(Answered) 1 consider a flat universe with only mattera prove that

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1. Consider a flat universe with only matter.

(a) Prove that ε=ε_e,0a^-3, where ε_e,0 is the critical density today.

(b) Prove that a(t) = (t/t0)^2/3.

(c) Find the current proper distance, comoving distance, luminosity distance, an angular diameter distance to a galaxy at redshift z.

(d) Find the horizon distance.

(e) Find the age of the Universe in terms of H0.

(f) Find the maximum angular diameter distance of the Universe.

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