We introduce both general relativity and its cosmological
implications. The standard cosmological model arose from Hubble's 1929
observation of an expanding universe, and triumphed in the 1960's with
observations of its two key predictions: the 
K cosmic microwave
background, and the abundances of light elements in the universe.
Our universe expands uniformly, driven by its particle content due to general relativity. In the standard big bang, matter-dominated expansion follows an epoch of slower, radiation-dominated expansion. Recent observation supports extending this big bang model: preceding it with the exponential expansion of inflation, and following it with today's era of accelerated expansion, due to nonzero cosmological constant -- a possibility introduced and dismissed by Einstein, resurrected due to observations of the past 5 years.
General relativity is both the theoretical foundation for cosmology, and a signal achievement of modern physics. It describes gravitational interactions as the warping, or curving, of spacetime by matter. This melds the mathematical description of spatial curvature -- differential geometry -- with a physical source for that curvature. Cosmology becomes the story of how the evolving matter content of the universe drives its evolving geometry. We establish basic understanding both of modern cosmology, and its origins in general relativity: understanding curvature well enough to understand Einstein's equations, and applying them to our universe to establish its cosmological history.
NOTE: The course level will mingle the conceptual and quantitative, targeted toward upper-level math and physics majors.
Prerequisites: Introductory Physics, and mastery of 3-dimensional mathematics (including vector calculus and coordinate systems). This means
For physics majors: Math 211, and 2 courses from the group Physics 253, 254, 361, 365 and 461.
For math majors: Physics 141, 142, and Math 211 or equivalents; one subsequent course in multidimensional math (e.g. Math 221, 321, 344, or others).
Breakdown of Static Newtonian Cosmology 2 weeks
Conceptual paradoxes; Hubble Expansion; A Quasinewtonian expanding universe
General Relativity 6 weeks
Special Relativity; Precepts of GR; Differential Geometry of Curved Space; Deriving Einstein's Equations
Cosmological Solutions 2 weeks
Friedmann-Robertson-Walker solutions; Evolution when radiation, matter, 
- dominated
Thermal History of the Universe 1.5 weeks
Big bang history, observational successes
Beyond the Big Bang Model 1.5 weeks
Problems, Inflation, Understanding today's