No one knows why space is expanding. The dark energy is just the 'label' they give to whatever is causing it to expand. Both dark matter and dark energy are postulated to be whatever shape of puzzle piece fits into the puzzle slot where the error in our formulas exists. What i'm saying is that it's more likely that the formula itself is wrong than it is that something magically exists to conveniently fit that slot.
> The dark energy is just the 'label' they give to whatever is causing it to expand
This depends on how you look at it.
In the standard cosmology we define a preferred frame wherein an observer will see the matter (that's in the most general sense of "not the gravitational field", so it includes atoms and their components, photons, and various types of dark matter (e.g. neutrinos, which are "hot" dark matter, since they move relativistically and do not experience electromagnetism)) content of the universe as homogeneous and isotropic. This is physically reasonable since along every unobscured line of sight we see a lot of galaxies of various shapes, "tilts", sizes, surface brightnesses, and spectral lines. Observations also lead us to conclude that there is a relationship between redshifting of the spectral lines of common types of galaxies (and common radiative occurrences within them, like type A supernovas), and the change of the other observables (angular size on the sky, luminosity, etc.) that correlate with greater distance. This in turn led to the discovery of the Hubble "constant", and provoked ever deeper field telescopic studies to prove its value.
So if we assume that along every line of sight, including obscured ones, we have much the same view of many many galaxies at a variety of distances, we can make a variation on the Friedmann equation that parameterize several things that would lead to the observables of galaxies when we model their known (and unknown) components as a set of perfect fluids.
We can take the Hubble "constant" and put it into a Robertson-Walker vacuum spacetime. RW spacetimes can be grokked by dimensional reduction. Consider a cylinder that we slice (foliate) along its axis into a set of infinitesimally thin circles stacked on top of each other. We describe the radius of each circle with a function r(h) where h is the height of the circle from the base of the cylinder. Where r(h) is constant, we have a cylinder, but if r(h) increases with h, then we have something like a cone balancing on its apex; r(h) can describe a wide variety of shapes. For an 3+1 RW spacetime that is similar to our universe, we foliate on the timelike axis and define a function a(t) where t_0 == now with the spacelike coordinates set on a chosen observer (us here on Earth, for example). "t" counts upwards as we go into the past from t_0, and a(t) goes to zero as t increases. "t" is the lookback time and a(t) is the scale factor. The chosen observer is the special observer mentioned above, who sees the matter of the universe as isotropic and homogeneous at the largest scales. The most useful coordinates on such a spacetime are comoving, that is each gravitationally bound galaxy cluster stays at the same coordinates at every time t.
If we mix together the Friedmann equations, the Lemaître idea of spacetime having a zero radius at some large lookback time, and the RW spacetime that can model that, we get the FLRW model of the standard cosmology. We take the RW case where there is no extrinsic curvature, that is, when we foliate on the timelike axis each spacelike hypersurface is spatially flat; that is similar to saying that when we slice up our dimensionally reduced solid along its height, we get a set of circles of the same radius (i.e. a cylinder rather than a cone). We absorb the expansion parameter into a(t) as another of the fluids.
We then consider two types of fluid: those that dilute away as t -> t_0 -> future and those that do not dilute away. The former is "matter", including dark matter; the latter is "dark energy".
When we consider them as components of an action, diluting-away fluids are attractive and non-diluting fluids are repuslive. When we consider them in terms of the matter tensor T in General Relativity, the diluting-away fluids have positive pressure and the non-diluting fluids have negative pressure.
It's important to return to the point that this model has a preferred frame, and that translating the non-diluting fluid into "the same for all observers in all frames of reference" physics leads one to assume that dark energy is just a feature of the Lorentz-invariant vacuum. So dark energy arises in the cosmological model but corresponds to the ground state of the empty-of-matter spacetime in frames of reference other than the preferred one picked out by the cosmological model.
That is, the statement that "dark energy drives the expansion (via negative pressure or repulsion)" is frame-dependent, and thus observer-dependent, and with a change of frames of reference (and even a change of coordinates on the preferred frame), the statement becomes untrue. What is true in all frames is that there is an intrinsic property of space in an expanding spacetime that has a constant energy-density no matter how large a volume of space is considered.
The exact equation of state of dark energy is an area of active research and also tests to make sure that the assumptions that inevitably lead to it (isotropy at huge scales, homogeneity, spatial flatness, redshift-distance relations and other things implying expansion) are not blown up by evidence from ever finer observations.
So it's not so much a 'label' as a phenomenon whose microscopic details have yet to be discovered.
There are lots of those in physics, and we've had a good century of probing the microscopic details of phenomena discovered at the end of the 19th century and since, so this shouldn't really be causing anyone sleepless nights.
in which Schrödinger (in 1918!) describes, "matter in the large essentially as a compressible fluid of constant density at rest under a constant spatially isotropic tension which ... must be equal to 1/3 of the rest density of energy".
The notation is old-fashioned, but check out Schrödinger's paragraph at the bottom of Harvey's page 5 !
Your statement that there's "an expanding space-time that has a constant energy-density", gets to the nub of it for sure, but in reality no one knows if any of the fundamental field strengths are indeed constant. To me the need for "dark" stuff to be postulated, is more likely to indicate that gravity strength, or light speed, are more likely to NOT be constant over large space-time ranges, than the likelihood that there is a whole class of 'dark' particles and waves that currently don't interfere with any other matter in a provable way.
So if someone asked me what's my 'evidence' that gravity or light-speed are not universally constant, my answer is simply: "The evidence for dark-energy/matter, is that exact same evidence". There should be some wave-function (possibly resulting from what we call a big bang), in terms of G and C, that once integrated out over the current life of the universe, will yield precisely that positions and velocities of the galaxies that we currently observe. To me it seems far less likely that there's an entirely new set of particles we cannot see, despite the Standard Model of particles being proven correct out to 40 decimal places.
You already have the neutrino which interacts only via weak force and gravity, They show up much the same in bubble chambers as dark matter does in our telescopes; they don't. We only see where they interact with more observable matter, is it really that far fetched to imagine a particle that interacts through gravity only?
I'm not sure what you're trying to argue here, or even why. I'll guess that you're interested in physical cosmology and would like a set of brief and not-too-technical reactions to your ideas (which I take to be implied questions) from someone who knows the \Lambda-CDM cosmology reasonably well.
Dark energy it is a property of empty space that does not dilute away as more space appears in an expanding universe. The only way to abolish dark energy is to eliminate the expansion of the universe. It only has a "fundamental field strength" in particular chosen frames of reference in which one can represent it as a field with a constant energy-density. The comoving frame of the standard cosmology is one such frame of reference. However, in most other frames this energy density vanishes, and when that happens a general relativist will decide that the energy density was an artifact of the choice of frame of reference or system of coordinates and ditch the word "fundamental".
Now, there are lots of ways we can complicate the action S_{\Lambda-CDM} in a Lagrangian formulation of the standard cosmology by introducing further repulsive terms into it beyond constant * \Lambda (as in the Einstein-Hilbert action or an expansion of it) or L_{repulsivematter} in a parameterization, and indeed there have been numerous attempts to do so. However, short of eliminating the expansion of space at all times and in all reference frames there is no way to get rid of a repulsive, non-diluting, non-concentrating (when time-reversed or if the critical density of the universe turns out to lead to a contraction of space in the future) term.
But in the standard cosmology, we have \Lambda, which is just the cosmological constant, i.e., dark energy is a property of the ground state, which is the vacuum. When there's more vacuum, there's more dark energy. Mathematically, we start with an action that leads to the standard write-down of the EFEs. Physically, this matches observational tests at large scales, which is convenient because the standard write-down of the EFEs is almost the only way to match observational tests within our solar system (c.f. the parameterized post-Newtonian formalism).
> gravity or light speed are not universally constant
What exactly do you mean by "gravity ... not universally constant"? In particular, what do you mean by gravity?
In General Relativity speeds are something that are extremely hard to talk about except in the local neighbourhood around a single point. In fact, many general relativists would argue that talking about "universal" speeds violates the spirit of general relativity. However, if our universe continues to be modellable as a smooth manifold with a Lorentz metric, we get a sort of quasi-universality of "c" in that at every point one can construct an infinitesimal region of spacetime in which "c" is a parameter in the action of matter and takes on the same _locally measured_ value in each such region for an observer in that region. There is ample evidence that favours this up to energy scales accessible to us on Earth and visible with observational platforms on and near our planet.
There are certainly metric theories other than GR that allow for different sources to couple to different metrics, but most of these have to undergo a phase change to an effective single metric with universal coupling in the early universe or we would see clear evidence for them (in particular, the distribution of heat in the early dense phase of the universe still has to produce the Standard Model at lab energies and also stars and galaxies and labs). Some productive and well-regarded physical cosmologists have proposed these types of theories, even recently (e.g. Afshordi & Magueijo), and they explictly reject a universal value of "c" (in particular c approaches infinity in their model's extremely early universe).
But in the standard cosmology we have General Relativity, and we don't vary the value of G or of c when grinding through the Einstein Field Equation; we take those values as given to us by nature, and have no evidence for them varying in the observable universe (and a pretty substantial amount of evidence against such variations, in particular including petabytes of spectroscopic data from objects in the sky).
> "There should be some wave-function (possibly resulting from what we call a big bang), in terms of G and C, that once integrated out...
I'm sorry, I don't understand this. Could you explain further?
> To me it seems far less likely that there's an entirely new set of particles we cannot see, despite the Standard Model of particles being proven correct out to 40 decimal places.
Dark energy is not particles. As I said above, it's a feature of the vacuum, and the most fundamental feature of the vacuum is that it is empty of particles. A tl;dr here is that we don't know what creates more space rather than less space, but we know that when more space is created there's more dark energy in the comoving frame but not more particles.
Are you thinking of dark matter here, rather than dark energy? If so, we already have hot dark matter in the form of neutrinos. Neutrinos are "hot" because they move relativistically, and thus are prone to carry momentum far away from galaxies very quickly. Cold dark matter is "cold" because it moves non-relativistically and so the momentum CDM carries lingers in place in and around galaxy clusters. While it would be convenient if CDM were like heavy neutrinos, there is no reason in the standard cosmology that CDM has to be particles at all, or even just one species; the only requirement is that it be almost entirely collisionless and non-radiative so that we don't see it and so that it doesn't release its trapped momentum (e.g. by converting some of it into hot dark matter or light or standard model particles).
Finally, the Standard Model is mute on gravity, and yet you -- made up of Standard Model particles -- are feeling it right now. So I'm not sure how your argument about the correctness of the Standard Model fits with your argument.