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

TL;DR

This paper explores a cosmological model with non-linear dark sector interactions, showing certain parameter sets reduce the coincidence problem and align with observations, especially at late universe stages with inhomogeneities.

Contribution

It introduces a non-linear interaction model between dark matter and dark energy, identifying specific parameters that address the coincidence problem and fit observational constraints.

Findings

Two parameter sets, (w=-2/3, γ=1/3) and (w=-1, γ=1/3), are consistent with scalar perturbation theory.

The model reduces the severity of the coincidence problem compared to ΛCDM.

The set (w=-1, γ=1/3) aligns with observational data.

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 $Q = 3\mathcal{H}\gamma \bar\varepsilon_{\mathrm{DE}} \bar\varepsilon_{\mathrm{DM}} / (\bar\varepsilon_{\mathrm{DE}} + \bar\varepsilon_{\mathrm{DM}})$, where $\gamma$ 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 $\bar\varepsilon_{\mathrm{DM}} / \bar\varepsilon_{\mathrm{DE}} \sim \left({a_0} / {a} \right)^{-3(w+\gamma)}$. 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 $(w,\gamma)$ which do not contradict it. We conclude that two sets: $(w=-2/3,\gamma=1/3)$ and $(w=-1,\gamma=1/3)$ 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 $\Lambda$CDM. Third, the set $(w=-1,\gamma=1/3)$ is within the observational constraints. Finally, we also obtain an expression for the gravitational potential in the considered model.