Cosmology

Cosmology is the branch of physics and astrophysics that studies the origin, evolution, and ultimate fate of the universe as a single, coherent system. It seeks to provide a comprehensive physical model for the entire cosmos, from its initial moments in the Big Bang to its ongoing expansion and the formation of large-scale structures like galaxies and galaxy clusters. Cosmologists utilize Albert Einstein's theory of general relativity as a primary framework and draw upon observational evidence, such as the cosmic microwave background radiation and the distribution of galaxies, to investigate the fundamental nature of dark matter, dark energy, and the very fabric of spacetime.

1. Foundations of Modern Cosmology
   1. Historical Development of Cosmological Models
      1. Ancient Cosmologies
         1. Mesopotamian Models
         2. Egyptian Cosmology
         3. Greek Philosophical Models
            1. Aristotelian Universe
            2. Platonic Cosmology
            3. Atomistic Models
      2. Medieval Cosmology
         1. Islamic Astronomical Contributions
         2. Scholastic Synthesis
      3. Geocentric Models
         1. Ptolemaic System
         2. Epicycles and Deferents
         3. Mathematical Refinements
      4. Heliocentric Revolution
         1. Copernican Model
         2. Galilean Observations
            1. Telescopic Discoveries
            2. Phases of Venus
            3. Moons of Jupiter
         3. Kepler's Laws
            1. Elliptical Orbits
            2. Area Law
            3. Harmonic Law
      5. Newtonian Cosmology
         1. Infinite Static Universe
         2. Gravitational Theory Applications
         3. Olbers' Paradox
         4. Mach's Principle
      6. Transition to Modern Era
         1. Advances in Observational Astronomy
         2. Spectroscopy Development
         3. Stellar Classification
         4. Discovery of Nebulae
   2. Fundamental Cosmological Principles
      1. The Cosmological Principle
         1. Homogeneity
            1. Definition and Scale
            2. Observational Evidence
         2. Isotropy
            1. Definition and Measurements
            2. Statistical Tests
         3. Large-Scale Structure Implications
      2. The Copernican Principle
         1. Earth's Non-Special Position
         2. Extension to Solar System
         3. Galactic Perspective
         4. Philosophical Implications
      3. Principle of Relativity
         1. Special Relativity Foundations
         2. General Covariance
         3. Invariance of Physical Laws
   3. Einstein's General Relativity Framework
      1. Conceptual Foundations
         1. Equivalence Principle
            1. Weak Equivalence Principle
            2. Einstein Equivalence Principle
            3. Strong Equivalence Principle
         2. Spacetime Geometry
            1. Curved Spacetime Concept
            2. Geodesics
            3. Tidal Effects
      2. Mathematical Framework
         1. Metric Tensor
         2. Riemann Curvature Tensor
         3. Einstein Field Equations
            1. Mathematical Formulation
            2. Energy-Momentum Tensor
            3. Cosmological Constant Term
      3. Early Cosmological Applications
         1. Einstein's Static Universe
            1. Motivation and Construction
            2. Instability Problem
         2. De Sitter Solution
         3. Cosmological Constant Introduction