Part I: The Expanding Universe
Foundations of Modern Cosmology
The discovery that our universe is expanding stands as one of the most profound achievements of 20th-century science. Starting from Einstein's field equations and the cosmological principle, we derive the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and the Friedmann equations that govern the dynamics of the expanding universe. These equations connect the geometry of spacetime to its matter-energy content through the scale factor a(t).
67.4
H₀ (km/s/Mpc)
13.8 Gyr
Age of the Universe
46.5 Gly
Observable Radius
Topics in This Part
1. The FLRW Metric & Friedmann Equations
Derivation from the cosmological principle, scale factor dynamics, and the Friedmann equations governing cosmic expansion
2. Scale Factor Evolution
Solutions for radiation, matter, and dark energy dominated eras; the deceleration parameter q(t)
3. Cosmological Redshift
Wavelength stretching from expansion, redshift-distance relation, and the Hubble–Lemaître law
4. Distance Measures
Comoving, proper, luminosity, and angular diameter distances in an expanding universe
5. Cosmological Horizons
Particle horizon, event horizon, and the Hubble sphere; causal structure of the universe