- #1
Wong
- 80
- 0
Is it true that for an isotropic, homogeneous flat universe with dust
and a positive cosmological constant, the universe necessarily expands
forever? The argument may be,
(a_t/a)^2 = (8*pi*G/3)*rho + lambda/3 (Friedmann equation)
where a_t refers to the first derivative of a with respect to t. Now
the right hand side is strictly positive (as rho is positive and
proportional to a^3 for dust), so a_t is always positive.
If this is true, why is it said that in a universe with a positive
cosmological constant, the fate of the universe has no direct relation
with the curvature (k) but depends on the exact proportion of
[(matter+radiation) density] / vacuum energy density?
and a positive cosmological constant, the universe necessarily expands
forever? The argument may be,
(a_t/a)^2 = (8*pi*G/3)*rho + lambda/3 (Friedmann equation)
where a_t refers to the first derivative of a with respect to t. Now
the right hand side is strictly positive (as rho is positive and
proportional to a^3 for dust), so a_t is always positive.
If this is true, why is it said that in a universe with a positive
cosmological constant, the fate of the universe has no direct relation
with the curvature (k) but depends on the exact proportion of
[(matter+radiation) density] / vacuum energy density?