Coupled Quintessence

TL;DR

The paper investigates a coupled quintessence model with an exponential potential and linear coupling to matter, which is mathematically equivalent to Brans-Dicke-type theories. It identifies a novel $\phi$MDE phase during the matter era, through which perturbation growth is suppressed and the CMB and acoustic peaks are altered. By fitting to CMB and sigma8 data, the work constrains the coupling to $|beta| ≤ 0.1$ and discusses implications for Brans-Dicke models via the beta-mu mapping. Overall, the study highlights distinctive observational signatures that could test coupled quintessence with future high-precision cosmological data.

Abstract

A new component of the cosmic medium, a light scalar field or ''quintessence '', has been proposed recently to explain cosmic acceleration with a dynamical cosmological constant. Such a field is expected to be coupled explicitely to ordinary matter, unless some unknown symmetry prevents it. I investigate the cosmological consequences of such a coupled quintessence (CQ) model, assuming an exponential potential and a linear coupling. This model is conformally equivalent to Brans-Dicke Lagrangians with power-law potential. I evaluate the density perturbations on the cosmic microwave background and on the galaxy distribution at the present and derive bounds on the coupling constant from the comparison with observational data. A novel feature of CQ is that during the matter dominated era the scalar field has a finite and almost constant energy density. This epoch, denoted as $φ$MDE, is responsible of several differences with respect to uncoupled quintessence: the multipole spectrum of the microwave background is tilted at large angles, the acoustic peaks are shifted, their amplitude is changed, and the present 8Mpc$/h$ density variance is diminished. The present data constrain the dimensionless coupling constant to $|β|\leq 0.1$.

Figures (9)

• Figure 1: The figure shows the parameter space of the model. Each region is labelled by the critical point that is stable in that region. The shaded area indicates the values for which the attractor is accelerated.
• Figure 2: CQ phase space for values that lie in the $a$ region, $\mu =0.1$ and $\beta$ as indicated. The attractor $a$ is the same as in the uncoupled model, but for $\beta \neq 0$ there is a saddle for a non-zero value of the scalar field density. The phase spaces for the values of $\beta$ investigated in this paper are qualitatively similar to the $\beta =0.5$ case. The trajectory that falls almost vertically from top is similar to the background solution effectively employed.
• Figure 3: Behavior of $\Omega _{M}$ (dotted line), $\Omega _{R}$ (dashed line) and $\Omega _{\phi }$ (thick line) as a function of $\log (a)$ for $\mu =0.1$ and $\beta$ as indicated. Notice that for CQ there is the transient regime $\phi$MDE in which both the matter and the scalar field energy density are non-vanishing. Notice also that in this case, and for all values of $\beta \neq 0$, the matter-radiation equivalence occurs earlier than in the uncoupled model. For the small values of $\beta$ used for the perturbation calculations, however, this is a small effect.
• Figure 4: Phase space of CQ for values that lie in the $b_{M}$ region. There is a saddle $c_{RM}$ at $\left( x,y,z\right) \simeq \left( 0.12,0,0.95\right)$ that attracts the trajectory that falls from top, similar to the one adopted in the perturbation calculation.
• Figure 5: Behavior of $\Omega _{M}$ (dotted line), $\Omega _{R}$ (dashed line) and $\Omega _{\phi }$ (thick line) as a function of $\log (a)$ for the same parameters as in Fig. 4 (label $w_{\text{eff}}=0.4$) and for $\beta =\mu =2.37$ (label $w_{\text{eff}}=0.5$). Notice the transient epoch in which radiation and field share the total energy density (saddle $c_{RM}$).