Cosmology Lecture Notes

Introduction to Cosmology

• Cosmology is an very old subject, dating back thousands of years.
• Modern cosmology is considered new, starting from the mid-20th century.
• Key Discoveries:
  • Hubble's discovery of the expanding universe.
  • Discovery of the Big Bang and the cosmic microwave background radiation in the 1960s.

Modern Cosmology

• Shifted from natural science to a more precise physics-based science.
• Important to study the universe with equations and physical principles.

Basic Concepts in Cosmology

• Isotropy: Universe looks the same in every direction.
• Homogeneity: Universe is the same throughout, not just in appearance.
• Cosmological Principle: Universe is isotropic and homogeneous.

The Structure of the Universe

• Universe contains about 10 to the 11th galaxies and about 10 to the 22nd stars.
• Distribution of matter is sometimes in clusters and superclusters, but appears homogeneous on a large scale.

Newtonian Cosmology

• Introduce a coordinate system where galaxies remain fixed on a grid.
• Scale Factor (A(t)): Used to measure the actual physical distance between galaxies.
• Hubble's Law: Velocity between any two galaxies is proportional to their distance (V = H ).

Dynamics of the Universe

• Newton's Theorem: Gravitational force is influenced by mass within a given sphere.
• Formulation of gravitational field equations and dynamics of expanding universe using Newton's laws.

The Friedmann Equation

• Derived from Newton's laws and energy conservation principles.
• Used to describe the expansion of the universe.
• Dependent on the matter density rho and scale factor.

Model Universes

• Different scenarios for universe dynamics:
  • Expanding universe at critical escape velocity.
  • Re-collapsing universe.
  • Universes with different energy conditions.
• Critical Density and Velocity: Related to escape velocity and energy balance.

Historical and Philosophical Context

• Newton and other historical figures had limitations due to their era's philosophical beliefs.
• Advancements were made, leading to modern cosmological theories.

Current Understanding of the Universe

• Universe is accelerating in its expansion, contrary to older Newtonian model predictions.
• Supported by observations such as cosmic microwave background radiation and supernova studies.

Additional Considerations

• Local movements of galaxies (e.g., Milky Way and Andromeda) can deviate from the overall expansion trend.
• Homogeneity and isotropy are average properties over large scales.

Conclusion

• Cosmology has evolved significantly with new discoveries and advanced mathematical models.
• Continuous research and observations continue to refine our understanding of the universe.

Note:

• For further study, refer to resources at Stanford University and related cosmological research publications.