Consider a flat expanding universe with no cosmological constant
and no curvature (k=0 in the Einstein equations). Show that if the
Universe is made of "dust", so the energy density scales like
1/a^3, then the scale factor, a(t), grows as t^(2/3). Show if it is
made of radiation (so the energy density scales as 1/a^4 -- the
extra factor of a comes from the redshift), then it grows as
t^(1/2). In both cases, show that for early times, the scale...