Cosmology

  1. The Expanding Universe
    1. Observational Discovery
      1. Early Observations of Nebulae
        1. Spiral Nebulae Debate
          1. Cepheid Variable Stars
          2. Redshift Measurements
            1. Spectroscopic Techniques
              1. Doppler Effect Interpretation
                1. Vesto Slipher's Observations
                2. Hubble's Contributions
                  1. Distance Measurements
                    1. Velocity-Distance Relation
                      1. Hubble's Law Formulation
                      2. The Hubble Constant
                        1. Definition and Units
                          1. Measurement Methods
                            1. Cepheid Variables
                              1. Type Ia Supernovae
                                1. Surface Brightness Fluctuations
                                2. Current Value and Uncertainties
                              2. Theoretical Framework
                                1. Friedmann-Lemaître-Robertson-Walker Metric
                                  1. Mathematical Formulation
                                    1. Assumptions and Symmetries
                                      1. Coordinate Systems
                                      2. Scale Factor Evolution
                                        1. Definition of Scale Factor
                                          1. Physical Interpretation
                                            1. Time Dependence
                                            2. Comoving Coordinates
                                              1. Proper Distance
                                                1. Comoving Distance
                                                  1. Angular Diameter Distance
                                                    1. Luminosity Distance
                                                      1. Light Travel Time
                                                    2. Geometry of Space
                                                      1. Spatial Curvature
                                                        1. Flat Geometry (k=0)
                                                          1. Euclidean Properties
                                                            1. Infinite Extent
                                                            2. Closed Geometry (k=+1)
                                                              1. Spherical Properties
                                                                1. Finite Volume
                                                                2. Open Geometry (k=-1)
                                                                  1. Hyperbolic Properties
                                                                    1. Infinite Extent
                                                                  2. Observational Constraints
                                                                    1. CMB Measurements
                                                                      1. Supernova Observations
                                                                        1. BAO Measurements
                                                                      2. Friedmann Equations
                                                                        1. Derivation from General Relativity
                                                                          1. First Friedmann Equation
                                                                            1. Energy Conservation
                                                                              1. Critical Density
                                                                              2. Second Friedmann Equation
                                                                                1. Acceleration Equation
                                                                                  1. Pressure Effects
                                                                                  2. Density Parameters
                                                                                    1. Matter Density Parameter
                                                                                      1. Radiation Density Parameter
                                                                                        1. Dark Energy Density Parameter
                                                                                          1. Curvature Parameter
                                                                                          2. Solutions for Different Epochs
                                                                                            1. Radiation-Dominated Era
                                                                                              1. Matter-Dominated Era
                                                                                                1. Dark Energy-Dominated Era

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                                                                                            1. Foundations of Modern Cosmology

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                                                                                            3. The Standard Model of Cosmology