Growth of perturbations in dark matter coupled with quintessence

TL;DR

The paper studies linear perturbations in two string-inspired dark energy–dark matter coupling scenarios and shows that the coupling can dramatically enhance small-scale dark matter clustering during the transition to acceleration. Using the coupled-field equations and perturbation theory in synchronous gauge, it demonstrates that the effective gravitational coupling and nonadiabatic pressure perturbations drive rapid growth of dark-matter overdensities, producing a matter power spectrum and CMB signature incompatible with observations. The two models examined—the two-dark-matter-species model and the polynomial-coupling model—predict excessive structure growth in the late universe, effectively ruling them out without additional mechanisms. The work highlights how structure formation constraints provide powerful tests of coupled dark sector theories and clarifies the role of an effective small-scale sound speed in these frameworks.

Abstract

We consider the evolution of linear perturbations in models with a nonminimal coupling between dark matter and scalar field dark energy. Growth of matter inhomogeneities in two examples of such models proposed in the literature are investigated in detail. Both of these models are based on a low-energy limit of effective string theory action, and have been previously shown to naturally lead to late acceleration of the universe. However, we find that these models can be ruled out by taking properly into account the impact of the scalar field coupling on the formation of structure in the dark matter density. In particular, when the transition to acceleration in these models begins, the interaction with dark energy enchances the small scale clustering in dark matter much too strongly. We discuss the the role of an effective small scale sound speed in such models with a coupled dark sector.

Figures (8)

• Figure 1: Evolution of the fractional energy densities in model of section III. The solid line is $\Omega_\phi$, the dashed line $\Omega_X$, the dotted line is $\Omega_r$ and the dash-dotted line $(\Omega_c+\Omega_b)$.
• Figure 2: Left panel: Total equation of state $w$ (solid line) and the effective $w_X^{(eff)}$ (dashed line) for interacting CDM in the model of section III. Since $w<-1/3$ today, the universe accelerates. Right panel: Equation of state for the quintessence in the same model. Solid line is the formal $w_\phi$, and dashed line is the effective $w_\phi^{(eff)}$.
• Figure 3: Interacting DM overdensities in the model of section III. The slope $s$ of the curves in the logarithmic plot is $s \approx 2$, $1$, $11.2$ early in the radiation domination (when the scale is outside the horizon), during matter domination and during the transition to accelerating universe, respectively. The $k$-values from bottom to top are $k = 2.4 \cdot 10^{-6}$, $2.4 \cdot 10^{-5}$, $2.4 \cdot 10^{-4}$, $0.0024$, $0.024$ and $0.24$ Mpc$^{-1}$.
• Figure 4: Evolution of the fractional energy densities in the model of section IV. The solid line is $\Omega_\phi$, the dashed line $\Omega_X$. Dotted line is $\Omega_r$ and the dash-dotted line $\Omega_b$.
• Figure 5: Left panel: Total equation of state $w$ (solid line) and the effective $w_X^{(eff)}$ (dashed line) for interacting DM in the model of section IV. Since $w<-1/3$ today, the universe accelerates. Right panel: Equation of state for the quintessence for the same model. Solid line is the formal $w_\phi$, and dashed line is the effective $w_\phi^{(eff)}$.