In other discussions the possibility was considered that a curl free field accompanies CMB because of the interference patterns that microwaves are known to make with each other in design of antennas. Quanta of the curl free field are also thought to interfere with each other, regenerating the microwaves that would otherwise become depleted.
The present question is asking how the curl free field might fit into other research. Dark Energy is one possibility. The curl free field is kinetic energy, meaning it counteracts gravity potential energy in the Lagrangian Density. Otherwise the curl free field has a quadrupole convex geometry of quantized stress energy. like a saddle, that only reacts with other curl free fields of the same geometry.
One possible exception is a super conducting Josephson Junction that might detect fluctuations in the curl free field, interpreting them as noise.
The curl free field adds to acceleration of cosmic expansion that is reported for clusters of galaxies. It does not require any new fundamental force or particles other than geometries of stress energy.
Is Dark Energy A Curl Free Field In Equilibrium With Isotropic CMB?
The quanta are vectored, but equal intensity in all directions averaged to a scalar, but of kinetic energy.
Like Dark Energy the curl free field interacts only with gravity and itself. Also like Dark Energy the curl free field opposes gravity as shown in the Lagrangian Density..
Microwaves interfere with each other in well known science and engineering. There seems to be no way that a curl free component could be totally absent in the interference pattern of CMB.
The novel idea is that quanta of curl free stress energy can interact at a slow rate to produce microwaves in an equilibrium that is shifted toward the curl free field.
Dark energy appears to be identical with the curl free field produced by electromagnetic interference in CMB.
Conventional wisdom says that Dark Energy arises from the cosmological constant and does not have any anisotropic dipole aligned with CMB as viewed from our solar system. A research group made this assumption and concluded in an Oxford University publication of 2019 that Dark Energy is not correlated with their observations of accelerating galaxy clusters.
Colin, Malayalee, Rameez, Sarkar, Astronomy & Astrophysics 631, L13, 2019 found evidence for anisotropic acceleration of galaxy clusters viewed from Earth for 740 observations which correlated well with anisotropic CMB, but acceleration was not correlated with uniform Dark Energy derived from the cosmological constant.
https://www.mpls.ox.ac.uk/latest/news/evidence-for-anisotropy-of-cosmic-acceleration
One possible interpretation is that the conventional wisdom needs to be changed to align a dipole of Dark Energy with the dipole of CMB. Then the research article could correlate acceleration with Dark energy.
Assumptions have continued for a long time without proof. When proof is found, the assumptions should be revisited. Assumptions have been that Dark energy causes acceleration, and Dark Energy has no anisotropy viewed from Earth. Now it seems that Dark Energy must have anisotropy.
For a long time CMB was assume to nave no anisotropy, then proof was found.
With a slow reverse reaction in the equilibrium, most of the energy could be in the curl free component, and it could lag behind the evolution of CMB by some temperature difference and by some offset angle in the dipole orientation.
The 2019 article found a 23 degree offset angle between acceleration and CMB dipole, within measurement uncertainties, close enough for a conclusion, but leaving room for a modified view of dark energy to give a better explanation.