Answer Happy

2. A possible type of vacuum energy is “phantom energy", a component with equation-of-state parameter w<-1. We know our universe is very close to spatially flat, 2 =1, with density parameter for matter .0. Thus, for the phantom energy, ph,0 =1-2,0 m,0 (a) (2 pts) Show that the energy density of phantom energy increases as the universe expands. am, ph (b) (3 pts) Determine the scale factor for matter-phantom energy equality. (c) (3 pts) Solve the Friedmann equation in the limit a » am.ph, that is, for the distant future when phantom energy dominates almost completely. Determine the finite time, trip (known sometimes as the Big Rip), in the future when the scale factor becomes infinite. (That is, at that time distances between any two points in space becomes infinite: space as we know it ceases to exist.) (d) (2 pts) Present-day observations are consistent with wph = −1.1. Use this value, together in years. with m = 0.3, H = 68 kms¯¹ Mpc`¯¹, to calculate trip m,0