of spacetimes that can be Taylor expanded around a background. Since the choice of the latter is crucial, sometimes it is convenient to have a perturbative formalism based on two (or more) parameters. A good example is the study of rotating stars, where generic perturbations are constructed on top of an axisymmetric configuration built by using the slow rotation approximation. Here, we discuss the gauge dependence of non-linear perturbations depending on two parameters and how to derive explicit higher order gauge transformation rules.Comment: 5 pages, LaTeX2e. Contribution to the Spanish Relativity Meeting (ERE 2002), Mao, Menorca, Spain, 22-24.September.200

Computing General Relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach

We present the first calculation of an intrinsically relativistic quantity in fully non-linear cosmolog- ical large-scale structure studies. Traditionally, non-linear structure formation in standard {\Lambda}CDM cosmology is studied using N-body simulations, based on Newtonian gravitational dynamics on an expanding background. When one derives the Newtonian regime in a way that is a consistent ap- proximation to the Einstein equations, a gravito-magnetic vector potential - giving rise to frame dragging - is present in the metric in addition to the usual Newtonian scalar potential. At leading order, this vector potential does not affect the matter dynamics, thus it can be computed from Newtonian N-body simulations. We explain how we compute the vector potential from simulations in {\Lambda}CDM and examine its magnitude relative to the scalar potential. We also discuss some possible observable effects.Comment: 5 pages, 3 figur

Phenomenology of Unified Dark Matter models with fast transition

A fast transition between a standard matter-like era and a late $\Lambda$CDM-like epoch generated by a single Unified Dark Matter component can explain the observed acceleration of the Universe. UDM models with a fast transition should be clearly distinguishable from $\Lambda$CDM (and alternatives) through observations. Here we focus on a particularly simple model and analyse its viability by studying features of the background model and properties of the adiabatic UDM perturbations.Comment: 4 pages, 1 figure, Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho, Guimar\~aes, Portugal, September 3-7, 201

The Effect of Motivations on Social Indirect Reciprocity: an Experimental Analysis

This paper investigates the effects of motivations on the perceived kindness of an action within the context of strong social indirect reci- procity. We test experimentally the hypothesis that, for a given dis- tributional outcome, an action is perceived by a third party to be less kind if it can be strategically motivated. The results do not support this hypothesis: social indirect reciprocity is indeed found to be signif- icantly stronger when strategic motivations cannot be ruled out. We interpret these findings as an indication of the role played by team reasoning in explaining reciprocal behavior.Indirect Reciprocity, Motivations, Social Preferences, Laboratory Experiments