[E]xplore the extent to which "EU theory" addresses the key sets of astronomical observations that have lead to (and support) 'cold dark, non-baryonic matter' (CDM) as a component of the universe, comprising some ~5 times as much mass as baryonic matter.
As there are a very large number of relevant, very good astronomical observations, it may be worthwhile classifying them into a small(ish) number of boxes, and addressing each separately.
First, though, a re-statement of what this step is intended to achieve. Astronomers (astrophysicists, cosmologists) have, in thousands of papers published in relevant, peer-reviewed journals, shown a detailed and consistent match between observations and 'CDM theory'1; in a nutshell: the 'mass budget' of the universe comprises approx 15% 'baryonic matter' and ~85% CDM (there's also a very small hot DM component, in the form of neutrinos). This universal composition is (approximately) reflected in the largest-scale structures (sheets, filaments, voids), rich clusters of galaxies, and in galaxy groups. In galaxies, it ranges from almost entirely CDM (e.g. certain dwarf spheroids) to (possibly) approximate equality of baryonic matter and CDM2.
So, here's a suggested categorisation of astronomical observations of direct relevance to the existence and amount of CDM:
+ rich clusters: dispersion of galaxy line-of-sight velocities ('Zwicky and the virial theorem')
+ rich clusters: gravitational lensing, both strong and weak
+ rich clusters: X-ray observations
+ rich clusters: the Sunyaev-Zel'dovich effect
+ CMB angular power spectrum (and supporting observations)
+ P(k) (a.k.a. large-scale structure)
+ individual galaxies: gravitational lensing, both strong and weak
+ individual galaxies: rotation curves of spirals
+ (other categories to be added later).
My intention is to examine each of these, in turn (no more than one per post), and to ask "Which "EU theory" papers, published in relevant peer-reviewed journals, demonstrate quantitative consistency between 'theory' and the astronomical observations?"
And to repeat my earlier comment, AFAIK, there are only a very few such papers, and all of them address just one of the above categories.
Finally, I do hope that this thread will, for at least the next little while, focus on these; after all, in astronomy (and cosmology), you don't get more empirical than thousands (or even millions) of high quality observations, all potentially independently verifiable.
1A necessary short-hand; it's not really necessary to elaborate on it here, as it's been covered already in this thread, and in many others.
2Caveat: I've not researched this; there may be good observations which point to an even smaller proportion of CDM in some galaxies.