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:
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 , and therefore , 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 : 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]. -body and hydro-simulations have also been done [604, 79, 76, 77, 80, 565, 562, 75, 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 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.
Living Rev. Relativity 16, (2013), 6
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