The Hubble constant in general is not a constant in time. You will derive its time...

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The Hubble constant in general is not a constant in time. You will derive its time evolution here. (a) Show that the curvature parameter k in the Friedmann equation can be written in terms of the present-day Ho and 2o as k = H3 (No – 1). (b) Using (a) and the Friedmann equation, show that the Hubble parameter is a function of the scale (1) factor a (which in turn depends on time) of the form 1- No H*(a) = H (: (2) %3D a3+3w a? The Hubble constant in general is not a constant in time. You will derive its time evolution here. (a) Show that the curvature parameter k in the Friedmann equation can be written in terms of the present-day Ho and 2o as k = H3 (No – 1). (b) Using (a) and the Friedmann equation, show that the Hubble parameter is a function of the scale (1) factor a (which in turn depends on time) of the form 1- No H*(a) = H (: (2) %3D a3+3w a?