Stationary dark energy with a baryon-dominated era: solving the coincidence problem with a linear coupling

TL;DR

This paper investigates cosmologies with a dark-energy scalar field exponentially coupled to dark matter, seeking a stationary accelerated attractor that naturally addresses the coincidence problem. The authors show that including a baryon-uncoupled requirement leads to a three-phase background (radiation, baryon, then dark-energy attractor) with a final stationary regime where dark matter and dark energy share a constant fraction, and the coupling strength is constrained by present densities and acceleration. However, linear perturbation analysis reveals rapid growth of density fluctuations in the final era and an overly strong ISW effect in the CMB, making the simple exponential-potential, linear-coupling model incompatible with nucleosynthesis and CMB data. Consequently, realistic stationary models likely require a time-dependent coupling or a more complex potential, guiding future work toward viable cosmologies within this framework.

Abstract

We show that all cosmological models with an accelerated stationary global attractor reduce asymptotically to a dark energy field with an exponential potential coupled linearly to a perfect fluid dark matter. In such models the abundance of the dark components reaches a stationary value and therefore the problem of their present coincidence is solved. The requirement of a vanishing coupling of the baryons in order to pass local gravity experiments induces the existence of an intermediate baryon-dominated era. We discuss in detail the properties of these models and show that to accomodate standard nucleosynthesis they cannot produce a microwave background consistent with observations. We conclude that, among stationary models, only a time-dependent coupling or equation of state might provide a realistic cosmology.

Figures (5)

• Figure 1: Parameter space. Each region is labelled by the point that is a global attractor there. Within the gray region the attractor is accelerated.
• Figure 2: Trend of the radiation (dashed green line), dark energy (thick black line), dark matter (thin red line) and baryon (dotted blue line) density fractions, for $\mu =8$ and $\beta =16$ (here and in Figs. 3 and 6 the abscissa is $\log _{10}a$.)
• Figure 3: The effective equation of state $w_{eff}=1+p_{tot}/\rho _{tot}$ for the same parameters as in the previous figure. Below the dashed line the expansion is accelerated.
• Figure 4: The evolution of a 10 Mpc/$h$ perturbation for $\beta =9.8$ and $\mu =7$. The baryon fluctuations $\delta _{b}$ are represented by the dotted (blue) line, the CDM $\delta _{c}$ by the continuous (red) line.
• Figure 5: CMB power spectra $C_{\ell }$ for two set of parameters: $\beta =4$,$\mu =3.5$ (top curve) and $\beta =3.3$,$\mu =4.2$ (bottom curve), compared with observational data from Boomerang net and COBE bon. The other input values for CMBFAST are $h=0.8,\Omega _{b}=0.04,\Omega _{c}=0.3,n=1$. The strong ISW effect at small multipoles is evident. Larger values of $\mu$, as needed from the nucleosynthesis constraint, enhance the problem.