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

One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

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The classical-quantum boundary for correlations: Discord and related measures

Generating the curvature perturbation without an inflaton

1 Introduction 2 Models: the QCD axion; the strong CP problem; PQWW, KSVZ, DFSZ; anomalies, instantons and the potential; couplings; axions in string theory 3 Production and IC's: SSB and non-perturbative physics; the axion field during inflation and PQ SSB; cosmological populations - decay of parent, topological defects, thermal production, vacuum realignment 4 The Cosmological Field: action; background evolution; misalignment for QCD axion and ALPs; cosmological perturbation theory - ic's, early time treatment, axion sound speed and Jeans scale, transfer functions and WDM; the Schrodinger picture; simualting axions; BEC 5 CMB and LSS: Primary anisotropies; matter power; combined constraints; Isocurvature and inflation 6 Galaxy Formation; halo mass function; high-z and the EOR; density profiles; the CDM small-scale crises 7 Accelerated expansion: the cc problem; axion inflation (natural and monodromy) 8 Gravitational interactions with black holes and pulsars 9 Non-gravitational interactions: stellar astrophysics; LSW; vacuum birefringence; axion forces; direct detection with ADMX and CASPEr; Axion decays; dark radiation; astrophysical magnetic fields; cosmological birefringence 10 Conclusions A Theta vacua of gauge theories B EFT for cosmologists C Friedmann equations D Cosmological fluids E Bayes Theorem and priors F Degeneracies and sampling G Sheth-Tormen HMF

Axion Cosmology

Non-Gaussianity from inflation: theory and observations

We numerically investigate the formation of D-dimensional black holes in high-energy particle collisions with the impact parameter and evaluate the total cross section of black hole production. We find that the formation of an apparent horizon occurs when the distance between the colliding particles is less than 1.5 times the effective gravitational radius of each particle. Our numerical result indicates that although both the one-dimensional hoop and the $(D\ensuremath{-}3)$-dimensional volume corresponding to the typical scale of the system give a fairly good condition for horizon formation in the higher-dimensional gravity, the $(D\ensuremath{-}3)$-dimensional volume provides a better condition to judge the existence of the horizon.

Black hole formation in the grazing collision of high-energy particles

We investigate the instability of charged massive scalar fields in Kerr-Newman spacetime. Due to the super-radiant effect of the background geometry, the bound state of the scalar field is unstable, and its amplitude grows in time. By solving the Klein-Gordon equation of the scalar field as an eigenvalue problem, we numerically obtain the growth rate of the amplitude of the scalar field. Although the dependence of the scalar field mass and the scalar field charge on this growth rate agrees with the result of the analytic approximation, the maximum value of the growth rate is three times larger than that of the analytic approximation. We also discuss the effect of the electric charge on the instability of the scalar field.

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Instability of Massive Scalar Fields in Kerr-Newman Spacetime

If expanding and contracting regions coexist in the universe, the speed of the cosmic volume expansion can be accelerated. We construct simple inhomogeneous dust-filled universe models in which the speed of the cosmic volume expansion is accelerated for finite periods. These models are constructed by removing spherical domains from the Einstein-de Sitter �

Can Inhomogeneities Accelerate the Cosmic Volume Expansion

Stochastic Approach to Chaotic Inflation and the Distribution of Universes

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Yasusada Nambu

Papers

Black hole formation in the grazing collision of high-energy particles

Instability of Massive Scalar Fields in Kerr-Newman Spacetime

Can Inhomogeneities Accelerate the Cosmic Volume Expansion

Stochastic Approach to Chaotic Inflation and the Distribution of Universes

Stochastic Dynamics of New Inflation