Dark Interactions and Cosmological Fine-Tuning

TL;DR

This work analyzes cosmologies with a dark-matter–dark-energy coupling of the form $Q=\lambda_x\rho_x+\lambda_c\rho_c$ within a duo-scaling framework to address the CP, DEICP, and SIC. By casting the dynamics in an autonomous system with fixed points $A=(X_A,Y_A,0,0)$ and $B=(X_B,Y_B,0,0)$, the authors identify conditions under which a saddle matter-dominated epoch is followed by a late-time accelerated attractor, and they quantify observational viability using SNIa and CMB shift parameter data. The paper introduces and employs measures $\zeta$ and $\Delta$ to assess DEICP and SIC, respectively, showing that couplings can dramatically improve these fine-tuning metrics but often at the expense of early-Universe observables or require negative past DE densities. Through a two-parameter toy model with analytic solutions, they illustrate potential reductions of CP and DEICP but also reveal sensitivity and practical challenges in achieving a realistic cosmology. Overall, while dark interactions can ease certain fine-tuning issues, fully solving the CP and DEICP within current observational constraints remains challenging, suggesting the need for additional scaling regimes or more intricate dynamics.

Abstract

Cosmological models involving an interaction between dark matter and dark energy have been proposed in order to solve the so-called coincidence problem. Different forms of coupling have been studied, but there have been claims that observational data seem to narrow (some of) them down to something annoyingly close to the $Λ$CDM model, thus greatly reducing their ability to deal with the problem in the first place. The smallness problem of the initial energy density of dark energy has also been a target of cosmological models in recent years. Making use of a moderately general coupling scheme, this paper aims to unite these different approaches and shed some light as to whether this class of models has any true perspective in suppressing the aforementioned issues that plague our current understanding of the universe, in a quantitative and unambiguous way.

Figures (9)

• Figure 1: Phase space trajectories together with the fixed points $A$, $B$, $C$ and $D$. From top to bottom we have $\,\lambda_x=\lambda_c=0\,$, $\,\lambda_x=\lambda_c=0.04\,$ and $\,\lambda_x=-\lambda_c=-0.15$, while $w_x=-1$ for all three plots. Note that some trajectories cross either the $\,X=0\,$ or $\,Y=0\,$ surfaces. The gray volume represents the region where the constraint (\ref{['eq:constraint-3d']}) is violated. The black dashed line corresponds to a trajectory that passes through the present (observational) energy densities, which in turn is depicted by the red star.
• Figure 2: Combined results from supernovae and shift parameter tests. The volumes represent $1$ and $2\sigma$ confidence levels, marginalized over $\Omega_{c0}$ with a gaussian prior based on WMAP3+SDSS results. The vertical contours are drawn at $\lambda_x = 0$ (white) and $\lambda_c=0$ (black). The yellow horizontal cut is made at $w_x = -1$ (see figure \ref{['fig:Contours-wx=-1']}), and further dashed cuts are made to aid the eye at $w_x = -1.5$, $w_x = -2.0$ and $w_x = -2.5$.
• Figure 3: $1$, $2$ and $3\sigma$ confidence level contours for $w_x$ fixed at $-1$. The brown dashed line shows the particular case of $\,\lambda_x~=~\lambda_c\,$, as considered in Chimento03, and the yellow dot stands for the $\Lambda$CDM case. The gray area on top is the region for which the system enters the "catastrophical abyss" characterized by the fixed point $F$, which in practice means that $\,H(z^\ast) = 0\,$ for some $z^\ast < \,z_{\rm recombination}$.
• Figure 4: Marginalized $1$, $2$ and $3\sigma$ contours for each of the three different model parameters, and the one dimensional likelihoods. All priors were taken to be flat. The black vertical lines on the one dimensional plots and the yellow dots on the contour plots represent $w_x = -1$, $\lambda_c =0$ and $\lambda_x =0$ respectively. The brown dashed line on the bottom middle plot stands for the $\,\lambda_x = \lambda_c\,$ case.
• Figure 5: Intersection of the $1$ and $2\sigma$ contours with the regions of the parameter space that allow for a duo-scaling regime. Inside the green transparent region we have a $A_1-B_2$ type of scaling, whereas inside the gray opaque checkered region the scaling is of the type $A_2-B_2$. The gray borders are drawn in such a way to guarantee that $X_{A_2} < 0.1$, so as not to compromise the formation of structures during the MDE. The 2D contours are the same as in figure \ref{['fig:Combined-3D']}.