We have explained how the peaks in the CMB temperature fluctuation spectrum arise because the sound waves

Question:

We have explained how the peaks in the CMB temperature fluctuation spectrum arise because the sound waves all began at the same time and are all effectively observed at the same time, while they entered the horizon at different times. Suppose that the universe had been radiation dominated up to recombination, so that Eq. (28.51) is valid and oscillatory waves of constant amplitude were created with different values of k. Calculate the total relative density perturbation δ̃(k) at recombination. Describe the main changes in standard cosmology that are introduced.

Equation 28.51.