Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S2 / 3 / 2

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- Solution 2

Solution

Set the spatial-curvature constant to zero in the stipulated matter-only Friedmann equation to get

ρ_{c} = 3 H^{2} / (8 π G)

. Conservation of pressureless matter with

R (t_{0}) = 1

gives

ρ = ρ_{0} / R^{3}

, and therefore

\dot{R}^{2} = \frac{8 π G ρ _{0}}{3 R}, R^{3/2} = \frac{3}{2} \frac{8 π G ρ _{0}}{3} t .

Choosing the Big Bang as

t = 0

yields

R = (t / t_{0})^{2/3}

and

H = 2/ (3 t)

. Consequently

t_{0} = 2/ (3 H_{0}) ≃ 9.3 Gyr

for the supplied

H_{0}

. This is the age of the flat pressureless model without a cosmological constant, not a determination in the current multi-component cosmological model.

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