Consider a flat expanding universe with no cosmological constantand no curvature (k=0 in the Einstein equations). Show that if theUniverse is made of \"dust\", so the energy density scales like1/a^3, then the scale factor, a(t), grows as t^(2/3). Show if it ismade of radiation (so the energy density scales as 1/a^4 -- theextra factor of a comes from the redshift), then it grows ast^(1/2). In both cases, show that for early times, the scale factorgrows faster than light. Is this a problem?
