Robert H. Brandenberger

Theory of cosmological perturbations

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.

Superstrings in the Early Universe

We investigate some aspects of thermodynamics and cosmology for superstrings. By a rather delicate computation using the microcanonical ensemble we show that the thermodynamic description of strings is sound (specific heat is positive at large energies) only for strings propagating in spaces where all the spatial directions are compact. Using this result and by considering a simple model, we show how strings resolve the initial singularity of the Big Bang. We also discuss a cosmological scenario which has the potential of explaining the space-time dimensionality.

Universe reheating after inflation

We study the problem of scalar particle production after inflation by a rapidly oscillating inflaton field. We use the framework of the chaotic inflation scenario with quartic and quadratic inflaton potentials. Particular attention is paid to parametric resonance phenomena which take place in the presence of the quickly oscillating inflaton field. We have found that in the region of applicability of perturbation theory the effects of parametric resonance are crucial, and estimates based on first order Born approximation often underestimate the particle production. In the case of the quartic inflaton potential

Matter bounce in Horava-Lifshitz cosmology

V(\varphi) = \lambda \varphi^4

Producing a Scale-Invariant Spectrum of Perturbations in a Hagedorn Phase of String Cosmology

, the particle production process is very efficient even for small values of coupling constants. The reheating temperature of the universe in this case is

Reheating in Inflationary Cosmology: Theory and Applications

\left[\lambda\, \log\, (1/\lambda) \right]^{- 1}

Brane gases in the early Universe

times larger than the corresponding estimates based on first order Born approximation. In the case of the quadratic inflaton potential the reheating process depends crucially on the type of coupling between the inflaton and the other scalar field and on the magnitudes of the coupling constants. If the inflaton coupling to fermions and its linear (in inflaton field) coupling to scalar fields are suppressed, then, as previously discussed by Kofman, Linde and Starobinsky (see e.g. Ref. 13), the inflaton field will eventually decouple from the rest of the matter, and the residual inflaton oscillations may provide the (cold) dark matter of the universe. In the case of the quadratic inflaton potential we obtain the lowest and the highest possible bounds on the effective energy density of the inflaton field when it freezes out.

THE ROBUSTNESS OF INFLATION TO CHANGES IN SUPER-PLANCK-SCALE PHYSICS

Horava-Lifshitz gravity, a recent proposal for a UV-complete renormalizable gravity theory, may lead to a bouncing cosmology. In this article we argue that Horava-Lifshitz cosmology may yield a concrete realization of the matter bounce scenario and thus give rise to an alternative to inflation for producing a scale-invariant spectrum of cosmological perturbations. In this scenario, quantum vacuum fluctuations exit the Hubble radius in the prebounce phase, and the spectrum is transformed into a scale-invariant one on super-Hubble scales before the bounce because the long wavelength modes undergo squeezing of their wave functions for a longer period of time than shorter wavelength modes. The scale invariance of the spectrum of curvature fluctuations is preserved during and after the bounce. A distinctive prediction of this scenario is the amplitude and shape of the bispectrum.

Nonsingular cosmology with a scale-invariant spectrum of cosmological perturbations from Lee-Wick theory

We study the generation of cosmological perturbations during the Hagedorn phase of string gas cosmology. Using tools of string thermodynamics we provide indications that it may be possible to obtain a nearly scale-invariant spectrum of cosmological fluctuations on scales which are of cosmological interest today. In our cosmological scenario, the early Hagedorn phase of string gas cosmology goes over smoothly into the radiation-dominated phase of standard cosmology, without having a period of cosmological inflation.

Inflationary cosmology: Progress and problems

Reheating is an important part of inflationary cosmology. It describes the production of Standard Model particles after the phase of accelerated expansion. We review the reheating process with a focus 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.