The Growth of Structure in Interacting Dark Energy Models

TL;DR

The paper investigates whether an interaction between dark energy and dark matter leaves observable imprints on structure formation and weak lensing. It formulates a covariant perturbation framework with a linear dark-sector energy exchange governed by constants $\Gamma_c$ and $\Gamma_x$ and analyzes two limits: $\Gamma_x=0$ (DM$\rightarrow$DE) and $\Gamma_c=0$ (DE$\rightarrow$DM) using a CPL-like equation of state $w(a)=w_0+w_a(1-a)$. The main findings show that DM-to-DE transfer generally enhances growth and the weak-lensing signal due to higher past DM density, while DE-to-DM transfer can either enhance or suppress growth depending on the sign and magnitude of the coupling, with modifications to background evolution, Hubble friction, and an effective Newton constant $G_{\rm eff}$. These results provide a framework for constraining dark-sector interactions with growth and lensing observations, while acknowledging limitations to linear scales and the need for nonlinear and ISW analyses for complete observational viability.

Abstract

If dark energy interacts with dark matter, there is a change in the background evolution of the universe, since the dark matter density no longer evolves as a^{-3}. In addition, the non-gravitational interaction affects the growth of structure. In principle, these changes allow us to detect and constrain an interaction in the dark sector. Here we investigate the growth factor and the weak lensing signal for a new class of interacting dark energy models. In these models, the interaction generalises the simple cases where one dark fluid decays into the other. In order to calculate the effect on structure formation, we perform a careful analysis of the perturbed interaction and its effect on peculiar velocities. Assuming a normalization to today's values of dark matter density and overdensity, the signal of the interaction is an enhancement (suppression) of both the growth factor and the lensing power, when the energy transfer in the background is from dark matter to dark energy (dark energy to dark matter).

Figures (6)

• Figure 1: The densities of dark matter, $\Omega_c$ (thin lines), and dark energy, $\Omega_x$ (thick lines), in the interacting models (dashed-dotted lines), with $\Gamma_c=\pm 0.3H_0$, and non-interacting models (solid lines), normalized to today's values.
• Figure 2: Linear growth function $D_+=\delta_c/\delta_{c0}$, normalized to today's value, relative to its value in a pure-matter model ($D_+=a$). The interacting models (dashed-dotted lines), with $\Gamma_c=\pm 0.3H_0$, are shown in comparison to non-interacting models (solid lines).
• Figure 3: Weak lensing convergence power spectra $\ell(\ell+1) C_k(\ell) /2\pi$ in the interacting models (dashed-dotted lines), with $\Gamma_c=\pm 0.3H_0$, in comparison to non-interacting models (solid lines).
• Figure 4: The densities of dark matter, $\Omega_c$ (thin lines), and dark energy, $\Omega_x$ (thick lines), in the interacting models (dashed-dotted lines), with $\Gamma_x=+ 0.3H_0, -0.2H_0$, and non-interacting models (solid lines), normalized to today's values.
• Figure 5: Linear growth function $D_+=\delta_c/\delta_{c0}$, normalized to today's value, relative to its value in a pure-matter model ($D_+=a$). The interacting models (dashed-dotted lines), with $\Gamma_x=+ 0.3H_0, -0.2H_0$, are shown in comparison to non-interacting models (solid lines).