ΛXCDM: a cosmon model solution to the cosmological coincidence problem?

Abstract

We consider the possibility that the total dark energy (DE) of the Universe is made out of two dynamical components of different nature: a variable cosmological term, Λ, and a dynamical "cosmon", X, possibly interacting with Λ but not with matter -which remains conserved. We call this scenario the ΛXCDM model. One possibility for X would be a scalar field χ, but it is not the only one. The overall equation of state (EOS) of the ΛXCDM model can effectively appear as quintessence or phantom energy depending on the mixture of the two components. Both the dynamics of Λ and of X could be linked to high energy effects near the Planck scale. In the case of Λ it may be related to the running of this parameter under quantum effects, whereas X might be identified with some fundamental field (say, a dilaton) left over as a low-energy "relic" by e.g. string theory. We find that the dynamics of the ΛXCDM model can trigger a future stopping of the Universe expansion and can keep the ratio ρ D /ρ m (DE density to matter-radiation density) bounded and of order 1. Therefore, the model could explain the so-called "cosmological coincidence problem". This is in part related to the possibility that the present value of the cosmological term can be Λ 0 < 0 in this framework (the current total DE density nevertheless being positive). However, a cosmic halt could occur even if Λ 0 > 0 because of the peculiar behavior of X as "Phantom Matter". We describe various cosmological scenarios made possible by the composite and dynamical nature of ΛXCDM, and discuss in detail their impact on the cosmological coincidence problem.For instance, consider the so-called "cosmological coincidence problem" [40], to wit: why do we find ourselves in an epoch t = t 0 where the DE density is similar to the matter density (ρ D (t 0 ) ≃ ρ M (t 0 ))? In the ΛCDM model this is an especially troublesome problem because ρ Λ remains constant throughout the entire history of the Universe. In the ordinary dynamical DE models the problem has also its own difficulties. Thus, in a typical quintessence model the matter-radiation energy density ρ m = ρ M + ρ R decreases (with the expansion) faster than the DE density and we expect that in the early epochs ρ m ≫ ρ D , whereas at present and in the future ρ m ≪ ρ D . Therefore, why do we just happen to live in an epoch t 0 where the two functions ρ D (t 0 ) ≃ ρ m (t 0 )? Is this a mere coincidence or there is some other, more convincing, reason? The next question of course is: can we devise a model where the ratio ρ m /ρ D stays bounded (perhaps even not too far from 1) in essentially the entire span of the Universe lifetime? This is certainly not possible neither in the standard ΛCDM model, nor in standard quintessence models 2 . And it is also impossible for a model whose DE consists only of a running Λ [23]. However, in this paper we will show that we can produce a dynamical DE model with such a property. Specifically, we investigate a minimal realization of a composite DE model made out of just two components: a runnin...

Composite dark energy: Cosmon models with running cosmological term and gravitational coupling

“…This problem has been addressed from different perspectives within modified quintessence models [17]. Remarkably, RG models can also tackle efficiently the coincidence problem [18], a point that will be reexamined here too.…”

“…In a subsequent work a general algorithm was established to compute the effective EOS for general cosmological models with variable cosmological parameters [20]. A further generalization (the so-called ΛXCDM models [18]) is to admit the possibility that the DE is a composite medium made out of a running Λ and a dynamical component X that we called the "cosmon" in [18] 3 . In the present work we elaborate further along this line but we allow the gravitational coupling G being variable.…”

“…(2.1) generalizes into 2) where ρ D = ρ Λ + ρ X is the total DE density. Following [18] we call the resulting composite DE model the ΛXCDM model. There are, however, different possible implementations of the ΛXCDM model: if we assume that ρ D and ρ m are separately conserved, then G must be constant and we obtain precisely the sort of ΛXCDM framework studied in detail in Ref.…”

“…There are, however, different possible implementations of the ΛXCDM model: if we assume that ρ D and ρ m are separately conserved, then G must be constant and we obtain precisely the sort of ΛXCDM framework studied in detail in Ref. [18], which will be referred hereafter as type I cosmon models. Alternatively, if we take as conserved quantities ρ X and ρ m , then we must haveρ i + α i ρ i H = 0 for both ρ i = ρ m , ρ X , and in this case (2.2) implies that G must vary in time in combination with ρ Λ according to the equatioṅ…”

“…if ω X < −1 and ρ X < 0 we obtain a kind of unusual fluid which has been called "phantom matter" (see Fig. 1 of [18]). Phantom matter does preserve -in contrast to usual phantom energy -the strong energy condition, as ordinary matter does.…”