PHY 402: Cosmology

3 credits | Prerequisites: PHY 221 for Major; PHY 102 for Minor

Course rationale

Cosmology is the study of cosmos. In a more technical language this is the study of Einstein equation (and in some limits) applied to the universe. This course will introduce the basic concepts of cosmology, and also some important observations.

Course content

Review of General Relativity: manifold, vectors, dual vectors, tensors, covariant differentiation, geodesic, Lie differentiation, Killing vector, curvature, geodesic deviation, Fermi normal coordinates, differential forms, tetrad formalism, Cartan’s structure equation, Einstein equation, Bianchi identities; The Expanding Universe: symmetric three-spaces, Robertson-Walker metric, geodesics, redshift, distances, perfect fluid, matter and radiation, dark energy, spacetime curvature, Friedmann equations, exact solutions, our universe; Hot Big Bang: some statistical mechanics, primordial plasma, entropy and expansion history, cosmic neutrino background, cosmic microwave background, Boltzmann equation, freeze-out, baryogenesis, big bang nucleosynthesis, recombination; Cosmic Inflation: the horizon problem, flatness problem, superhorizon correlators,  shrinking Hubble sphere, duration of inflation, scalar field dynamics, slow-roll inflation, creating the hot universe; Structure Formation: Newtonian perturbation theory, Jeans instability, linear growth function, transfer function, correlation functions, Gaussian random fields, Harrison-Zeldovich spectrum, spherical collapse, bound on Lambda; Relativistic Perturbation Theory: metric perturbations, matter perturbations, conservation equations, Einstein equations, superhorizon limit, adiabatic perturbations, curvature perturbation, primordial power spectrum, growth of matter perturbation, evolution of photon and baryons; Cosmic Microwave Background: angular power spectrum, gravitational redshift, light-of-sight solution, spatial to angular momentum projection, large and small scales, primordial sound waves, understanding power spectrum, LCDM cosmology, E and B modes; Quantum Initial Conditions: inflationary perturbations, equations of motion, quantum harmonic oscillators, inflationary power spectra, curvature perturbations, gravitational waves, slow-roll predictions, observational constraints.

Course objectives

  1. Understand the basics of General Relativity.
  2. Understand the geometry of the universe.
  3. Familiarize with the idea of inflation in cosmology.
  4. Classify different types of inflationary models and quantum cosmology.
  5. Familiarize with important results from Cosmic Microwave Background.


  1. Cosmology by Daniel Baumann
  2. Modern Cosmology (2nd edition) by Scott Dodelson, and Fabian Schmidt
  3. Introduction to Cosmology (2nd edition) by Barbara Ryden
  4. Cosmology by Steven Weinberg
  5. Cosmological Physics (1st edition) by John A. Peacock
  6. Principles of Physical Cosmology by P. J. E. Peebles