 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/15d/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

The conservation equation with

P = wρ

gives

d ρ / ρ = - 3 (1 + w) d a / a

, hence

ρ = ρ_{0} a^{- 3 (1 + w)} .

ρ_{crit} = \frac{3 c ^{2} H ^{2}}{8 π G}, Ω_{i} = \frac{ρ _{i}}{ρ _{crit}} .

 New to topics? Read the docs here!