Cosmic coincidence problem

Explain why, in the ΛCDM model where matter and dark energy are separately conserved with ρm ∝ a^{-3} and ρΛ = const, the dark-energy density becomes dynamically relevant only at low redshift such that ΩΛ and Ωm are of the same order today, rather than at much earlier or later epochs.

Background

In ΛCDM, the independently conserved components evolve as ρr ∝ a^{-4}, ρm ∝ a^{-3}, and ρΛ = const. Observationally, dark energy has become dominant only recently (z ≈ 0.3), raising the question of why the densities of matter and dark energy are comparable today despite their different time evolutions. This is referred to as the cosmic coincidence problem.

The chapter discusses this issue by highlighting its reformulations in terms of structure formation (growth of the matter density contrast) and age constraints of old astrophysical objects, which seem to point to a narrow range of ΩΛ that allows both adequate structure formation and a sufficiently old universe.