Models of coupled dark matter to dark energy

TL;DR

The paper introduces a general, action-based framework for coupling dark matter to dark energy using the pull-back formalism for fluids, revealing three distinct coupling types (Type-1, Type-2, Type-3) with differing energy and momentum transfer properties. It derives the full field equations, translates them to cosmological backgrounds and linear perturbations, and analyzes concrete subcases by selecting specific scalar potentials and coupling functions. Through modified background evolutions and perturbation dynamics, the authors show Type-1 and Type-2 couplings imprint noticeable changes on the CMB and matter power spectra, while Type-3, being a momentum-transfer-only interaction, yields subtler effects. The work demonstrates that coupling in the dark sector can be systematically explored at the level of the action, enabling identification of pathologies and paving the way for model-independent tests of coupled dark energy with upcoming data.

Abstract

We present three distinct types of models of dark energy in the form of a scalar field which is explicitly coupled to dark matter. Our construction draws from the pull-back formalism for fluids and generalises the fluid action to involve couplings to the scalar field. We investigate the cosmology of each class of model both at the background and linearly perturbed level. We choose a potential for the scalar field and a specific coupling function for each class of models and we compute the Cosmic Microwave Background and matter power spectra.

Figures (10)

• Figure 1: The embedding of the three-dimensional (timeless) matter space ${\cal F}$ to fluid-element worldlines in space-time ${\cal M}$. The maps $h^I(t,x^i)$ map the same point at coordinates $X^I$ to a point $x^i$ in ${\cal M}$. The motion of particles in space-time is constructed by stacking all mappings for all times $t$.
• Figure 2: The cosmological evolution of the CDM energy density parameter $\Omega_c$ for the Type 1 sub case under consideration. The solid black (dashed red) line is for $\alpha_0=0$ (0.15).
• Figure 3: Comparison between the Type 1 model with coupling strength $\alpha_0 = 0.15$ (dashed red line) and the uncoupled $\alpha_0=0$ (black solid line) model. Top: CMB power spectra. Bottom: Fractional differences $\Delta C_\ell$.
• Figure 4: Comparison of the linear (total) matter power spectra at $z=0$, $P_0(k)$ between the Type 1 model with coupling strength $\alpha_0 = 0.15$ (dashed red line) and the uncoupled $\alpha_0=0$ (solid black line) model.
• Figure 5: The cosmological evolution of the CDM energy density parameter $\Omega_c$ for the Type 2 sub case under consideration. The solid black (dashed red) line is for $\beta_0=0$ (1/11).