Relativistic cosmology and large-scale structure

Abstract

General relativity marked the beginning of modern cosmology and it has since been at the centre of many of the key developments in this field. In the present review, we discuss the general-relativistic dynamics and perturbations of the standard cosmological model, the Friedmann-Lemaitre universe, and how these can explain and predict the properties of the observable universe. Our aim is to provide an overview of the progress made in several major research areas, such as linear and non-linear cosmological perturbations, large-scale structure formation and the physics of the cosmic microwave background radiation, in view of current and upcoming observations. We do this by using a single formalism throughout the review, the 1+3 covariant approach to cosmology, which allows for a uniform and balanced presentation of technical information and physical insight.

Several minor changes, typos corrected, references added and updated (Physics Reports in press)

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• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• Weak Gravitational Lensing
• A direct empirical proof of the existence of dark matter
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• The 2dF Galaxy Redshift Survey: Power-spectrum analysis of the final dataset and cosmological implications
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• Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis
• Quantum Nature of the Big Bang: Improved dynamics
• Statistics of Cosmic Microwave Background Polarization
• Signature of Gravity Waves in Polarization of the Microwave Background
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
• Quantum deSitter cosmology and phantom matter
• Observational Constraints on the Nature of the Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey
• The Sunyaev-Zel'dovich Effect
• A Probe of Primordial Gravity Waves and Vorticity
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• The Cold Dark Matter Density Perturbation
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• Inflationary spacetimes are not past-complete
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• Gravitational Lensing Effect on Cosmic Microwave Background Polarization
• The Emergent Universe: inflationary cosmology with no singularity
• Anisotropies in the Cosmic Microwave Background: An Analytic Approach
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• CMB Anisotropies: Total Angular Momentum Method
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• The shape of the SDSS DR5 galaxy power spectrum
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• How Anisotropic is our Universe?
• Cosmic microwave background anisotropies in the CDM model: a covariant and gauge-invariant approach
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• Can superhorizon cosmological perturbations explain the acceleration of the universe?
• CMB Anisotropies at Second-Order II: Analytical Approach
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• Cold + Hot Dark Matter and the Cosmic Microwave Background
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• Nonlinear perturbations of cosmological scalar fields
• Dark energy transition between quintessence and phantom regimes - an equation of state analysis
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• Bianchi Model CMB Polarization and its Implications for CMB Anomalies
• Godel Universes in String Theory
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• Kantowski-Sachs String Cosmologies
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• The Scalar, Vector and Tensor Contributions to CMB anisotropies from Cosmic Defects
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• CMB Temperature and Polarization Anisotropy Fundamentals
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• The Spatial Averaging Limit of Covariant Macroscopic Gravity - Scalar Corrections to the Cosmological Equations
• A covariant and gauge-invariant analysis of cosmic microwave background anisotropies from scalar perturbations
• Cosmic Perturbations Through the Cyclic Ages
• Godel-type Universes in String-inspired Charged Gravity
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• Derivation of the Raychaudhuri Equation
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• Anisotropy of the Cosmic Neutrino Background
• Stability of Closed Timelike Curves in Goedel Universe
• Normalization of modes in an open universe
• Averaging anisotropic cosmologies
• Averaging and Cosmological Observations
• Newtonian nonlinear hydrodynamics and magnetohydrodynamics
• Quantization of perturbations during inflation in the 1+3 covariant formalism
• Illuminating the dark ages of the universe: the exact backreaction in the SFRW model and the acceleration of the universe
• Inhomogeneous perturbations of plane-wave spacetimes
• Cosmology and the Unexpected
• Kinetic theory of polarization in the Sunyaev-Zeldovich effect
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• Observational constraints on the deceleration parameter in a tilted universe
• Cosmological discordances: a new measure, marginalization effects, and application to geometry vs growth current data sets
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• Applicability of the linearly perturbed FRW metric and Newtonian cosmology
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• The cosmological background of vector modes
• Imperfect fluids, Lorentz violations and Finsler Cosmology
• Total Angular Momentum Waves for Scalar, Vector, and Tensor Fields
• The imprint of the interaction between dark sectors in galaxy clusters
• Is backreaction really small within concordance cosmology?
• Cosmological tachyon condensation
• Conserved cosmological perturbation in Galileon models
• The Linear Growth of Structure in the R_h=ct Universe
• Peculiar motions, accelerated expansion and the cosmological axis
• The seed magnetic field generated during recombination
• Covariant kinematics and gravitational bounce in Finsler space-times
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• The Raychaudhuri equation in spacetimes with torsion and non-metricity
• On the stability of static ghost cosmologies
• Can decaying modes save void models for acceleration?
• Kinematics of Einstein-Cartan universes
• Generalized second law of thermodynamics in scalar-tensor gravity
• The generalized second law of gravitational thermodynamics on the apparent horizon in f(R)-gravity
• Light propagation and the average expansion rate in near-FRW universes
• Relativistic numerical cosmology with Silent Universes
• Metric-Affine Gravity and Cosmology/Aspects of Torsion and non-Metricity in Gravity Theories
• The deceleration parameter in `tilted' Friedmann universes
• Qualitative analysis of Kantowski-Sachs metric in a generic class of $f(R)$ models
• Exact nonlinear inhomogeneities in $\Lambda$CDM cosmology
• Acoustic signatures in the Cosmic Microwave Background bispectrum from primordial magnetic fields
• On the relation between the isotropy of the CMB and the geometry of the universe
• Cosmological magnetic field survival
• A covariant treatment of cosmic parallax
• Note on the thermodynamics and the speed of sound of a scalar field
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• Shear free solutions in General Relativity Theory
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• Raychaudhuri's equation and aspects of relativistic charged collapse
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• The Cosmology of Quadratic Torsionful Gravity
• Density growth in Kantowski-Sachs cosmologies with cosmological constant
• From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect
• Cosmological backreaction within the Szekeres model and emergence of spatial curvature
• A conventional approach to the dark-energy concept
• Gravitational waves in Friedman-Lemaitre-Robertson-Walker cosmology, material perturbations and cosmological rotation, and the Huygens principle
• The deceleration parameter in `tilted' universes: generalising the Friedmann background
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• On spherical dust fluctuations: the exact vs. the perturbative approach
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• Spectral distortions in the cosmic microwave background polarization
• Relativistic approach to the kinematics of large-scale peculiar motions
• Dynamical apparent horizons in inhomogeneous Brans-Dicke universes
• Formulating Weak Lensing from the Boltzmann Equation and Application to Lens-lens Couplings
• Large-scale peculiar motions and cosmic acceleration
• Anisotropy in Pantheon+ supernovae
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• Vorticity survival in magnetised Friedmann universes
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• Cosmic magnetization in curved and Lorentz violating space-times
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