Particle Cosmology
A graduate course developing the theoretical framework connecting early-universe cosmology with particle physics — from metric geometry and thermodynamics through dark matter, inflation, and the CMB to the physics of axions and quantum-limited detection experiments.
Prerequisites
General Relativity (metric tensor, Einstein equations) • Quantum Field Theory (gauge theories, path integrals) • Statistical Mechanics (partition functions, Bose-Einstein/Fermi-Dirac distributions)
Essential Equations
$$H^2 = \frac{8\pi G}{3}\rho - \frac{k}{a^2},\quad \dot\rho+3H(\rho+p)=0,\quad p=w\rho$$
$$n_{eq}=\frac{g}{2\pi^2}\int_0^\infty \frac{p^2\,dp}{e^{(E-\mu)/T}\pm 1},\quad s=\frac{2\pi^2}{45}g_{*S}T^3$$
$$\epsilon=-\frac{\dot H}{H^2}=\frac{M_{\rm Pl}^2}{2}\left(\frac{V'}{V}\right)^2,\quad \Delta_s^2=\frac{H^2}{8\pi^2\epsilon M_{\rm Pl}^2}$$
Modules
FRW Cosmology
Friedmann equations, scale factor, horizons, distances
Thermal History & BBN
Boltzmann equation, nucleosynthesis, decoupling
Inflation
Slow-roll, power spectra, CMB seeds, reheating
Dark Matter
Freeze-out, axions, PQ mechanism, haloscopes
Baryogenesis
Sakharov conditions, leptogenesis, EW baryogenesis
Dark Energy
Cosmological constant, quintessence, w equation of state
CMB Physics
Boltzmann hierarchy, angular power spectrum, BAO
Structure Formation
Transfer function, halo mass function, DM imprint