Probing the imprints of generalized interacting dark energy on the growth of perturbations

TL;DR

This paper investigates a generalized coupled quintessence framework where dark energy and dark matter exchange energy through conformal and disformal couplings. It derives the background dynamics in the Einstein frame, provides an analytic estimate for the CMB peak spacing using an effective dark-energy fluid, and studies ISW effects, growth history, and the small-scale perturbation limit. A key result is that disformal couplings produce distinctive intermediate-scale, time-dependent damped oscillations in the growth rate f_m, while conformal couplings mainly alter growth and CMB peak positions; mixed couplings combine these effects. The findings indicate that CMB peak spacing strongly constrains the conformal sector, whereas growth- and structure-based observables, including potential cross-correlations with galaxy surveys, offer complementary constraints on disformal and mixed couplings, highlighting pathways for future surveys to probe the dark sector interaction.

Abstract

We extensively study the evolution and distinct signatures of cosmological models, in which dark energy interacts directly with dark matter. We first focus on the imprints of these coupled models on the cosmic microwave background temperature power spectrum, in which we discuss the multipole peak separation together with the integrated Sachs-Wolfe effect. We also address the growth of matter perturbations, and disentangle the interacting dark energy models using the expansion history together with the growth history. We find that a disformal coupling between dark matter and dark energy induces intermediate-scales and time-dependent damped oscillatory features in the matter growth rate function, a unique characteristic of this coupling. Apart from the disformal coupling, we also consider conformally coupled models, together with models which simultaneously make use of both couplings.

Figures (13)

• Figure 1: These figures show the redshift evolution of $w^{\text{eff}}_c$, $w^{\text{eff}}_{\phi}-w_{\phi}$, and the deceleration parameter $q$, as defined in section \ref{['sec:Model']}. The couplings and scalar field potential are defined in Eq. (\ref{['coupling_choice']}). For the conformal case we set $\alpha=0.2$ (top left), for the disformal case we choose $\beta=0$, and $D_M=0.43\,\text{meV}^{-1}$ (top right), and for the mixed case we use $\alpha=0.2$, $\beta=0$, and $D_M=0.43\,\text{meV}^{-1}$ (bottom). In all cases we set $\lambda=1.15$, and depict the abscissa by a dashed line.
• Figure 2: This is a contour plot of the peak separation $\Delta l$, illustrating conformal models with $\lambda=0.5\,(\diamond),\,1.0\,(\square),\,1.7\,(\triangle)$ as a function of $\overline{w}^{\,\text{eff}}_{\text{DE}}$ and $\overline{\Omega}^{ls}_{\text{DE,eff}}$, with $a_{ls}^{-1}=1099.52$ and $\bar{c}_s=0.515$. From right to left, the consecutive points for every choice of $\lambda$ depict conformal models with $\alpha=0.2,\,0.15,\,0.1,\,0.05,\,0.03,\,0.01,\,0$. The $\Lambda$CDM model peak separation is shown by the dashed contour.
• Figure 3: This is a contour plot of the peak separation $\Delta l$, illustrating disformal models with $\lambda=0.5\,(\diamond),\,1.0\,(\square),\,1.7\,(\triangle)$ and $\beta=0$ as a function of $\overline{w}^{\,\text{eff}}_{\text{DE}}$ and $\overline{\Omega}^{ls}_{\text{DE,eff}}$, with $a_{ls}^{-1}=1099.38$ and $\bar{c}_s=0.516$. For each choice of $\lambda$, the consecutive points starting from the $\overline{\Omega}_{\text{DE,eff}}^{ls}$ --axis, depict disformal models with $D_M=0,\,0.2,\,0.3,\,0.4,\,0.45,\,0.5,\,0.55,\,0.6,$$\,0.7,\,0.8,\,1$$\text{meV}^{-1}$. The $\Lambda$CDM model peak separation is shown by the dashed contour.
• Figure 4: This is a contour plot of the peak separation $\Delta l$, illustrating mixed models with $\beta=0$ and $\lambda=0.5\,(\diamond),\,1.0\,(\square),\,1.7\,(\triangle)$ together with models characterised by $\beta=0.8$ and $\lambda=1.0$$(\ast)$ as a function of $\overline{w}^{\,\text{eff}}_{\text{DE}}$ and $\overline{\Omega}^{ls}_{\text{DE,eff}}$, with $a_{ls}^{-1}=1096.04$ and $\bar{c}_s=0.515$. From left to right (in a counter--clockwise direction for the points denoted by a $\triangle$), the consecutive points for every choice of $\lambda$ and $\beta$ depict mixed models with $\alpha=0,\,0.01,\,0.03,\,0.05,\,0.1,\,0.15,\,0.2,\,0.25$. For all models, we set $D_M V_0=1$. The $\Lambda$CDM model peak separation is shown by the dashed contour.
• Figure 5: These figures show the relative difference of $H_1$, $H_2$, and $H_3$ to the $\Lambda$CDM model for conformally coupled models with coupling and potential functions as defined in Eq. (\ref{['coupling_choice']}). The slope of the potential has been set to $\lambda=0.5$ (left) and to $\lambda=1.0$ (right).