So far, say at the end of February 2019, no one seems to have explained how the current laws of physics explain what is called the accelerating expansion of the universe, or dark energy. Physicists have tried using the ideas of GR, MOND (modified Newtonian dynamics) and other ideas but so far without a result convincing physics. This approach might be analogized to the synthetic method of proof in mathematics. Start with known mathematical theorems and derive the sought after result. But what about the analytic approach?
The analytic approach in mathematics, roughly, starts from what it is desired to prove and, step by step, determines at each step what antecedent statements of mathematics would be required to lead to the current step. Has an analytic approach been applied to dark energy?
For example, does dark energy occur only at vast cosmological scales? If that were true (I suspect not, but perhaps it is true), then the applicable law must only apply at vast cosmological scales. Does gravity qualify? Should the law be isotropic at large cosmological scales? And here is a wrinkle. What if the expansion of space is scale invariant but has not yet been recognized yet at scales between quantum and cosmological? Then assumptions about what features the requisite law should have may be mistaken. What features do you think a law that explains dark energy should have?
Dark energy is an invented term meant to explain why the apparent geometry of the Universe is 'flat'. Prior to the late 1990's, cosmologists explained this by presuming that the mass density of normal and dark matter just happened to equal the "critical" density at which the geometry of the Universe is flat. (If the mass density is 100% of the critical density, then triangles have 180 degrees, and the expansion of the Universe should just coast along forever, at a gradually slowing pace, but never quite stop expanding. If the mass density were greater than 100% of the critical density, then triangles would have more than 180 degrees, just as on a sphere like the Earth, and the Universe would have expanded to a certain size, then collapsed to zero size, causing a sort of reversed Big Bang. And if the mass density were less than 100% of the critical mass density, then triangles would have less than 180 degrees, and the expansion of the Universe would be faster in the future than in the past -- how much faster being a matter of some debate, as it could approach some asymptotic value, such as 200 km/sec/Mpc, or it could increase forever.)
As noted above, despite many observational proofs that the assumption that the mass density of the Universe could not possibly be 100% of the critical density (or even close to that), most cosmologists clung to the idea until the late 1990's (See The Expansion of the Universe at http://cseligman.com/text/galaxies/universe.htm for an ancient discussion of that problem). Then a crisis occurred in which it was conclusively proven that their assumptions were wrong, and the total mass of the Universe, including both normal and dark matter, cannot possibly be 100% of the critical density (and in fact, is at most 27% of the critical density). But for decades cosmologists had gotten used to having the magic critical density of 100% as the explanation for the apparent 'flatness' of the Universe's geometry. So how to solve the problem? Just invent a new, probably nonexistent material (or non-material, depending on how you look at it) called "dark energy", and assign it a value that makes the total of mass and non-mass 100%. So really, all that dark energy is, is a way of saying that we don't know why the geometry of the Universe appears to be flat, when it doesn't have nearly enough mass to be that way.
It is certainly far too early (probably a few decades too early) to say when, if ever, the concept of dark energy will be proven (highly unlikely) or abandoned (also unlikely in the short term, hence my choice of a few decades -- enough time for everyone who likes the idea to get old and die). The simplest explanation, in my opinion, is the same reason that some idiots claim that the Earth is flat -- locally it looks flat, and it's just too big to see that it isn't unless you take a very wide view of things. We feel certain that the Universe itself is hundreds, thousands, or even thousands of trillions of times larger than the Observable Universe; so it may be that the Universe as a whole is hyperbolic, and the only reason the Observable Universe looks flat is that it is too small to tell that it isn't. But although that's as reasonable an explanation as any other, it is highly unlikely to be accepted by any of the people who are busy publishing papers about what dark energy might be, or actually trying to construct devices that would allow them to prove it.
For the moment dark energy is perfectly well described by the cosmological constant, that's as much a part of general relativity as is Newton's constant.
I think that you will find a good answer in this scientific approach. "A new alternative theory of gravity where gravity is particles behaving as a fluid forming two types of swirls Annular swirls and oval swirls".
https://www.researchgate.net/figure/Figure-3-Conceptual-depict-shows-the-entire-curvature-revolves-together-around-center_fig3_330763968 sincerely- ahmad
Robert Shour asks “What features do you think a law that explains dark energy should have?” In my work I take Hubble’s law to be strictly true, at least to leading order. This immediately means that cosmic acceleration must linearly increase with radial distance, which is satisfied by dark energy. The essential feature here, whether due to dark energy or new space/time physics exclusive of dark energy, is a nonlinearly increasing time-dilation (ie, d(t'-t)/dt ~ - r^2) extending outward into the cosmos. The challenge then—in deriving an alternative to dark energy per se—is to deepen relativity physics such that a\CA~r emerges across the epoch. In this the “analytic approach” would be to identify antecedent statements leading to “d(t'-t)/dt ~ - r^2”, after which the Lorentz transformation gives a\CA~r. Should these statements reside deeper than the current postulates and laws of physics, then a new paradigm could be at hand.
The observations support the hypothesis that the energy density is not changing with time locally which I believe (don't ask me to prove it) implies that the stress-energy tensor must have the same form as the Minkowski Metric, diagonal [+1, -1, -1, -1]. The contribution to gravity is the sum of the energy and three pressure terms hence totals to -2. That is why you often see it said that acceleration is driven by "negative pressure", the -2 factor creates an effective "repulsive gravity".
The implication is that every cubic metre of space contains exactly the same amount of dark energy, or you can put it on the other side of the equation and treat it as nothing more than a constant in the equation describing the geometry. The observations only tell us that there is no evidence at all for any spatial variation or variation over the history of the universe of its density.
GR fits what is observed exactly through the use of the Cosmological Constant.
MOND is nothing to do with this, it was an attempt to be a starting point for the development of an explanation for dark matter, not dark energy.
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