Learn how the universe began, expanded, and came to look the way it does.

The destination: cosmology

Year IV of the path. Each theme follows MIT 8.286 The Early Universe, with extra pages where a topic needs more room — the dark matter and structure formation pages come from the graduate course 8.902 in Year V.

The programme, read backwards

Cosmology stands on the rest of physics. Read the path backwards to see what each step needs, or start at Year 1 and walk forward.

1. Year VGraduate year: astrophysics and general relativity
   8.902 Astrophysics II68.962 General Relativity
2. Year IVCosmology
   8.286 The Early Universe44
3. Year IIIStatistical and advanced quantum physics
   8.044 Statistical Physics I8.05 Quantum Physics II8.06 Quantum Physics III

   The hot early universe is a gas in thermal equilibrium: blackbody radiation, the Boltzmann factor and entropy explain the CMB spectrum and the thermal history after the Big Bang. Quantum fields and their fluctuations are the seeds of all cosmic structure in inflationary cosmology; spin and identical particles decide how many particle species filled the early universe. Reaction rates and scattering cross sections decide when particles fell out of equilibrium in the early universe — the basis of Big Bang nucleosynthesis and of dark-matter relic abundances.

4. Year IIWaves, relativity, the quantum, and the mathematics behind them
   8.03SC Physics III: Vibrations and Waves18.03 Differential Equations8.033 Relativity18.06 Linear Algebra8.04 Quantum Physics I

   Redshift starts as a wave phenomenon (the Doppler effect), and the sound waves of the early plasma left the acoustic peaks we see in the CMB. The Friedmann equation is a differential equation for a(t); oscillators, waves and the growth of small density ripples into galaxies are all described by differential equations. Light travel time, the relativistic Doppler effect and E = mc² are used throughout cosmology, and the spacetime metric is the starting point for curved, expanding space. Quantum mechanics is written in linear algebra, a spacetime metric is a matrix, and rotations — like the one that proves a closed universe is the same everywhere — are orthogonal matrices. Photon energies and the hydrogen atom explain recombination — when the universe became transparent and the CMB was released — and the spectral lines used to measure redshift.

5. Year IMechanics, electromagnetism and calculus
   8.01SC Classical Mechanics618.01 Single Variable Calculus8.02T Electricity and Magnetism18.02 Multivariable Calculus

   Cosmology describes the whole universe with the tools of mechanics: vectors and rates of change (Hubble's law is a velocity proportional to a position vector), Newton's gravity (the Friedmann equation can be derived from a Newtonian expanding sphere), and energy conservation (which decides whether the universe expands forever). Every rate of change in cosmology is a derivative — the Hubble rate ȧ/a, the deceleration ä — and ages, horizon distances and volumes of the universe are integrals. Almost everything we know about the universe arrives as electromagnetic radiation. Maxwell's equations explain light, its spectrum and energy flux — the basis of the cosmic microwave background and of measuring distances with standard candles. Gauss's law, Poisson's equation and flux integrals — the tools behind Maxwell's equations and the Newtonian model of the expanding universe — are multivariable calculus.