Fermi coordinates and relative motion in inflationary power law cosmologies

A power law cosmology is a Robertson-Walker spacetime in which the scale factor, a(t), is of the form a(t) = t^α. This work has two primary goals: to give exact Fermi coordinates for geodesic observers, and to give formulas for the Fermi relative velocity, both in the context of power law cosmologies. To those ends, the author gives the necessary mathematical and physical background, beginning at the level that a first- year graduate student of mathematics should find comfortable. In Chapter 2, we develop the theory of manifolds, focusing on Lorentzian manifolds. In Chapter 3, the necessary components of Einstein’s general theory of relativity are presented. A cosmology is said to be inflationary if it expands at an accelerated rate; in Chapter 4, the author shows that formulas which were known to hold for non-inflationary cosmologies also hold for inflationary power law cosmologies. This is of particular interest because there are multiple recent papers which suggest modeling the universe as an inflationary power law cosmology.