 Solution

ID: past-exam-of-the-relativistic-astrophysics-and-cosmology-course-of-the-university-of-cambridge/2012/paper-1/2/c/solution

Comparing photons with the constant vacuum density gives

Ω_{γ 0} (1 + z)^{4} = 0.7

, so

z_{γ Λ} = (\frac{0.7}{4.8032 \times 1 0 ^{- 5}})^{1/4} - 1 ≃ 9.98735 .

Matter dominates both at this crossing: its density in units of today's critical density is

0.3 (10.98735)^{3} ≃ 398

, compared with

0.7

for each of the other components. radiation-vacuum density equality therefore does not itself mark a switch in the dominant component.

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