AST/PHYS Syllabus 5022, Cosmology, Fall 2008 http://www.astro.umn.edu/llrw/a5022 f08.html Instructor: Liliya L.R. Williams Relativity: Special; Lorentz transformations, time dilation and length contraction, causality, simultaneity, four-vectors, stress-energy tensor. General; basic ideas, equivalence principle, geometry of curved spaces; outline of the derivation of Einstein field equations; Friedmann equation from the field equations. Global Geometry: cosmological principle, Friedmann-Robertson-Walker metric, the scale factor, dynamics: Friedmann equation, particular cases with radiation, dust, cosmological constant. Applications of Friedmann eqns: relations between proper time, redshift, angular diameter distance, luminosity distance, volume element; horizons. Cosmological tests of global geometry: standard candles, standard rulers, age tests, volume tests, and other miscellaneous ones; ways to measure the Hubble parameter. Inflation: difficulties with the Standard Big Bang model, mechanism of inflation, reheating/preheating, spectrum of density perturbations from inflation, limits on the observed spectrum, Harrison-Zeldovich spectrum, fine-tuning of the potential and other features of inflation. Early Universe: phase transitions and topological defects; thermal history; main events in chronological order: baryogenesis, primordial nucleosynthesis of D, He3, He4, Li7; photon-to-baryon ratio and expansion rate of the Universe; observational determinations of the light element abundances. Cosmic Microwave Background: overall observed properties of the CMB, temperature fluctuations: dipole and higher multipoles. Primary temperature anisotropies: super-horizon scales and the Sachs-Wolfe effect, sub-horizon scales the and acoustic peaks, damping scale. Secondary anisotropies. Polarization of the CMB; cosmological parameters from the CMB; detecting CMB. Dark matter: evidence; baryonic vs. non-baryonic DM; cold DM and hot DM. Structure formation: evolution of structure in the early Universe: growth of super- and sub-horizon sized perturbations, transfer function. Evolution of density perturbations before and after matter-radiation equality. Linear theory of gravitational instability; Jeans analysis; evolution of mass clustering; Press-Schechter formalism and statistics of discrete objects. Measuring mass inhomogeneities: correlation functions, counts in cells, power spectrum, mass and luminosity functions, biasing. Measuring mass inhomogeneities via dynamical means: bulk flows on large scales, dipole from galaxies vs. CMB, galaxy redshift surveys, pair-wise velocities, velocity dispersions in galaxies and clusters. Grading Homework (problem sets about every other week) Mid-term (Thu Sep 25th, and Tue Nov 4th) Presentations (30 mins eac...