Introduction to Cosmology Ryden · Problem 5.7

Model Universes

Physics — Astrophysics · big-crunch-blueshift-contracting-universe

Problem

Consider a positively curved universe containing only matter (the ``Big Crunch'' model discussed in Section 5.4.1). At some time t0>tcrunch/2t_0 > t_{\rm crunch}/2, during the contraction phase of this universe, an astronomer named Elbbuh Niwde discovers that nearby galaxies have blueshifts (−1≤z<0-1 \leq z < 0) proportional to their distance. He then measures H0H_0 and Ω0\Omega_0, finding H0<0H_0 < 0 and Ω0>1\Omega_0 > 1. Given H0H_0 and Ω0\Omega_0, how long a time will elapse between Dr. Niwde's observations at t=t0t = t_0 and the final Big Crunch at t=tcruncht = t_{\rm crunch}? What is the highest amplitude blueshift that Dr. Niwde is able to observe? What is the lookback time to an object with this blueshift?

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