Introduction to Cosmology Ryden · Problem 5.6

Model Universes

Physics — Astrophysics · static-universe-dark-energy-matter-balance

Problem

Suppose you wanted to ``pull an Einstein,'' and create a static universe (

\dot{a} = 0

\ddot{a} = 0

) in which the gravitational attraction of matter is exactly balanced by the gravitational repulsion of dark energy with equation-of-state parameter

-1/3 < w_q < -1

and energy density

\varepsilon_q

. What is the necessary matter density (

\varepsilon_m

) required to produce a static universe, expressed in terms of

\varepsilon_q

and

w_q

? Will the curvature of this static universe be negative or positive? What will be its radius of curvature, expressed in terms of

\varepsilon_q

and

w_q