4.1 Coincidences
What is generally considered as the biggest problem for the
CDM model is that it requires a
large and still unexplained fine-tuning to reduce by 120 orders of magnitude the theoretical
expectation of the vacuum energy to yield the observed cosmological-constant value, and, even
more importantly, that it faces a coincidence problem to explain why the dark energy density
is precisely of the same order of magnitude as the other cosmological components
today.
This uncanny coincidence is generally seen as evidence for some yet-to-be-discovered underlying
cosmological mechanism ruling the evolution of dark energy (such as quintessence or generalized additional
fluid components, see, e.g., [106]). But it could also indicate that the effect attributed to dark energy is
rather due to a breakdown of general relativity (GR) on the largest scales [158].
Then, as we shall see in more detail in Section 4.3, another coincidence, which is central to this
whole review, is the appearance of a characteristic scale – dubbed
– in the behavior of
the dark matter sector, a scale with units of acceleration. This acceleration scale appears in
various seemingly unrelated galactic scaling relations, mostly unpredicted by the
CDM
model (see Section 4.3). The value of this scale is
, which yields in natural
units,
(or, more precisely,
). It is perhaps even more meaningful [51, 298, 304
] to note
that, in these same units:
where
is the currently-favored value of the cosmological
constant.
Whether these numerical coincidences are physically relevant or just true (insignificant) coincidences
remains an open question, closely related to the nature of the dark sector, which we are going to elaborate
on in Sections 5 – 10. But, at this stage, it is in any case striking that the dark matter and dark energy
sectors do have such a common scale. This coincidence of scales, together with the coincidence of energy
densities at redshift zero, might perhaps be a strong indication that one should cease to consider dark
energy as an additional component physically independent from the dark matter sector [7], and/or cease
to consider that GR correctly describes gravity on the largest scales and in extremely weak
gravitational fields, in order to perhaps address the two above coincidence problems at the same
time.
Finally, let us note that the existence of the
-scale is actually not the only dark-matter–related
coincidence, as there is also, in principle, absolutely no reason why the mechanism leading to the baryon
asymmetry (between baryonic matter and antimatter) would simultaneously leave both the baryon and dark
matter densities with a similar order of magnitude (
). If the effects we attribute to dark
matter are actually also due to a breakdown of GR on cosmological scales, then such a coincidence might
perhaps appear more natural as the baryons would then be the actual source of the effect attributed to the
dark matter sector.