Dark Coupling and Gauge Invariance

TL;DR

This work develops a gauge-invariant perturbation framework for a dark energy–dark matter coupling proportional to the expansion rate, highlighting that the perturbation of the expansion rate $\delta H$ is required for consistency. It provides general gauge-invariant evolution equations for coupled fluids, then specializes to the covariant coupling $Q^{\nu}_{\rm dm}=\xi H \rho_{de} u^{\nu}_{\rm dm}$, including the expansion-rate perturbation ${\cal K}$ via the total-fluid expansion $\Theta_T$. Initial conditions are derived from the early-time eigenstructure, showing that adiabatic initial conditions for standard fluids automatically impose adiabaticity on dark energy. A full MCMC analysis with WMAP7 (plus external data) reveals that including ${\cal K}$ leaves parameter constraints effectively unchanged, while continuing to favor negative $\xi$ with a reduced present-day dark-matter density; the results support a covariant, gauge-consistent treatment of dark-sector interactions. Overall, the study confirms that the gauge-invariant approach yields robust cosmological constraints on dark coupling scenarios with Hubble-rate–driven energy exchange.

Abstract

We study a coupled dark energy-dark matter model in which the energy-momentum exchange is proportional to the Hubble expansion rate. The inclusion of its perturbation is required by gauge invariance. We derive the linear perturbation equations for the gauge invariant energy density contrast and velocity of the coupled fluids, and we determine the initial conditions. The latter turn out to be adiabatic for dark energy, when assuming adiabatic initial conditions for all the standard fluids. We perform a full Monte Carlo Markov Chain likelihood analysis of the model, using WMAP 7-year data.

Figures (1)

• Figure 1: Left (right) panel: 1$\sigma$ and 2$\sigma$ marginalized contours in the $\xi$--$\Omega_{dm} h^2$ ($\xi$--w) plane. The contours show the current constraints from WMAP7, HST, SN, $H(z)$ and LSS data taking into account the expansion rate perturbation ${\mathcal{K}}$.