- #1

michael879

- 698

- 7

[itex]\rho \approx a^{-3(1+w)}[/itex]

where w=0 for matter, 1/3 for radiation, and -1 for dark energy, and

[itex]a_m(t) \approx \dfrac{2}{3}t[/itex]

[itex]a_r(t) \approx \dfrac{1}{2}t[/itex]

[itex]a_Λ(t) \approx e^{\sqrt{1/3Λt}}[/itex]

for matter, radiation, or dark energy dominated universes. Now for a matter or radiation dominated universe, it is very clear why the (Ω-1) parameter is unstable at 0, since it grows as a power of time. However, if you look at the case of a dark energy dominated universe you find that (Ω-1) goes to 0 exponentially! Since our universe now is 70% dark energy, how can anyone claim its obvious that (Ω-1)=0 is unstable?? Clearly I've used the usual over-approximations so its certainly possible that if you make various assumptions about the history of the universe you can get an answer. However, I can't find a single source that mentions this point, and all they say is that inflation is the only way to fix it! Naively it seems possible that (Ω-1) grew until some point where it went back down to the 0 we observe today right?