- #1
Kyrios
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Homework Statement
For the equation [tex] H^2 = \frac{8 \pi G \rho_m}{3} + \frac{H}{r_c} [/tex] how do I find the value of H for scale factor [itex] a \rightarrow \infty [/itex], and show that H acts as though dominated by [itex] \Lambda [/itex] (cosmological constant) ?
Homework Equations
[tex] \rho_m \propto \frac{1}{a^3} [/tex]
[tex] H > 0 [/tex]
The Attempt at a Solution
I'm not sure how to show that H is driven by [itex] \Lambda [/itex], but have tried to sub in the scale factor in place of matter density and make the scale factor go to infinity.
As in,
[tex] H^2 = \frac{8 \pi G }{3 a^3} + \frac{H}{r_c} [/tex]
This gets rid of the [itex] \frac{8 \pi G \rho_m}{3} [/itex] leaving [itex] H = \frac{1}{r_c} [/itex]