Question

Let's consider the growth of linear structure in a cosmological context. (a) What is the proper horizon distance at matter-radiation equality (take aeq = 1/3000)? You can assume that prior to this point, radiation dominates the energy density, and the cosmological parameters are as in the earlier problem. What is the wavenumber keq corresponding to this distance? (b) Consider two perturbations with wavenumbers k1 = 1/2 keq and k2 = 2keq. Assuming the primordial matter power spectrum is P(k) ∝ k, what is the ratio of the matter power spectrum of the two modes at very early times? In other words, what is P (k2)/P(k1), where P(k) = < |δ|2 >1/2, as usual? (c) What is the ratio of the matter power spectrum of the two modes at aeq/2? Note that for scales larger than the horizon, General Relativity indicates that δ ∝ a2 in a radiation-dominated universe. What is the ratio of the matter power spectrum of the two modes at radiation-matter equality?

          Let's consider the growth of linear structure in a cosmological context. (a) What is the proper horizon distance at matter-radiation equality (take aeq = 1/3000)? You can assume that prior to this point, radiation dominates the energy density, and the cosmological parameters are as in the earlier problem. What is the wavenumber keq corresponding to this distance? (b) Consider two perturbations with wavenumbers k1 = 1/2 keq and k2 = 2keq. Assuming the primordial matter power spectrum is P(k) ∝ k, what is the ratio of the matter power spectrum of the two modes at very early times? In other words, what is P (k2)/P(k1), where P(k) = < |δ|2 >1/2, as usual? (c) What is the ratio of the matter power spectrum of the two modes at aeq/2? Note that for scales larger than the horizon, General Relativity indicates that δ ∝ a2 in a radiation-dominated universe. What is the ratio of the matter power spectrum of the two modes at radiation-matter equality?

Added by Bailey I.

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