Question about the cosmological constant

[Gerinski]

Layman here, please excuse my ignorance. I believe to understand the basics of SR, GR, cosmic expansion, etc but questions come to mind now and then.

As I understand, dark energy, the cosmological constant, vacuum energy, whatever you may call it, remains a constant per space volume unit. Empty space has an intrinsic tendency to expand. Mass-energy in space has the opposite effect, slowing down this expansion. If the mass-energy density is higher than the cosmological constant, space will contract. If it is lower, space expansion will continue at an accelerating rate. So far so good.

What I do not understand is the "equilibrium" situation of a flat universe, in which the mass-energy contents of the universe exactly balances the rate of expansion. Frequently I have read that this results in a universe which keeps expanding forever but at a fixed rate, neither accelerating nor slowing down.

I do not understand why this "equilibrium" should not be a space which does neither expand not contract, a static spatial extension where neither expansion nor contraction can beat each other. If space keeps on expanding (at a non-accelerating, not-decelerating rate as it is said for a flat universe), the mass-energy density per space volume unit should decrease. Dark energy remains constant per space volume unit, while mass-energy density per space volume unit would decrease as space expands. Intuitively this would mean that per space volume unit, the rate of dark energy to mass-energy would be constantly increasing, boosting space expansion to a faster and faster rate. I do not understand why such an expanding space without mass-energy being added can remain not-accelerating expanding.

Where is the flaw in my understanding?

Thanks for the answers!

 

[mfb]

If the mass-energy density is higher than the cosmological constant, space will contract.

Not necessarily. An expansion will slow down, or a collapse will speed up. It is mainly acting on the derivative.

There is no stable configuration where the size stays constant. Without cosmological constant (!), there is a border case where expansion slows down over time with a limit of zero expansion rate at "infinite" expansion. With it, that cannot happen - it either collapses or expands exponentially in the long run.

 

[Ken G]

Frequently I have read that this results in a universe which keeps expanding forever but at a fixed rate, neither accelerating nor slowing down.

This seems to be the source of your problem-- where have you read that? It isn't true at all. Expansion at a fixed rate (meaning that the rate of change of distance from us to some distant galaxy cluster remains constant with time) is the situation if there is negligible gravity, which is an open universe with negative curvature, not a flat universe. To get an expanding universe to be flat, you need to put gravity in, and the gravity will respond to the expansion to keep the universe flat, but the expansion will not be constant. For example, the way things apparently work, dark energy is accelerating the expansion, even though the universe is spatially flat.