1
$\begingroup$

One probably very trivial issue which is bothering me. Standard cosmology says that in a FRW metric, in a matter dominated flat universe (Pressure $P = 0$ and $K = 0$), the scale factor, $a \propto t^{2/3}$.

This gives $\dot{a} \propto \frac{2}{3}t^{-1/3}$ and $\ddot{a} \propto \frac{-2}{9}t^{-4/3}$.
In other words, $\ddot{a} < 0$, always.

Now, if current observations indicate that the universe is accelerating i.e. $\ddot{a} > 0$, does it imply that the good old result $a \propto t^{2/3}$ is incorrect?

Or am I interpreting something incorrectly?

$\endgroup$
  • $\begingroup$ Yes, all you say is perfectly correct. The scale factor $a(t) \propto t^{2/3}$ doesn't apply to our universe. $\endgroup$ – Cham Apr 3 at 10:01
  • $\begingroup$ For a flat universe with both matter and dark energy, $a\propto\sinh^{2/3}(t/t_\Lambda)$. (This neglects radiation, but radiation was important only early, not now.) You can see how this transitions from $t^{2/3}$ at small $t$ when matter dominates to exponential in $t$ at large $t$ when dark energy dominates.. $\endgroup$ – G. Smith Apr 3 at 16:40
  • $\begingroup$ Thanks everybody for all the explanation $\endgroup$ – Angela Apr 3 at 20:59
1
$\begingroup$

The result you quote is for a matter dominated universe, but the universe is dark energy dominated in the accelerating epoch. You could say that matter domination tried to halt expansion, but failed: dark energy started to dominate before expansion halted.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.