# Does the cosmological constant represent anti-gravity? [duplicate]

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Does the cosmological constant represent anti-gravity?

According to the current Lambda-CDM cosmological model, there must be a fair amount of the dark energy in the universe responsible for the acceleration of the expansion and other things. This idea is represented by the cosmological constant, introduced by Einstein.

If the cosmological constant (dark energy) is responsible for repulsion, can it be considered a gravitational repulsion? And consequently, can gravity be considered both attractive and repulsive? I feel the answer is no, but why specifically is this a wrong way of thinking?

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First a point that is often mis-stated: The cosmological constant is not the same as dark energy. We observe that the universe is accelerating (growing big at an ever-increasing rate). Since we do not know what is causing this accelerated expansion, we dub the "stuff" that sources this accelerated expansion "dark energy". A cosmological constant (a type a fluid that never dilutes) is one possible explanation for dark energy, but there exist other possible fluids (such as scalar field quintessence) that can also lead to an accelerated expansion.

In gravity (general relativity), go back to the Einstein Field Equations: $G_{\mu\nu}=8\pi G T_{\mu\nu}$. The (energy-density and pressure of the) stuff that fills the universe ($T_{\mu\nu}$) will affect the way the background curves (in other words, $T_{\mu\nu}$ sources gravity).

As the universe expands, the energy density of normal matter will dilute (planets, dust, etc.) proportional to $1/\text{Volume}$. The energy density of relativistic matter will dilute proportional to $1/\text{Volume}^{4/3}$. A cosmological constant will never dilute: the energy density is constant at all times.

The behavior of the background on which all other particles live (e.g. the curvature of the background, or $G_{\mu\nu}$) will depend on the stuff on that lives on background $T_{\mu\nu}$. It is this behavior of the background that is "gravity". A $T_{\mu\nu}$ described by a cosmological constant will grow at an ever increasing rate. A universe that is homogenous and filled with a $T_{\mu\nu}$ that dilutes in a manner similar to normal everyday matter will tend to eventually collapse on itself.

Basically, you may say that the manner in which the energy-density of "stuff" dilutes determines how that "stuff" gravitates.

• If you don't mind, a follow-up question: let's imagine you have a flat universe without a cosmological constant into which you put two separated chunks of "cosmological constant mass"- that is, two regions of uniform energy density which, like the cosmological constant, do not dilute. Is it correct to say that these two objects will gravitationally attract each other, while the space inside each object expands? – Rococo Sep 15 '17 at 3:24
• Do you mean that the universe contains only 2 regions: half of the universe contains cosmological constant with value $\Lambda_1$ and the other half of the universe contains cosmological constant with value $\Lambda_2$? Or do you mean a two small objects made of cosmological constant stuff in an otherwise empty universe (with cosmological constant of zero everywhere else)? – Bob Sep 15 '17 at 4:29
• I was thinking of the second situation. – Rococo Sep 15 '17 at 4:43