On extended sign-changeable interactions in the dark sector

TL;DR

This work addresses sign-changeable interactions in the dark sector by extending prior proposals to decouple the sign flip from the deceleration parameter and dark-density ratios, while including a non-interacting baryonic component. It develops a flat FRW framework with two interacting dark fluids and a baryon, derives exact solutions for three interaction forms, and constrains them with $H(z)$ and SNIa data to examine the cosmological coincidence problem, age crisis, and early dark-energy behavior. The three models — $\mathcal{Q}_{1_{\alpha=0}}$, $\mathcal{Q}_{1_{A=0}}$, and $\mathcal{Q}_2$ — yield explicit evolutions for the dark-sector densities and observables, with $z_{acc}$ typically in the range $0.57$–$0.80$ and sign-change redshifts $z_{\mathcal{Q}}$ in $[0.48,1.19]$. Among them, $\mathcal{Q}_{1_{A=0}}$ provides the best balance of early-time dark-energy density, current matter content, and age-consistency, while maintaining a viable transition to acceleration and addressing the coincidence problem. These results demonstrate the viability of sign-changeable dark-sector couplings with a non-interacting baryon and offer concrete predictions for high-redshift evolution to discriminate models with future data.

Abstract

We extend the cosmological couplings proposed in Sun et al. and Wei, where they suggested interactions with change of signs along the cosmological evolution. Our extension liberates the changes of sign of the interaction from the deceleration parameter and from the relation of energy densities of the dark sector and considers the presence of non interactive matter. In three cases we obtain the general solutions and the results obtained in models fitted with Hubble's function and SNe Ia data, are analyzed regarding the problem of the cosmological coincidence, the problem of the crisis of the cosmological age and the magnitude of the energy density of dark energy at early universe. Also we graphically study the range of variation of, the actual dark matter density parameter, the effective equation of state of the dark energy and the redshift of transition to the accelerated regimen, generated by variations at order $1σ$ in the coupling parameters.

Figures (19)

• Figure 1: Evolution of the interaction $\mathcal{Q}_{1_{\alpha=0}} = \beta(\sigma-1+\frac{3}{2}\gamma)\rho_2$ (solid magenta curve) and corresponding deceleration parameter $q$ (dashed blue curve) for the best fit model with parameters $H_0=71.81~{\rm km~s^{-1}\,Mpc^{-1}}$ , $b_m=0.225$, $\gamma_1=\gamma_m=1$, $\gamma_2=0$, $\beta=-0.1$, $\sigma=0.6$ and $c_1= 0.05$. With a minimum $\chi^2_{dof}=0.816543$ per degree of freedom, this interactive cosmological model supports a coupling between CDM and cosmological constant $\Lambda$ in the presence of non interactive dust. $q$ tends to 0.5 at early times and to -1.07 in the distant future. Transition to the accelerated regime is checked at $z_{acc} = 0.8$, different of the redshift at which the interaction changes its sign $z_{\mathcal{Q}_{1_{\alpha=0}} } = 1.19$ from which energy is transferred from the DM to the DE.
• Figure 2: Energy densities and ratio of dark densities for the best fit model with the interaction $\mathcal{Q}_{1_{\alpha=0}}$. The contribution to the total energy density $\rho_{t}$ comes mainly from non interactive matter (mostly dark matter) until $z \sim 0.5$ and the ratio of dark fluids becomes 1 at $z^{\scriptsize{(\mathcal{Q}_{1_{\alpha=0}})}} = 0.443$. The dark matter fluid used to calculate this ratio, in this case, consists of dark matter that participates in the interaction but also by the part of the conserved fluid which cannot be considered baryonic as suggested by its density parameters. See Table \ref{['tab:tabla2']}.
• Figure 3: Evolution of the all effective equations of state involved in the best fit model for the interaction $\mathcal{Q}_{1_{\alpha=0}}$. At early times, $\omega_{t}$ and $\omega_{1eff}$, both tend to zero, showing the dominance of dust fluid. The dark energy fluid has an asymptotic value $\omega_{2eff}=-0.89$ at early times and crosses the PDL just before the present time where has the value $\omega_{2eff}=-1.04$.
• Figure 4: $1\sigma$ CL for the present matter content in the $\beta$ vs. $\sigma$ parameter space for the best fit model with the interaction $\mathcal{Q}_{1_{\alpha=0}}$. The restriction on the possible values of $\Omega_1$ plus $\Omega_m$ is obtained by overlapping the confidence region $1\sigma$ of plane $\beta$ vs. $\sigma$ (lilac region) on contours of the total density parameter of matter $\Omega_{M0}$. At $1\sigma$ CL, the present values of $\Omega_{M0}$ belong to the interval $[0,0.3]$ with the best fit value 0.23 (white dot).
• Figure 5: $1\sigma$ CL for the actual effective dark energy EoS in the $\beta$ vs. $\sigma$ parameter space for the best fit model with the interaction $\mathcal{Q}_{1_{\alpha=0}}$. The restriction on the possible values of $\omega_{2eff}$ is obtained by overlapping the confidence region $1\sigma$ of plane $\beta$ vs. $\sigma$ (blue region) on contours of the effective equation of state of the DE density (dashed curves). There it can be seen that at $1\sigma$ CL, the present values of $\omega_{2eff}$ belong to the interval $[-0.95,-1.45]$ with the best fit value -1.04 (white dot).