We present in a manifestly gauge-invariant form the theory of classical linear gravitational perturbations in part I, and a quantum theory of cosmological perturbations in part II. Part I includes applications to several important examples arising in cosmology: a univese dominated by hydrodynamical matter, a universe filled with scalar-field matter, and higher-derivative theories of gravity. The growth rates of perturbations are calculated analytically in most interesting cases. The analysis is applied to study the evolution of fluctuations in inflationary universe models. Part II includes a unified description of the quantum generation and evolution of inhomogeneities about a classial Friedmann background. The method is based on standard canonical quantization of the action for cosmological perturbations which has been reduced to an expression in terms of a single gauge-invariant variable. The spectrum of density perturbations originating in quantum fluctuations is calculated in universe with hydrodynamical matter, in inflationary universe models with scalar-field matter, and in higher-derivative theories of gravity.

The gauge-invariant theory of classical and quantized cosmological perturbations developed in parts I and II is applied in part III to several interesting physical problems. It allows a simple derivation of the relation between temperature anistropes in the cosmic microwave background. radiation and the gauge-invariant potential for metric perturbations. The generation and evolution of gravitational waves is studied. As another example, a simple analysis of entropy perturbations and non-scale-invariant spectra in inflationary universe models is presented. The gauge-invariant theory of cosmological perturbations also allows a consistent and gauge-invariant definition of statistical fluctuations.

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Theory of Cosmological Perturbations

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

There is accumulating evidence that (fundamental) scalar fields may exist in nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. As with white dwarfs and neutron stars, a limiting mass exists similarly, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation; however, modifications of general relativity, as in the case of Jordan?Brans?Dicke theory as a low-energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to the constituent mass, an effective radius and a large particle number. Due to the Heisenberg principle, a completely stable branch exists, and as a coherent state, it allows for rotating solutions with quantized angular momentum. In this review, we concentrate on the fascinating possibilities of detecting the various subtypes of (excited) BSs: possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.

https://iopscience.iop.org/article/10.1088/0264-9381/20/20/201/pdf

General relativistic boson stars

Reheating is an important part of inflationary cosmology. It describes the production of Standard Matter particles after the phase of accelerated expansion. We give a review of the reheating process, focusing on an in-depth discussion of the preheating stage which is characterized by exponential particle production due to a parametric resonance or tachyonic instability. We give a brief overview of the thermalization process after preheating and end with a survey of some applications to supersymmetric theories and to other issues in cosmology such as baryogenesis, dark matter and metric preheating.

/pdf/reheating-in-inflationary-cosmology-theory-and-applications-4cmnm3moly.pdf

Reheating in Inflationary Cosmology: Theory and Applications

We present a model for the distribution of void sizes and its evolution in the context of hierarchical scenarios of gravitational structure formation. We find that at any cosmic epoch the voids have a size distribution that is well-peaked about a characteristic void size that evolves self-similarly in time. This is in distinct contrast to the distribution of virialized halo masses, which does not have a small-scale cut-off. In our model, the fate of voids is ruled by two processes. The first process affects those voids which are embedded in larger underdense regions: the evolution is effectively one in which a larger void is made up by the mergers of smaller voids, and is analogous to how massive clusters form from the mergers of less massive progenitors. The second process is unique to voids, and occurs to voids that happen to be embedded within a larger-scale overdensity: these voids get squeezed out of existence as the overdensity collapses around them. It is this second process which produces the cut-off at small scales. In the excursion set formulation of cluster abundance and evolution, the solution of the cloud-in-cloud problem, i.e. counting as clusters only those objects which are not embedded in larger clusters, requires the study of random walks crossing one barrier. We show that a similar formulation of void evolution requires the study of a two-barrier problem: one barrier is required to account for voids-in-voids, and the other for voids-in-clouds. Thus, in our model, the void size distribution is a function of two parameters, one of which reflects the dynamics of void formation, and the other the formation of collapsed objects.

http://lss.fnal.gov/archive/2004/pub/fermilab-pub-04-152-a.pdf

A hierarchy of voids: much ado about nothing

Initial conditions for inflation

We study numerically the onset of inflation under inhomogeneous initial conditions for various inflationary scenarios and various initial parameters. We solve the full Einstein equations for the gravitational field coupled to scalar-field and radiation-field sources, under the assumptions of spherical symmetry and a closed-universe background. We find that a large initial inhomogeneity suppresses the onset of inflation, and that the scalar field must have values suitable for inflation over a region of several horizon sizes for the inflationary phase to begin.

Inhomogeneity and the onset of inflation.

Observational constraints on the isotropy of the microwave background on angular scales greater than 1° seriously limit the possible fluctuations in the gravitational potential in the universe because of the Sachs-Wolfe effect. Consequently, they also provide a limit on the initial density inhomogeneities in the universe. We use these limits to show that the typical voids in the mass distribution in an Ω = 1 universe have limiting diameter D 130 h −1 Mpc

The largest possible voids

We present a numerical study of the gravitational collapse of a massless scalar field. We calculate the future evolution of new initial data, suggested by Christodoulou, and we show that in spite of the original expectations these data lead only to singularities engulfed by an event horizon.

Gravitational collapse of massless scalar field and cosmic censorship

We describe a spherically symmetric code for inhomogeneous cosmological problems. Our main goal is to study the onset of inflation under inhomogeneous conditions. We would like to explore the influence of inhomogeneity on inflation. In particular we address the question of whether large inhomogeneity during the very early Universe can prevent the Universe from entering an inflationary era. In this paper we describe the equations, the numerical techniques, tests, and some preliminary results. A detailed discussion of the results will follow in a subsequent paper.

Dalia S. Goldwirth

Papers

Initial conditions for inflation

Inhomogeneity and the onset of inflation.

The largest possible voids

Gravitational collapse of massless scalar field and cosmic censorship

Spherical inhomogeneous cosmologies and inflation: Numerical methods.