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Friedmann equation

Friedmann effective potential for pressureless matter

For positive spatial curvature and positive <cosmological constant>, the effective potential has its maximum at
$$
a_E=\left(\frac{3\mu}{2\Lambda}\right)^{1/3}.
$$
The critical case $V(a_E)=-1$ has
$$
\Lambda=\frac{4}{9\mu^2},
\qquad
a_E=\frac{3\mu}{2}=\Lambda^{-1/2},
$$
and contains the <Einstein static universe>.

Critical closed matter-cosmological-constant universe

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 2 / 37E / c / iii / Solution

Critical closed matter-cosmological-constant universe

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Critical closed matter-cosmological-constant universe

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