Effects of dark sectors' mutual interaction on the growth of structures

TL;DR

This paper addresses the growth of dark-matter perturbations in a flat FRW universe in the presence of dark-energy perturbations and a mutual dark-sector coupling. It develops a general analytical formalism with gauge-invariant perturbation variables and derives second-order equations for the DM and DE density contrasts under a subhorizon approximation, equipped with a phenomenological coupling characterized by constants $\delta_1$ and $\delta_2$. A key finding is that the stability of structure growth strongly depends on the coupling form: coupling proportional to the DE density ($\delta_1=0$, $\delta_2>0$) can yield stable DM growth, whereas coupling proportional to the DM density ($\delta_1>0$, $\delta_2=0$) can cause rapid growth or blow-up. The authors show that the interaction can dominate over DE perturbations in shaping the DM growth function, with the growth index $\gamma_m=\left(\ln \Omega_m\right)^{-1}\ln\left(\frac{a}{\Delta_m}\frac{d\Delta_m}{da}\right)$ exhibiting observable shifts for modest coupling ($\delta_2\sim10^{-2}$). These results suggest that future measurements of the growth history could reveal or constrain dark-sector interactions beyond the standard $\\Lambda$CDM picture, motivating comparisons with expansion-history data and incorporation into large-scale structure simulations.

Abstract

We present a general formalism to study the growth of dark matter perturbations when dark energy perturbations and interactions between dark sectors are present. We show that dynamical stability of the growth of structure depends on the type of coupling between dark sectors. By taking the appropriate coupling to ensure the stable growth of structure, we observe that the effect of the dark sectors' interaction overwhelms that of dark energy perturbation on the growth function of dark matter perturbation. Due to the influence of the interaction, the growth index can differ from the value without interaction by an amount within the observational sensibility, which provides a possibility to disclose the interaction between dark sectors through future observations on the growth of large structure.

Figures (4)

• Figure 1: This figure shows the blow up of the DM perturbation when the coupling between dark sectors is proportional to the energy density of DM. $\Delta_R^2=2.41\times10^{-9}$ is the amplitude of curvature perturbations from WMAP five-year results and $\Delta_m$ is the density contrast of DM.
• Figure 2: These figures illustrate the behaviors of dark fluctuations in different cases when varying the effective sound speed,dark energy EoS,wave number,and coupling. The solid lines are for the DM perturbation while the dotted lines are for the DE perturbation. The solid lines in each panel are largely overlapped, except for that part circled in panel (d)
• Figure 3: These figures illustrate the behaviors of dark fluctuations in different cases when varying the effective sound speed,dark energy EoS,wave number,and coupling. The solid lines are for the DM perturbation while the dotted lines are for the DE perturbation.
• Figure 4: The growth index behavior when the interaction between DE and DM presents. Solid lines are for the result with DE perturbation, while dotted lines are for the result without DE perturbation.