1,721,558 research outputs found
On the Classical and Quantum Irrotational Motions of a Relativistic Perfect Fluid: I. Classical Theory
No full textSome aspects of perfect fluid general-relativistic hydrodynamics under the assumption of irrotationality and isentropicity are analyzed. A new derivation of the known fact that the Lagrangian for these fluids is just the pressure is given. Then we study the fluctuations around a given background configuration, extracting a rule that connects the order at which a Taylor expansion of the action functional possibly stops with the fluid equation of state. From a classical invariance of the action we deduce the conserved Noether current. Because of the spontaneous breaking of such an invariance of the vacuum state Goldstone bosons arise, which turn out to be just phonons (quantized sound waves). Some useful results concerning the linear theory of sound waves are also given
Computational cosmology: A general relativistic approach
No full textNumerical simulations of the large-scale formation of the Universe, which is largely governed by gravity,
are traditionally based on Newton’s lawof gravitation. But general relativistic effects should be included to achieve a realistic cosmological framework that can be compared with the increasingly high-quality data from large cosmological surveys ). In Nature Physics, Julian Adamek et al. discuss the results of computer simulations of structure formation in the Universe. Their numerical code aims to solve Einstein’s field equations relative to the dynamics of cold collisionless matter, with a minimum set of physically motivated simplifying assumptions. Here we comment on this paper and discuss how to progress further in this direction
The Growth of Structure in the Intergalactic Medium
No full textA `stochastic adhesion' model is introduced, with the purpose of describing the formation and evolution of mildly non-linear structures, such as sheets and filaments, in the intergalactic medium (IGM), after hydrogen reionization. The model is based on replacing the overall force acting on the baryon fluid - which results from the combination of local gravity, pressure gradients and Hubble drag - by a mock external force, self-consistently calculated from first-order perturbation theory. A small kinematic viscosity term prevents shell-crossing on small scales (which arises because of the approximate treatment of pressure gradients). The emerging scheme is an extension of the well-known adhesion approximation for the dark matter dynamics, from which it differs only by the presence of a small-scale `random' force, characterizing the IGM. Our algorithm is the ideal tool to obtain the skeleton of the IGM distribution, which is responsible for the structure observed in the low column density Lyα forest in the absorption spectra of distant quasars
Kinematical Properties of Generalized Inflation
No full textThe kinematical properties of Robertson-Walker models which allow a solution of the cosmological horizon and flatness problems are studied: these are called models of generalized inflation. A useful illustration of such inflation is considered in which the background equation of state assumes the form p/ρ = const. < - 1/3. In this context we also discuss a possible solution of the Ω-problem. The general properties of the spectrum of tensor and scalar perturbations generated during the inflationary phase are analyzed. Finally we discuss some examples of generalized inflation which occur mainly in the frame of some recently proposed models of Kaluza-Klein cosmology
Detectability of the effect of inflationary non-Gaussianity on halo bias
No full textWe consider the description of the clustering of halos for physically motivated types of non-Gaussian initial conditions. In particular, we include non-Gaussianity of the type arising from single-field slow roll, multifields, curvaton (local type), higher-order derivative type (equilateral), vacuum-state modifications (enfolded type), and horizon-scale GR corrections type. We show that large-scale halo bias is a very sensitive tool for probing non-Gaussianity, potentially leading, for some planned surveys, to a detection of non-Gaussianity arising from horizon-scale GR corrections. In tandem with cosmic microwave background constraints, the halo bias approach can help enormously to discriminate among different shapes of non-Gaussianity and thus among models for the origin of cosmological perturbations
Post-Newtonian Cosmological Dynamics in Lagrangian Coordinates
No full textWe study the non-linear dynamics of self-gravitating irrotational dust in a general relativistic framework, using synchronous and comoving (i.e. Lagrangian) coordinates. All the equations are written in terms of a single tensor variable, the metric tensor of the spatial sections orthogonal to the fluid flow. This treatment allows an unambiguous expansion in inverse (even) powers of the speed of light. To lowest order, the Newtonian approximation - in Lagrangian form - is derived and written in a transparent way; the corresponding Lagrangian Newtonian metric is obtained. Post-Newtonian corrections are then derived and their physical meaning clarified. A number of results are obtained: (i) the master equation of Lagrangian Newtonian dynamics, the Raychaudhuri equation, can be interpreted as an equation for the evolution of the Lagrangian-to-Eulerian Jacobian matrix, complemented by the irrotationality constraint; (ii) the Lagrangian spatial metric reduces, in the Newtonian limit, to that of Euclidean 3-space written in time-dependent curvilinear coordinates, with non-vanishing Christoffel symbols, but vanishing spatial curvature (a particular example of it is given within the Zel'dovich approximation); (iii) a Lagrangian version of the Bernoulli equation for the evolution of the `velocity potential' is obtained. (iv) The Newtonian and post-Newtonian content of the electric and magnetic parts of the Weyl tensor is clarified. (v) At the post-Newtonian level, an exact and general formula is derived for gravitational-wave emission from non-linear cosmological perturbations; (vi) a straightforward application to the anisotropic collapse of homogeneous ellipsoids shows that the ratio of these postNewtonian terms to the Newtonian ones tends to diverge at least like the mass density. (vii) It is argued that a stochastic gravitational wave background is produced by non-linear cosmic structures, with present-day closure density Ωgw ̃10-5-10-6 on 1-10 Mpc scales
Cosmic Microwave Background Anisotropies from Second Order Gravitational Perturbations
No full textThis paper presents a complete analysis of the effects of second order gravitational perturbations on cosmic microwave background anisotropies, taking explicitly into account scalar, vector and tensor modes. We also consider the second order perturbations of the metric itself obtaining them, for a universe dominated by a collisionless fluid, in the Poisson gauge, by transforming the known results in the synchronous gauge. We discuss the resulting second order anisotropies in the Poisson gauge, and analyze the possible relevance of the different terms. We expect that, in the simplest scenarios for structure formation, the main effect comes from the gravitational lensing by scalar perturbations that is known to give a few percent contribution to the anisotropies at small angular scales
The Effect of Non-Gaussian Statistics on the Mass Multiplicity of Cosmic Structures
No full textThe mass function of cosmic structures is computed in the framework of the hierarchical clustering picture for a general statistics of density perturbations. 'Hierarchical' distributions are extensively analyzed; it is found that the multiplicity function preserves the Press-Schechter functional form with enhanced power on large scales compared to the Gaussian case. A class of scale-invariant non-Gaussian statistics, among which are a model due to Peebles and the lognormal distribution, are also analyzed. All these predict a mass function which is a decreasing power law at low mass followed by an exponential decay at high mass; none of them, however, yields a mass function of the Press-Schechter type. The effect of a statistical bias on the origin of condensations is also discussed. The comparison of these theoretical formulae with the observed mass multiplicity of galaxies, groups, and clusters may represent a powerful tool to test the statistics of cosmological perturbations
The effect of primordial non-Gaussianity onhalo bias
Full text linkIt has long been known how to analytically relate the clustering properties of the collapsed structures (halos) to those of the underlying dark matter distribution for Gaussian initial conditions. Here we apply the same approach to physically motivated non-Gaussian models. The techniques we use were developed in the 1980s to deal with the clustering of peaks of non-Gaussian density fields. The description of the clustering of halos for non-Gaussian initial conditions has recently received renewed interest, motivated by the forthcoming large galaxy and cluster surveys. For inflationary-motivated non-Gaussianities, we find an analytic expression for the halo bias as a function of scale, mass, and redshift, employing only the approximations of high peaks and large separations
Large-scale Curvature Perturbations with Spatial and Time Variations of the Inflaton Decay Rate
No full textWe present a gauge-invariant formalism to study the evolution of the curvature and entropy perturbations in the case in which spatial and time variations of the inflaton decay rate into ordinary matter are present. During the reheating stage after inflation, curvature perturbations can vary with time on super-horizon scales sourced by a gauge-invariant inflaton decay rate perturbation. We show that the latter is a function not only of the spatial variations of the decay rate generated during inflation, as envisaged in a recently proposed scenario, but also of the time variation of the inflaton decay rate during reheating. If only the second source is present, the final curvature perturbation at the end of the reheating stage is proportional to the curvature perturbation at the beginning of reheating, with a coefficient of proportionality which can be either smaller or larger than unity depending upon the underlying physics governing the time variation of the inflaton decay rate. As a consequence, we show that the standard consistency relation between the amplitude of curvature perturbations, the amplitude of tensor perturbations and the tensor spectral index of one-single-field models of inflation is violated and there is the possibility that the tensor-to-curvature amplitude ratio is larger than in the standard case
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