The late Universe with non-linear interaction in the dark sector: The coincidence problem

Abstract

Abstract. We study the Universe at the late stage of its evolution and deep inside the cell of uniformity. At such a scale the Universe is highly inhomogeneous and filled with discretely distributed inhomogeneities in the form of galaxies and groups of galaxies. As a matter source, we consider dark matter (DM) and dark energy (DE) with a non-linear interaction Q = 3Hγε DE ε DM /(ε DE + ε DM ), where γ is a constant. We assume that DM is pressureless and DE has a constant equation of state parameter w. In the considered model, the energy densities of the dark sector components present a scaling behaviour with ε DM /ε DE ∼ (a 0 /a) −3(w+γ) . We investigate the possibility that the perturbations of DM and DE, which are interacting among themselves, could be coupled to the galaxies with the former being concentrated around them. To carry our analysis, we consider the theory of scalar perturbations (within the mechanical approach), and obtain the sets of parameters (w, γ) which do not contradict it. We conclude that two sets: (w = −2/3, γ = 1/3) and (w = −1, γ = 1/3) are of special interest. First, the energy densities of DM and DE on these cases are concentrated around galaxies confirming that they are coupled fluids. Second, we show that for both of them, the coincidence problem is less severe than in the standard ΛCDM. Third, the set (w = −1, γ = 1/3) is within the observational constraints. Finally, we also obtain an expression for the gravitational potential in the considered model.

Does a generalized Chaplygin gas correctly describe the cosmological dark sector?

“…For w Λ = −1 the second term in the square bracket does not contribute. For this special case the interaction assumes a nonlinear structure similar to the cases studied in [31,32,38,39].…”

Scalar and vector perturbations in a universe with discrete and continuous matter sources

“…We note that coupled states of perfect fluids were investigated in the case of a perfect fluid with a constant equation of state parameter [25] and for the following cosmological scenarios and constituents of the Universe: quark-gluon nuggets [27], the CPL model [28], Chaplygin gas [29], nonlinear f (R) gravity [30], as well as the models with a scalar field [31,32] and dark sector interactions [33,34].…”

CMB and matter power spectra with non-linear dark-sector interactions

“…The complete set of equations for the dark-sector perturbations is obtained by inserting (45) forQ into the first-order balance equations. For the case w Λ = −1 we combine (45) and (46) with the equations (32), (34) and (35), for the case w Λ = −1 the expressions (45) and (46) are combined with equations (29), (33), (34) and (36).…”

“…Further recent studies of non-linearly interacting DE models are [34] and [37]. Systems with non-linear interactions do not allow, in most cases, an analytic treatment, not even for the homogeneous and isotropic background.…”