A model with interaction of dark components and recent observational data

TL;DR

The paper investigates a cosmological model in which dark energy and dark matter exchange energy via a linear interaction $Q = 3\\lambda_m H \\rho_{dm} + 3\\lambda_d H \\rho_d$ within an (possibly nonflat) FLRW universe, considering both constant and dynamically evolving dark-energy equations of state $w_d$. For constant $w_d$, the authors derive an analytic solution for the total dark sector density $\\rho_T$ and obtain explicit expressions for $\\rho_{dm}$, $\\rho_d$, and $H(z)$; they then explore seven variants including CPL and linear parametrizations for variable $w_d$, focusing on singularities and data-driven viability. The analysis combines Union 2.1 SNe, $H(z)$, BAO, and Planck CMB priors to constrain model parameters, finding that constant-$w_d$ cases generally provide better fits and that the interaction often changes sign around $z \sim 0.4$, with energy transferring from CDM to DE at late times in most successful variants. When compared to noninteracting models (e.g., MCG, GCG, quadratic EoS, CPL, linear), certain noninteracting models can achieve comparable fits, while the best-performing interacting variant (Ansatz V) yields the lowest $\\min\\chi^2_{\\Sigma}$, though CMB-including fits may be challenged by singular behaviors; overall, the results underscore the viability of interacting dark sectors and highlight the relative strengths of competing models against the $\\Lambda$CDM benchmark.

Abstract

In the proposed model with interaction between dark energy and dark matter, we consider cosmological scenarios with different equations of state ($w_d$) for dark energy. For both constant and variable equation of state, we analyze solutions for dark energy and dark matter in seven variants of the model. We investigate exact analytic solutions for $w_d={}$ constant equation of state, and several variants of the model for variable $w_d$. These scenarios are tested with the current astronomical data from Type Ia Supernovae, baryon acoustic oscillations, Hubble parameter $H (z)$ and the cosmic microwave background radiation. Finally, we make a statistical comparison of our interacting model with $Λ$CDM as well as with some other well known non-interacting cosmological models.

Figures (5)

• Figure 1: For the model (\ref{['interaction1']}) with $w_d={}$const in the first and third rows of panels we present dependence of $\min\chi^2_\Sigma$ and $\min\chi^2_{tot}$ on $H_0$, $\Omega_{m0}$, $\Omega_k$ , $\lambda_m$, $\lambda_d$ and $w_d$ and also (in the panels below) the correspondent dependence for parameters of a minimum point. In the bottom panels the contour plots in the planes of 2 parameters are drawn at $1\sigma$, $2\sigma$ and $3\sigma$ confidence levels for $\chi^2_\Sigma$ (blue lines) and $\chi^2_{tot}$ (filled contours).
• Figure 2: Evolution of the scale factor $a(\tau)$ and densities $\Omega_m (\tau)$, $\Omega_d (\tau)$ for Ansatz I (\ref{['sol1-GA']}) is shown for the regular solution (top) with optimal parameters from Table \ref{['Estim']} and for the singular solution (bottom) with type (c1) singularity (\ref{['singul']}) (here $\lambda_m= -0.01$, other parameters are the same).
• Figure 3: For Ansatz I (\ref{['sol1-GA']}) and Ansatz II (\ref{['sol2-GA']}) with $\Omega_{k}=0$ we present one dimensional distributions of $\min\chi^2_\Sigma$ and $\min\chi^2_{tot}$. For Ansatz I we also draw two dimensional contour plots with notations from Fig. \ref{['F1']}: the blue lines for $\chi^2_\Sigma$, but the filled contours and red dashed lines for $\chi^2_{tot}$. We note that the circles and stars in the plots mark minimum points obtained respectively for $\chi^2_{tot}$ and $\chi^2_\Sigma$.
• Figure 4: For different variants of the model with optimal parameters from Table \ref{['Estim']} we show the plots for $D_L(z)$ (upper panel) describing the SNe data Suzuki2012, $H(z)$ functions with the data from Table \ref{['H-data']} (middle panel) and $Q(z)$ dependence (lower panel). We note that the same labels in the lower panel follow for the other two plots (i.e. upper and middle plots). We further note that the plots for different variants of the models both in upper and middle panel are almost indistingushable from each other while although in the lower panel the plots for $Q(z)/Q_0$ are distingushable for large reshift but for low redshifts they are also indistinguishable from each other.
• Figure 5: Dependence of $\min\chi^2_\Sigma$ on $H_0$, $\lambda_m$, $\lambda_d$, $\Omega_{m0}$, $w_{d0}$, $w_1$ for Ansatz IV (\ref{['Ans4']}) (red and magenta lines) and for Ansatz V (\ref{['Ans5']}) (green and aquamarine lines). The contour plots with $1\sigma$, $2\sigma$ and $3\sigma$ confidence levels in the bottom panels are shown for Ansatz IV in notations of Fig. \ref{['F1']} where the red lines stands for $\chi^2_\Sigma$ and the filled one for $\chi^2_{tot}$. The circles and stars in the contour plots mark minimum points obtained respectively for $\chi^2_{tot}$ and $\chi^2_\Sigma$.