2.11 Dark energy and dark matter

In Section 1.4, we have illustrated the possibility that dark energy, seen as a dynamical scalar field (quintessence), may interact with other components in the universe. When starting from an action such as Eq. (1.4.20View Equation), the species which interact with quintessence are characterized by a mass function that changes in time [514, 33Jump To The Next Citation Point, 35Jump To The Next Citation Point, 724Jump To The Next Citation Point]. Here, we consider the case in which the evolution of cold dark matter (CDM) particles depends on the evolution of the dark-energy scalar field. In this case the general framework seen in Section 1.4 is specified by the choice of the function mc = mc (ϕ ). The coupling is not constrained by tests of the equivalence principle and solar system constraints, and can therefore be stronger than the coupling with baryons. Typical values of β presently allowed by observations (within current CMB data) are within the range 0 < β < 0.06 at 95% CL for a constant coupling and an exponential potential, [114Jump To The Next Citation Point, 47Jump To The Next Citation Point, 35Jump To The Next Citation Point, 44Jump To The Next Citation Point], or possibly more if neutrinos are taken into account or more realistic time-dependent choices of the coupling are used [539Jump To The Next Citation Point, 531Jump To The Next Citation Point]. As mentioned in Section 1.4.4, this framework is generally referred to as ‘coupled quintessence’ (CQ). Various choices of couplings have been investigated in the literature, including constant β [33Jump To The Next Citation Point, 619Jump To The Next Citation Point, 35Jump To The Next Citation Point, 518Jump To The Next Citation Point, 414, 747, 748, 724] and varying couplings [76Jump To The Next Citation Point], with effects on Supernovæ, CMB and cross-correlation of the CMB and LSS [114, 47, 35Jump To The Next Citation Point, 44, 539, 531, 612Jump To The Next Citation Point].

The presence of a coupling (and therefore, of a fifth force acting among dark matter particles) modifies the expansion of the universe, linear perturbations and most relevantly, structure formation. Coupled quintessence is a concrete model in which a non-negligible amount of dark energy is present at early times. The presence of such an early dark-energy component is accompanied specific features, as illustrated in Section 1.4 for a general framework:

  1. a fifth force ∇ [Φα + β ϕ] with an effective G&tidle;α = GN [1 + 2β2 (ϕ )];
  2. a velocity-dependent term ( ) H&tidle;v α ≡ H 1 − β (ϕ)ϕ˙ vα H;
  3. a time-dependent mass for each particle α, evolving according to Eq. (1.4.25View Equation).

All these effects, and in particular the first two, contribute significantly to structure formation. Note that the second and third terms are not independent of each other as they are a direct consequence of momentum conservation. Depending on the function mc (ϕ), and therefore β (ϕ), the first two terms can partially balance: the fifth force increases gravitational attraction whilst the velocity-dependent term, if the CDM mass decreases with time, tries to dilute the concentration of the virialized haloes. In particular, a striking difference between constant and variable-coupling models concerning the interplay of all these three effects has been highlighted in [76Jump To The Next Citation Point]: whilst for constant couplings only the latter two effects can alter the virial equilibrium of an already-collapsed object, for the case of a variable coupling the time evolution of the effective gravitational constant can also modify the virial status of a halo, and can either enhance or counteract the effect of reducing halo concentrations (for decreasing and increasing couplings, respectively). Nonlinear evolution within coupled quintessence cosmologies has been addressed using various methods of investigation, such as spherical collapse [611, 962, 618, 518, 870, 3, 129] and alternative semi-analytic methods [787, 45]. N-body and hydro-simulations have also been done [604, 79Jump To The Next Citation Point, 76Jump To The Next Citation Point, 77Jump To The Next Citation Point, 80Jump To The Next Citation Point, 565Jump To The Next Citation Point, 562Jump To The Next Citation Point, 75Jump To The Next Citation Point, 980].

We list here briefly the main observable features typical of this class of models:

As discussed in subsection 1.6.1, when a variable coupling β(ϕ) is active the relative balance of the fifth-force and other dynamical effects depends on the specific time evolution of the coupling strength. Under such conditions, certain cases may also lead to the opposite effect of larger halo inner overdensities and higher concentrations, as in the case of a steeply growing coupling function [see 76]. Alternatively, the coupling can be introduced by choosing directly a covariant stress-energy tensor, treating dark energy as a fluid in the absence of a starting action [619, 916, 193, 794, 915, 613, 387, 192, 388]. For an illustration of nonlinear effects in the presence of a coupling see Section 1.6.

  Go to previous page Go up Go to next page