Adventures in Friedmann Cosmology: An Educationally Detailed Expansion of the Cosmological Friedmann Equations

Abstract

The general relativistic cosmological Friedmann equations which describe how the scale factor of the universe evolves are expanded explicitly to include energy forms not usually seen. The evolution of the universe as predicted by the Friedmann equations when dominated by a single, isotropic, stable, static, perfect-fluid energy form is discussed for different values of its gravitational pressure to density ratio $w$. These energy forms include phantom energy ($w<-1$), cosmological constant ($w=-1$), domain walls ($w = -2/3$), cosmic strings ($w = -1/3$), normal matter ($w = 0$), radiation and relativistic matter ($w = 1/3$), and a previously little-discussed form of energy called "ultralight" ($w>1/3$). A brief history and possible futures of Friedmann universes dominated by a single energy form are discussed.