4.1 Coincidences

What is generally considered as the biggest problem for the ΛCDM 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 Ω Λ is precisely of the same order of magnitude as the other cosmological components today7. 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 a0 – 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 ΛCDM model (see Section 4.3). The value of this scale is a0 ≃ 10− 10 m s−2, which yields in natural units8, a0 ∼ H0 (or, more precisely, a0 ≈ cH0 ∕2π). It is perhaps even more meaningful [51, 298, 304Jump To The Next Citation Point] to note that, in these same units:

a20 ∼ Λ, (1 )
where Λ is the currently-favored value of the cosmological constant9. 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 510. 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 a0-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 (ΩDM ∕Ωb = 5). 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.

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