mister i said:
TL;DR Summary: Could the dark energy be associated with an (unknown) dark force acting at great distances?
I am not a physicist but if someone can answer this question: It seems that there is a dark energy in the universe. Could it be associated with an (unknown) dark force acting at great distances?: I don't quite understand that when we talk about the approach of galaxies we talk in terms of force (gravity) and when we talk about the moving away of galaxies we talk in terms of terms of energy (dark)
In the paradigmatic LambdaCDM a.k.a. ΛCDM model of cosmology, "dark energy" is described in terms of the cosmological constant, Λ, of general relativity, which is part of the equations of general relativity that usually appears on the left hand side of Einstein's field equations shown below:
In Einstein's field equations, above, the Lambda term (Λ) which stands for the cosmological constant, is immediately to the left of the equals sign, and is part of what are basically the force equations for gravity in general relativity. The cosmological constant Λ is a single, dimensionful number (without an imaginary number component) which has a measured value on the order of 10
−52 per meter squared.
So, what you are suggesting is, in one sense, the
status quo.
The language we use is inconsistent. We conventionally put the cosmological constant on the "force" side of Einstein's field equations, even though we call the effects it gives rise to "dark energy" which implies something that would be on the "stuff" side on the right hand side of Einstein's field equations.
But these conventions are based on little more than what "looks pretty" in the equation, and what "sounds nice" when we say it aloud. Sometimes it is more useful, intuitively, to think of the cosmological constant as part of Einstein's field equations. Sometimes is is more useful, intuitively, to think of the cosmological constant as "stuff" that is spread evenly throughout the universe.
Of course, equations are just equations and only have the labels we attach to them. You can call the cosmological constant part of a "force equation" but you could also call it part of the distribution of "stress-energy" to which Einstein's field equations are applied and hence part of "stuff" rather than a "force".
It is trivial, with simple algebra, to show that we can move the cosmological constant term from the left hand side of Einstein's field equations, which we conceptually think of as the "force formula" that tells us how stuff on the right hand side gives rise to gravitational effects, to the right hand side, which we conceptually think of as "stuff" that causes gravitational effects. Both versions are correct. These are just different ways of presenting the same equations. So, ultimately, the question of whether "dark energy" is a force or is "stuff" is an arbitrary distinction in the current paradigm.
"Dark energy" gets its name because the cosmological constant, Λ, in the equation above, is physically equivalent to a field of energy, with a constant amount of energy per volume of space, everywhere in the
light cone of the Big Bang. If you wanted to, you could replace the cosmological constant term with a slight, almost infinitesimal, increase to the T
00 element of the stress-energy tensor shown below, everywhere.
As an aside, the mass-energy of "dark matter", "ordinary matter", and photons, as well as linear momentum, angular momentum, "shear stress", and pressure (which can be thought of as different kinds of energy), are all "inside" the term T
μν, in the Einstein's field equations. This term is called the
stress-energy tensor. The stress-energy tensor is a four by four matrix, conventionally arranged as follows (image from the link), although there is nothing sacred about that arrangement:
Another part of the reason that the force-stuff distinction for dark energy is an arbitrary labeling issue is that, as Peter Donis notes in post #3:
In GR, nothing associated with spacetime geometry is a "force" in the usual sense (something that "pushes" or "pulls" and produces nonzero proper acceleration, i.e., makes an object feel weight).
In order words, thinking in terms of "stuff" and forces caused by "stuff" is really a subtle
category error.
This particular category error is often harmless. Even professional GR physicists sometimes use those terms as a shorthand, recognizing their technical limitations. But, in the context of the question you are asking, this terminology is problematic.
An effort to make this force-stuff distinction that your question asks about illustrates the fact that your question is as much a question about how we label reality, as what it actually is in a real substantive sense. In truth, "dark energy", as currently understood, isn't exactly either a "force" or "stuff".
Modifications to Einstein's field equations that reproduce "dark energy" phenomena, without a cosmological constant, in a manner consistent with available observations (which aren't terribly precise), have been proposed by professional GR theory specialists. But no one alternative has gained wide acceptance. Still, even Einstein thought that the cosmological constant was ugly and possibly a mistake in the first place, so it is understandable that theorists would look for more elegant alternatives.
One area of active research is to consider variations on the cosmological constant that are more "force-like" or more "substance-like" than Einstein's field equations which are ambivalent about that question.
For example, some researchers consider the possibility of matter-dark energy interactions in a way that resolves this ambiguity in favor of a "substance-like" over a "force-like" understanding of it. These "substance-like" interpretations are easier to tweak and modify freely to fit observational astronomy data that isn't a perfect fit for GR with a cosmological constant, in beyond GR models, than "force-like" interpretations of the cosmological constant. But this freedom to tweak the model is both a blessing and a curse, because with a rigid single number description of dark energy (which is still a decent fit to the data although high precision data is showing some tensions with it) you don't need to come up with a theory about why implicit dark energy densities might be different in one part of space-time than it is in another.
