Problem 2. Assuming the scale factor a(t) evolves as a power law with time as - (-:-)^, 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?

Problem 2. Assuming the scale factor a(t) evolves as a power law with time as - (-:-)^, 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?