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**1. Homework Statement**

A closed Friedmann universe contains a single perfect fluid with an equation of state of the form [tex]p=w\rho c^2[/tex]. Transforming variables to conformal time [tex]\tau[/tex] using [tex]dt=a(t)d\tau[/tex], show that the variable [tex]y=a^{(1+3w)/2}[/tex] is described by a simple harmonic equation as a function of [tex]\tau[/tex]. Hence argue that all closed Friedmann models with a given equation of state have the same conformal lifetime.

**2. The attempt at a solution**

Please give me a starter. I haven't got a clue...