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5.5 One speculation in cosmology is that the dark energy may take the form of "phantom energy" with an equation-of-state parameter w < -1. Suppose that the universe is spatially flat and contains matter with a density parameter 2m.o, and phantom energy with a density parameter = 1 - 2m.0 and equation-of-state parameter wp factor amp are the energy density of phantom energy and matter equal? Write down the Friedmann equation for this universe in the limit that a >> < -1. At what scale %3D » amp. Integrate the Friedmann equation to show that the scale factor a goes to infinity at a finite cosmic time tip, given by the relation Ho(trip – to) (1 3|1+Wpl (5.119) | This fate for the universe is called the "Big Rip." Current observations of our own universe are consistent with Ho = 68 km s-1 Mpc1, 2m.0 = 0.3, and %3D Wp -1.1. If these numbers are correct, how long do we have remaining until the %3D "Rig Rin"?

5.5 One speculation in cosmology is that the dark energy may take the form of "phantom energy" with an equation-of-state parameter w < -1. Suppose that the universe is spatially flat and contains matter with a density parameter 2m.o, and phantom energy with a density parameter = 1 - 2m.0 and equation-of-state parameter wp factor amp are the energy density of phantom energy and matter equal? Write down the Friedmann equation for this universe in the limit that a >> < -1. At what scale %3D » amp. Integrate the Friedmann equation to show that the scale factor a goes to infinity at a finite cosmic time tip, given by the relation Ho(trip – to) (1 3|1+Wpl (5.119) | This fate for the universe is called the "Big Rip." Current observations of our own universe are consistent with Ho = 68 km s-1 Mpc1, 2m.0 = 0.3, and %3D Wp -1.1. If these numbers are correct, how long do we have remaining until the %3D "Rig Rin"?

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5.5 One speculation in cosmology is that the dark energy may take the form of "phantom energy" with an equation-of-state parameter w < -1. Suppose that the universe is spatially flat and contains matter with a density parameter 2m.o, and phantom energy with a density parameter = 1 - 2m,0 and equation-of-state parameter w, < -1. At what scale 'm,0 Wp factor are the energy density of phantom energy and matter equal? amp Write down the Friedmann equation for this universe in the limit that a » amp. Integrate the Friedmann equation to show that the scale factor a goes to infinity at a finite cosmic time t,in, given by the relation Ho(trip – to) = (1 – m.o)-1/2. (5.119) 3|1 + Wpl This fate for the universe is called the "Big Rip." Current observations of our own universe are consistent with Ho = 68 km s-1 Mpc-1, 2m.0 = 0.3, and w, -1.1. If these numbers are correct, how long do we have remaining until the "Big Rip"?
Transcribed Image Text:5.5 One speculation in cosmology is that the dark energy may take the form of "phantom energy" with an equation-of-state parameter w < -1. Suppose that the universe is spatially flat and contains matter with a density parameter 2m.o, and phantom energy with a density parameter = 1 - 2m,0 and equation-of-state parameter w, < -1. At what scale 'm,0 Wp factor are the energy density of phantom energy and matter equal? amp Write down the Friedmann equation for this universe in the limit that a » amp. Integrate the Friedmann equation to show that the scale factor a goes to infinity at a finite cosmic time t,in, given by the relation Ho(trip – to) = (1 – m.o)-1/2. (5.119) 3|1 + Wpl This fate for the universe is called the "Big Rip." Current observations of our own universe are consistent with Ho = 68 km s-1 Mpc-1, 2m.0 = 0.3, and w, -1.1. If these numbers are correct, how long do we have remaining until the "Big Rip"?
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