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Problem 2. Assuming the scale factor a(t) evolves as a power law with time as
a(t) = (²-)",
where the power law index I > 0, and to is the age of the universe.
1. Derive an expression for the Hubble parameter H(z) as a function of to, I, and the redshift z at time t.
2. What is the age of the universe if I = 1/2 and Ho = 70 km/s/Mpc ?
3. For what value of I is the age of the universe equal to the Hubble time?

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