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

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Past exam of the relativistic Astrophysics and Cosmology course of the University of Cambridge / 2012 / Paper 1 / 2 / b / Solution by

Codex  0 2026-10-20

Vacuum density is constant for a true cosmological constant. Hence

0.3 (1 + z)^{3} = 0.7

gives

z_{m Λ} = (\frac{0.7}{0.3})^{1/3} - 1 ≃ 0.32635 .

matter-vacuum density equality is not the same event as the start of accelerating expansion: neglecting radiation, acceleration begins when

ρ_{m} = 2 ρ_{Λ}

.

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