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Preface List of frequently used symbols 1 Overview 2 Expansion history of the Universe 2.1 Friedmann equations 2.2 Hubble's law 2.3 Matter species in the Universe 2.4 Cosmic distances 2.5 The equation of state of dark energy 2.6 Problems 3 Correlation function and power spectrum 3.1 The correlation function 3.2 The n-point correlation function 3.3 The power spectrum 3.4 From the power spectrum to the moments 3.5 Problems 4 Basics of cosmological perturbation theory 4.1 Perturbing General Relativity 4.2 The Newtonian gauge 4.3 Single-fluid model 4.4 Scales larger than the horizon 4.5 Scales smaller than the Hubble radius 4.6 Two-fluid solutions 4.7 Velocity field 4.8 The redshift distortion 4.9 Baryons, photons, and neutrinos 4.10 The matter power spectrum 4.11 Perturbed photon propagation 4.12 Problems 5 Observational evidence of dark energy 5.1 The age of the Universe 5.2 Supernova observations 5.3 Cosmic Microwave Background 5.4 Baryon acoustic oscillations 5.5 Large-scale structure 5.6 Problems 6 Cosmological constant 6.1 Einstein equations with the cosmological constant 6.2 History of the cosmological constant 6.3 The fine tuning problem 6.4 The coincidence problem 6.5 Supersymmetric models 6.6 Cosmological constant and the anthropic principle 6.7 The decoupling of the cosmological constant from gravity 6.8 Problems 7 Dark energy as a modified form of matter I: Quintessence 7.1 Quintessence 7.2 Dynamical system approach 7.3 Early dark energy 7.4 Quintessence potentials in particle physics 7.5 Reconstruction of quintessence from observations 7.6 Problems 8 Dark energy as a modified form of matter II 8.1 k-essence 8.2 Phantoms 8.3 Coupled dark energy 8.4 Chameleon scalar fields 8.5 Dark energy models with scaling solutions 8.6 Unified models of dark energy and dark matter 8.7 Future singularities 8.8 Problems 9 Dark energy as a modification of gravity 9.1 f(R) gravity 9.2 Scalar-tensor theories 9.3 Gauss-Bonnet dark energy models 9.4 Branewodd models of dark energy 9.5 Problems 10 Cosmic acceleration without dark energy 10.1 Void models 10.2 Backreaction 10.3 Problems 11 Dark energy and linear cosmological perturbations 11.1 Perturbations in a general dark energy cosmology 11.2 Perturbations of a scalar field 11.3 From dark energy to dark force 11.4 A massive dark energy field 11.5 Sound speed of a scalar field 11.6 Perturbations in modified gravity models 11.7 Problems 12 Non-linear cosmological perturbations 12.1 Second-order perturbations 12.2 The bispectrum and the higher-order correction to the power spectrum 12.3 Spherical collapse 12.4 The mass function of collapsed objects 12.5 Dark energy N-body simulations 12.6 Problems 13 Statistical methods in cosmology 13.1 The likelihood function 13.2 Model selection 13.3 Fisher matrix 13.4 The Fisher matrix for the power spectrum 13.5 Principal component analysis 13.6 Problems 14 Future observational constraints on the nature of dark energy 14.1 Dark energy and the CMB 14.2 Large-scale structure 14.3 Growth function 14.4 Cosmic shear 14.5 Cluster abundances and baryon fraction 14.6 Other probes 14.7 Problems 15 Condusion and outlook 16 Answers to the problems 17 Mathematical Appendix References Index