Interacting models may be key to solve the cosmic coincidence problem

TL;DR

The paper addresses the cosmic coincidence problem by exploring energy exchange between dark energy and dark matter via a nonzero $Q$ in a flat FRW universe. It analyzes three phenomenological forms for the interaction: $Q=3αH(ρ_m+ρ_φ)$, $Q=3βHρ_m$, and $Q=3ηHρ_φ$, deriving how each yields a constant or slowly varying ratio $r=\rho_m/ρ_φ$ and potential attractor behavior. Using model-independent observables $y(z)$, $y'(z)$, and $y''(z)$ from SN Ia and radio galaxies, the authors extract $E(z)$, $q(z)$, and $P_φ(z)$ and find compatibility with current data as well as with ΛCDM, though not enough to discriminate among models. They then propose a strategy linking $r$ to the Hubble rate through $dr/dH=\mathcal{I}/H$, obtaining closed-form $H(r)$ and $r(z)$ for each model and showing that the resulting $H(z)$ curves remain consistent with existing measurements. The work highlights what data would be required to decisively test interacting scenarios and assesses their capacity to address the coincidence problem within general relativity.

Abstract

It is argued that cosmological models that feature a flow of energy from dark energy to dark matter may solve the coincidence problem of late acceleration (i.e., "why the energy densities of both components are of the same order precisely today?"). However, much refined and abundant observational data of the redshift evolution of the Hubble factor are needed to ascertain whether they can do the job.

Figures (11)

• Figure 1: From left to right, evolution of the ratio $r=\rho_{m}/\rho_{\phi}$ with redshift for models alpha, beta, and eta. For all of them $r$ either tends to a constant or varies very slowly at small redshift. In drawing the curves we have fixed $r_{0}= 3/7 \,$ and $\, w= -0.9$.
• Figure 2: Same as Fig.1 except for that in this case $w= -1.1$.
• Figure 3: From top to bottom, dimensionless coordinate distance, $y(z) = H_{0} \, (a_{0}\, \tilde{r})$, in terms of the redshift for models alpha, beta, and eta. For comparison, the prediction of the $\Lambda$CDM model is also shown.
• Figure 4: From top to bottom, first derivative of the dimensionless coordinate distance in terms of redshift for models alpha, beta, and eta. For comparison, the prediction of the $\Lambda$CDM model is also shown.
• Figure 5: From top to bottom, second derivative of the dimensionless coordinate distance in terms of redshift for models alpha, beta, and eta. For comparison, the prediction of the $\Lambda$CDM model is also shown.