Will the universe continue to expand forever? To attack this question, make the (reasonable?) assumption that the
Question:
Will the universe continue to expand forever? To attack this question, make the (reasonable?) assumption that the recessional speed v of a galaxy a distance r from us is determined only by the matter that lies inside a sphere of radius r centered on us. If the total mass inside this sphere is M, the escape speed v e from the sphere is v e = √2GM/r, (Equation 13-28).
(a) Show that to prevent unlimited expansion, the average density p inside the sphere must be at least equal to p = 3H2 / 8πG
(b) Evaluate this "critical density" numerically; express your answer in terms of hydrogen atoms per cubic meter. Measurements of the actual density are difficult and are complicated by the presence of dark matter.
Step by Step Answer:
Fundamentals of Physics
ISBN: 978-0471758013
8th Extended edition
Authors: Jearl Walker, Halliday Resnick