5.8 Consider an expanding, positively curved universe containing only a cosmological constant (2, = 2.0 > 1). Show that such a universe underwent a "Big Bounce" at a scale factor 1/2 Apounce = (5.120) and that the scale factor as a function of time is

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With the aid of a diagram, explain the physical origin of cosmological redshift in an expanding universe, and how this differs from the Doppler shift due to relative motion. Observations of distantgalaxies indicate that their recession velocities, v, and their distances, d, follow a Hubble Law:v = H0d, where H0 is a constant. Using the analogy of an expanding grid or ruler, demonstratethat Hubble’s Law indicates that the Universe is undergoing uniform expansion.

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