General Relativity: An Introduction for Physicists · Problem 15.28

Cosmological models — Hobson, Efstathiou & Lasenby

Physics · flatness-problem-single-component

Problem

For a Friedmann model dominated by a single source of energy density, show that Ωi−1(z)−1=Ωi,0−1−1(1+z)1+3wi,\Omega_i^{-1}(z) - 1 = \frac{\Omega_{i,0}^{-1} - 1}{(1+z)^{1+3w_i}}, where wiw_i is the equation-of-state parameter of the source. Use this result to comment on the flatness problem.

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