A gauge-invariant approach to interactions in the dark sector

Abstract

We outline a gauge-invariant framework to calculate cosmological perturbations in dark energy models consisting of a scalar field interacting with dark matter via energy and momentum exchanges. Focusing on three well-known models of quintessence and three common types of dark-sector interactions, we calculate the matter and dark energy power spectra as well as the Integrated Sachs-Wolfe (ISW) effect in these models. We show how the presence of dark-sector interactions can produce a large-scale enhancement in the matter power spectrum and a boost in the low multipoles of the cosmic microwave background anisotropies. Nevertheless, we find these enhancements to be much more subtle than those found by previous authors who model dark energy using simple ansatz for the equation of state. We also address issues of instabilities and emphasise the importance of momentum exchanges in the dark sector.

Figures (9)

• Figure 1: Left: The equation of state $w_{\phi}(z)$ of dark energy for the cosmological constant (CC), Ratra-Peebles (RP), SUGRA and double exponential (DExp) models (see section \ref{['models']}). Right: The evolution of the density parameter $\Omega_x=\rho_x/\rho$ for the CC and DExp models. Apparently large deviations from $w_{\phi}=-1$ lead to subtle differences in $\Omega$ at late times.
• Figure 2: Left: If there is no interaction in the dark sector, the linear matter power spectra for all four 'best-fit' dark energy models are essentially indistinguishable. Right: the fractional percentage difference between the matter power spectra of the quintessence models and the cosmological constant. The best-fit models all exhibit sub-percent differences from the cosmological constant.
• Figure 3: The linear power spectra for dark energy for the three quintessence models with no interactions. Note the 'turnover' on very large scales close to the Hubble radius ($\sim 2\times10^{-4} \mathrm{Mpc}^{-1}$) indicating the typical size of dark energy perturbations.
• Figure 4: The percentage differences between $C_{\ell}^{\mathrm{ISW}}$ for the three quintessence models and the CC model. The contributions from quintessence are overwhelmed by cosmic variance, hence the models are observationally indistinguishable via the ISW effect.
• Figure 5: Evolution of the variable $x\propto\dot\phi$ in the decaying dark energy model using the SUGRA potential. $x$ passes through zero and becomes negative at $\ln a=-12.336$ causing an instability in the power spectra. This behaviour occurs for interaction strengths larger than $\sim10^{-70}m_{\hbox{\scriptsize{Pl}}}$.