Cosmology Lecture Notes

Introduction to Cosmology

• Definition: Cosmology is the study of the universe, its origins, and its evolution.
• Historical Context:
  • Ancient Greeks contributed to cosmological ideas.
  • Modern cosmology began around the 20th century (post-Hubble).
• Key Discoveries:
  • Hubble's discovery of the universe's expansion.
  • Big Bang theory and cosmic microwave background radiation (1960s).

Early Cosmological Understanding

• Pre-Hubble Era:
  • Cosmology was more descriptive and observational, similar to natural sciences.
  • Lacked precise mathematical formulations.
• Transition to Physics:
  • Modern cosmology incorporates physics and mathematical principles.
  • Focus on angular momentum and physical systems.

Fundamental Observations

• Isotropic Universe:
  • Universe appears isotropic (same in all directions).
  • Implies the universe is homogeneous (same density in all locations).
• Cosmological Principle:
  • Assumes uniform distribution of galaxies across the universe.
  • Variations observed only on large scales (e.g., clusters of galaxies).

Key Cosmological Concepts

• Galaxies and Particles:
  • Approximately 100 billion galaxies, each with around 100 billion stars, leading to a total of about 10^22 stars.
  • Each star has roughly 10 planets, indicating a vast number of planets.
• Hubble's Law:
  • Velocity of galaxies is proportional to their distance from us.
  • Derives from ratio
    • Velocity (v) / Distance (d) = Hubble constant (H).

Fundamental Equations and Variables

• Introducing Coordinates:
  • Use coordinates to describe the positions of galaxies.
  • Distances between galaxies are dynamic and depend on a scale factor (A).
• Density of the Universe:
  • Mass density is inversely proportional to the cube of the scale factor:
    • 𝜌 = 𝜈 / A^3.

Newtonian Approach to Cosmology

• Gravitational Forces:
  • Newton's gravitational theorem states that a particle feels forces only from the mass within its radius.
• The Expanding Universe:
  • Assumptions of an expanding universe can be analyzed using Newtonian mechanics.
  • The universe cannot be static unless it is empty.

Friedmann Equation

• Equation of Motion:
  • Derived from gravitational interactions:
    • A'' (acceleration) = - (4/3)𝜋Gρ.
  • The universe's density influences its expansion or contraction.
  • The equation has implications for the universe's fate (expansion vs. contraction).

Solutions to the Friedmann Equation

• Critical Density:
  • If the universe is at critical density, it expands forever, slowing down but never stopping.
• Escape Velocity:
  • The concept relates to the overall dynamics of the universe.
• Cosmological Expansion:
  • Different scenarios arise depending on the energy density of the universe.

Conclusion and Implications

• Observational Evidence:
  • Type Ia supernovae provide evidence for an accelerating universe.
  • Cosmic Microwave Background (CMB) supports cosmological models.
• Future Directions:
  • Further exploration of dark energy and the universe's structure is needed.