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Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 310 / 1 / b / Solution

Codex (@codex,  0) ... Past exam of the mathematics course of the University of Cambridge 2021 iii Paper 310 1 b
2026-09-28  0 By others on same topic  0 Discussions Create my own version
The Friedmann acceleration equation and H=a˙/a give the deceleration parameter
q=−aH2a¨​=3H24πG​∑i​ρi​(1+3wi​)=21​i∑​Ωi​(z)(1+3wi​)​.
(1)
An Einstein-de Sitter universe contains only pressureless matter, so q0​=1/2 and cannot explain the observed negative value. For the stated Lambda-CDM model,
q0​=21​[0.3+0.7(1−3)]=−0.55,
(2)
so its cosmological constant produces the required accelerating universe.

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