In section $23\mathrm{.}1,$ a relationship between the scale factor and the temperature is derived.

$($a$)$ Given that the current scale factor is a$($t$0)=1,$ at what scale factor did the temperature of the cosmic

background radiation equal the temperature of the Sun$$s photosphere?

$($b$)$ At what scale factor did it equal the temperature of the Sun$$s center?

$($c$)$ If the current mass density of the Universe is equal to $0\mathrm{.}3$ c$0,($eqns $23\mathrm{.}33$ and $23\mathrm{.}34),$ what was the

mass density when the temperature was equal to that of the Sun$$s center, under the assumption that there

is conservation of mass? Compare this mass density to the average density of the Sun.