As the Universe expands, the dark energy in it also increases. I heard that the cosmological constant $\Lambda$ represents dark energy, so that constant must change as time passes, right? Correct me if I'm wrong...

  • $\begingroup$ The cosmological constant is an energy density, so it could be constant, even if the total amount of dark energy and the total size of the universe were increasing. Is it constant? Probably not. What causes it/dark energy and how does it/dark energy change in time? We don't know. $\endgroup$ – CuriousOne Jun 18 '16 at 6:30

Whether the dark energy is constant or not will ultimately be determined by experiment. At the moment there is no evidence that the dark energy is changing, but the experimental errors are still quite large so a change is not ruled out. There are lots of papers on this subject, but as yet no firm conclusions.

It is important to be clear that dark energy does not necessarily respond to the expansion in the way matter does. We describe the expansion using a scale factor $a(t)$, where we take the value of $a$ to be one right now. So $a=2$ means the universe has doubled in size. The average density of matter is given by:

$$ \rho_m(t) = \frac{\rho_0}{a^3(t)} $$

where $\rho_0$ is the current average density. This should make sense - if the universe expands by a factor of $2$ then the volume of any region within it increases by a factor of $2^3 = 8$ and the density of matter falls by a factor of eight.

However if dark energy is a cosmological constant then it is a property of spacetime itself and it does not change as the universe expands. This seems counter-intuitive, but it is why dark energy behaves as it does. It is precisely because a cosmological constant does not change as the universe expands that it causes the expansion to accelerate.


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