Constraints on the coupled quintessence from cosmic microwave background anisotropy and matter power spectrum

TL;DR

The paper investigates how a non-minimally coupled quintessence field to CDM affects cosmological perturbations, aiming to constrain the coupling from CMB anisotropies and the matter power spectrum. It develops linear perturbation theory in the conformal Newtonian gauge with an energy-momentum transfer due to the coupling, derives the modified background and perturbation equations, and analyzes entropy perturbations and isocurvature modes. The main results show that the coupling shifts the CDM scaling $ ho_c = ho_c^{(0)} a^{-3+\xi}$, enhances the ISW effect, and alters the CMB peak structure and the turnover of $P(k)$; using COBE/WMAP constraints yields $n_c \leq 0.01$, with higher-precision future CMB data capable of tightening the bound. These findings provide a direct observational handle on quintessence-CDM coupling and inform dark energy model-building by tying late-time dynamics to early-universe perturbations.

Abstract

We discuss the evolution of linear perturbations in a quintessence model in which the scalar field is non-minimally coupled to cold dark matter. We consider the effects of this coupling on both cosmic microwave background temperature anisotropies and matter perturbations. Due to the modification of the scale of cold dark matter as $ρ_{c} = ρ_{c}^{(0)} a^{-3 + ξ}$, we can shift the turnover in the matter power spectrum even without changing the present energy densities of matter and radiation. This can be used to constrain the strength of the coupling. We find that the phenomenology of this model is consistent with current observations up to the coupling power $n_{c} \leq 0.01$ while adopting the current parameters measured by WMAP. Upcoming cosmic microwave background observations continuing to focus on resolving the higher peaks may put strong constraints on the strength of the coupling.

Figures (4)

• Figure 1: (a) Cosmological evolution of the equation of state parameter, $\omega_{\phi}$, and the energy density parameters, $\Omega_{i}$, of each component for $\lambda =5$ and $n_c=10^{-2}$. The evolution of the parameters is similar for other choices of $\lambda$. (b) Deviations of the scaling of the CDM energy density ($\xi$) from $a^{-3}$ for couplings with $n_{c} = 10^{-3}$ (dashed line) and $n_{c} = 10^{-2}$ (dash-dotted line).
• Figure 2: (a) Cosmological evolution of the adiabatic sound speed $c_{\phi}^2$ of the scalar field for different values of $n_{c} = 0$ (dotted line), $n_{c} = 10^{-3}$ (dashed line), and $n_{c} = 10^{-2}$ (dash-dotted line) when $\lambda =5$. (b) Behavior of the coupling modification, ${\cal B}_{\phi}$ as a function of the scale factor $a$ for different values of $n_c$.
• Figure 3: (a) CMB large-scale anisotropy power spectra of $\Lambda$CDM (solid line), minimally coupled $n_{c} = 0$ (dotted line), and non-minimally coupled $n_{c} = 10^{-3}, 10^{-2}$ (dashed, dash-dotted line respectively) quintessence models. (b) Same spectra for the entire scales.
• Figure 4: Matter power spectra for the models using the same parameters in Fig. \ref{['fig:cl']}.