Instability Effects in F ( R )-Modified Gravity and in Gravitational Baryogenesis
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stability Effects in F(R)-Modified Gravity and in Gravitational Baryogenesis E. V. Arbuzovaa, b, * and A. D. Dolgovb, c, ** a
Dubna State University, Dubna, Moscow oblast, 141982 Russia bNovosibirsk State University, Novosibirsk, 630090 Russia c Alikhanov Institute for Theoretical and Experimental Physics, National Research Center Kurchatov Institute, Moscow, 117218 Russia *e-mail: [email protected] **e-mail: [email protected] Received June 24, 2019; revised July 15, 2019; accepted July 15, 2019
Abstract—The review is devoted to the development and subsequent application of methods for studying the stability of solutions of higher-order differential equations arising in various models of modified gravity and baryosynthesis. Major attention is paid to F(R)-modified theories proposed to describe the accelerated expansion of the universe and to baryon asymmetry generation in the framework of the spontaneous and gravitational baryogenesis. DOI: 10.1134/S1063779619060078
CONTENTS 1. INTRODUCTION 851 1.1. Accelerated Expansion of the Universe: History of the Discovery and Observed Phenomena 851 1.2. Standard Cosmological Model 852 1.3. GR and Einstein Equations 853 1.4. Basic Equations of Cosmology and Cosmological Parameters 855 1.5. Driving Force of Cosmological Acceleration 856 1.5.1. Dark energy 856 1.5.2. Modified gravity 857 1.6. Baryon Asymmetry of the Universe 859 1.7. Review Structure 860 2. INSTABILITY AND OSCILLATIONS OF CURVATURE IN F (R)-MODELS 861 2.1. Curvature Instability in Systems with Rising Energy Density 861 2.2. Curvature Oscillations in F (R)-Models of Modified Gravity 864 2.3. Particle Production by Oscillating Curvature 868 2.3.1. Regular region 869 2.3.2. Spike region 869 3. COSMOLOGICAL EVOLUTION IN R 2 THEORY 870
3.1. Evolution of the Universe from the Inflationary Cosmology to the Friedmann Cosmology 3.1.1. Solution ab ovo to γτ & 1 3.1.2. Solution for γτ * 1 3.1.3. Discussion and conclusions 3.2. Corrections to Classical Cosmology at the Radiation-Dominated Stage 3.2.1. Evolution Equations in Dimensionless Form and Their Solution 3.2.2. Back reaction of particle production to the curvature scalar evolution 3.2.3. Gravitational production of particles 3.2.4. Discussion and implications 4. JEANS INSTABILITY AND ANTIGRAVITY IN F(R) THEORIES 4.1. Spherically Symmetric Solutions in F (R) Gravity and Gravitational Repulsion 4.1.1. Schwarzschild case 4.1.2. Solutions in modified gravity 4.2. Evolution of Density Perturbations in Newtonian Gravity and in GR 4.2.1. Jeans instability in Newtonian theory in inhomogeneous and nonstationary background 850
870 873 880 883 883 883 888 891 892 892 892 894 895 896 896
INSTABILITY EFFECTS IN F(R)-MODIFIED GRAVITY
4.2.2. Evolution of density perturbations in General Relativity 898 4.3. Density Perturbations in Modified Gravity 900 4.3.1. Evolution equation 900 4.3.2. Modified Jeans instability 904 4.3.3. Parametric resonance 905 4.3.4. Amplification by antifriction 909 5. PROBLEMS OF SPONTANEOUS AND GRAVITATIONAL BARYOSYNTHESIS 914 5.1. Spontaneous B
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