. Read Section 12.5 of Ryden. [20 points] Consider an empty, negatively curved, expanding Universe, as described in Section 5.2 of Ryden. If a dynamically insignificant amount of matter (92m 1) is present in such a Universe, how do density fluctuations in the matter evolve with time? That is, what is the functional form of 8(t)? An empty, expanding universe might seem nothing more than a mathematical curiosity. 3 However, if a universe has a density which is very small compared to the critical density c (that is, if a 1), then the linear scale factor of equation (5.30) is a good approximation to the true scale factor. Suppose you were in an expanding universe with a negligibly small value for the density parameter 1, so that you could reasonably approximate it as an empty, negatively curved universe, with t0 = H -1 0 = RO/c. You observe a distant light source, such as a galaxy, which has a redshift z 01:51 . Read Section 12.5 of Ryden. [20 points] Consider an empty, negatively curved, expanding Universe, as described in Section 5.2 of Ryden. If a dynamically insignificant amount of matter (92m 1) is present in such a Universe, how do density fluctuations in the matter evolve with time? That is, what is the functional form of 8(t)? An empty, expanding universe might seem nothing more than a mathematical curiosity. 3 However, if a universe has a density which is very small compared to the critical density c (that is, if a 1), then the linear scale factor of equation (5.30) is a good approximation to the true scale factor. Suppose you were in an expanding universe with a negligibly small value for the density parameter 1, so that you could reasonably approximate it as an empty, negatively curved universe, with t0 = H -1 0 = RO/c. You observe a distant light source, such as a galaxy, which has a redshift z 01:51