Sunny Vagnozzi can't really be said to be suddenly coming up with the idea - there are several obviously related preprints at
https://arxiv.org/a/vagnozzi_s_1.htmlI'd like to give some broad background on the link at the top of this discussion.
If one substitutes "dark energy" with "quintessence field driving the accelerated expansion" one gets closer to what the press release (and associated paper, found at https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.0... ) discusses. The "quint" in "quintessence" refers to a "fifth fundamental force", which I'll get to below.
As early as the 1920s (per https://arxiv.org/abs/1211.6338 which is really good history of science) relativists were discussing whether some long-range force could stabilize a universe filled with dense matter, which would otherwise have a tendency to collapse over surprisingly short timescales (e.g., attempts to measure the age of the Earth by studying radioisotope ratios and coming up with billions of years of planetary age meant Earth should already be squashed into the remains of a collapsed universe). Einstein preferred a geometrical solution, the cosmological constant, to model the obvious non-collapse.
With the 1990s discovery of the accelerating expansion ( https://en.wikipedia.org/wiki/Accelerating_expansion_of_the_... ) this preference has been vindicated in the effectiveness of the standard cosmology, \Lambda-CDM, where \Lambda is the cosmological constant. It captures in one variable the measured value of the accelerated expansion, even taking into account disputes over the exact value of the Hubble constant.
The bulk scatter of redshifting luminous matter in universe is best approximated by the Friedmann-Lemaître-Robertson-Walker equations, with the Robertson-Walker term being a metric describing a universe that, if one considers 2d-plane-slicing of space, is like a stack of plates, where each plate is stacked upon an earlier plate, and in turn supports a stack of later plates. The Robertson-Walker metric has parameters which define how flat each plate is -- typical dinner plates, tea saucers, and so on tend to be curved so that liquids don't roll off the edges. (We observe distant galaxies "rolling out of sight", growing too dim and too red to see). The R-W metric also has parameters which define the evolution in size from one plate to the next. Plates may get bigger towards the future; stay the same size; decrease; or even oscillate; depending on the parameter function. Bigger here means that we consider the radius from the centre of the plate to the edge. When we add the Copernican Principle, which says our model should not require that Earth be at or even very close to the exact centre of the cosmos (if there even is such a centre), we take this to mean the distance from us (or any comparable observer) to the observer-centred cosmological horizon.
In our universe, we have exceptionally flat "plates" stacked in such a way that earlier plates are much smaller than larger plates. The "plates" at this age of the universe have a diameter of nearly a hundred billion light-years. The accelerated expansion means that the growth in the future direction is superlinear. And of course, we extend the 2-d planar plates to a 3-d volume.
However, we can go the route that Einstein did not prefer, namely that something non-geometrical is at work driving the accelerated expansion of the universe. In that case, we probably retain the ideas from Robertson-Walker and stack up "plates", but choose a function where either all the plates are the same size, or where the plates grow purely linearly -- no acceleration of the expansion. (The latter approach is how cosmology was modelled when the expansion was believed to be inertial, driven by some early-time impulse that went away around the time of the hot big bang).
To this non-accelerating universe, we have to add something to make galaxies continue to accelerate apart, rather than drifting apart inertially, or recollapsing in the distant future. We add nonzeros to the tension (aka pressure, but negative) components of the stress-energy tensor. That tensor is really a tensor-field where each point in spacetime has a tensorial value which describes the flow of energy-momentum in and out of a point, including in the timelike-direction. In general the tension term must be very small, or the accelerated expansion would look very different, and galaxies would look even more different. In general the tension must vanish inside stable gravitationally bound structures. Moreover, the tension term must also appear in vacuum in deep inter-galaxy-cluster space.
When we study mechanisms that can plausibly generate such stress-energy, we'd tend to be drawn towards our best fundamental theories for known forms of matter, namely the Standard Model of particle physics. We'd want to extend the Standard Model by introducing some particles which give rise to interpretation as carrying and feeling a new fundamental matter force to go with electromagnetism and the nuclear forces. This is usually called a fifth force, but maybe better to be just called yet another long (as in practically infinite) distance force comparable to electromagnetism or Newtonian gravitation.
Now, an aside. Manhattan is not undergoing cosmic expansion. The Earth-Moon system is not expanding. Neither is our solar system to the best of our ability to measure. Our galaxy and the cluster that it's in do not appear to be expanding. Distant galaxy clusters appear to be bound together against the cosmological accelerated expansion.
In the standard cosmology we are forced to say that the cosmos in bulk is best described by the Friedmann-Lemaître-Robertson-Walker model, but that local systems, like Earth, are best described with exterior Kerr metrics, or a Lemaître-Tolman-Bondi collapsing metric, which we can stitch together through an annoying process called the Israel-Darmois Junction, or alternatively we can use something inhomogeneous that captures a set of these Kerr/Schwarzschild-like metrics all at once. This is no big deal; general-relativists do this all the time at much smaller scales with good results. Cosmologically, for instance, "swiss-cheese" models are reasonably powerful, where the "cheese" is the increasingly sparse expanding space and the "holes" are voids where the matter is collapsing into ever denser arrangements.
A fifth force model also has to avoid an expanding solar system. It can do this in at least two ways. Firstly, one can distribute the sources of the fifth force carefully in such a way that they are almost exclusively found outside galaxy clusters. (We take a similar approach with Dark Matter, which is found mainly inside galaxy clusters; the exclusiveness of Dark Matter is less strict than what would have to apply to a fifth force particle family). Alternatively, one could create an interaction with matter which turns the fifth-force charge into something else, like a low-mass particle such as the axion. This process is called "screening" when a large object like the sun (or its magnetic field) encourages this conversion. One could then compare the environment around the sun and Jupiter to see a mass-dependence or magnetic-field-strength dependence on such screening, or even look to more extreme objects like magnetars.
This paper by Vagnozzi chases a small deviation from expected results towards this type of fifth-force screening by the sun driven by theoretical particles which [a] seek to solve a problem in the Standard Model of Particle physics, [b] are decent candidates for at least some of the dark matter energy-density, and [c] are still as far as I know theoretical rather than discovered. https://en.wikipedia.org/wiki/Axion
At this stage, this idea is a more complicated way of capturing the results we have from many astrophysical observations in a way that must practically completely reproduce what we get from the FLRW equations of \Lambda-CDM. More complicated because it adds parameters to the energy-density of the standard cosmology. It also almost certainly would require additional parameters in the Standard Model of Particle Physics. These are not impossible demands, but will be difficult enough to do in practice that few people will make realistic attempts without more compelling results than those reported by Vagnozzi et al.