Cosmology calculations almost without general relativity

Thomas F. Jordan

Published 2003-09-28, updated 2004-12-08Version 4

The Friedmann equation is derived for a Newtonian universe. Changing mass density to energy density gives exactly the Friedmann equation of general relativity. Accounting for work done by pressure then yields the two Einstein equations that govern the expansion of the universe. Descriptions and explanations of radiation pressure and vacuum pressure are added to complete a basic kit of cosmology tools. It provides a basis for teaching cosmology to undergraduates in a way that quickly equips them to do basic calculations. This is demonstrated with calculations involving: characteristics of the expansion for densities dominated by radiation, matter, or vacuum; the closeness of the density to the critical density; how much vacuum energy compared to matter energy is needed to make the expansion accelerate; and how little is needed to make it stop. Travel time and luninosity distance are calculated in terms of the redshift and the densities of matter and vacuum energy, using a scaled Friedmann equation with the constant in the curvature term determined by matching with the present values of the Hubble parameter and energy density. General relativity is needed only for the luminosity distance, to describe how the curvature of space, determined by the energy density, can change the intensity of light by changing the area of the sphere to which the light has spread. Thirty-one problems are included.