4. Suppose the universe is not expanding, but that light somehow steadily loses energy as it travels through space. Furt

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4 Suppose The Universe Is Not Expanding But That Light Somehow Steadily Loses Energy As It Travels Through Space Furt 1 (64.8 KiB) Viewed 44 times

4. Suppose the universe is not expanding, but that light somehow steadily loses energy as it travels through space. Further assume that the energy loss per unit distance obeys the differential equation dE dr where a is a constant, E is the energy of the photon, and r is the distance traveled. (a) (8 pts) Show that this assumption implies a linear relationship between distance and redshift for z <<<1. (b) (2 pts) Given a Hubble constant H = 68 km s¯¹Mpc¯¹, what would be the value of a ? -αE