Tracking quintessence by cosmic shear - Constraints from VIRMOS-Descart and CFHTLS and future prospects

Abstract

Dark energy can be investigated in two complementary ways, by considering either general parameterizations or physically well-defined models. Following the second route, we explore the constraints on quintessence models where the acceleration is driven by a slow-rolling scalar field. The analysis focuses on cosmic shear, combined with supernovae Ia and CMB data. Using a Boltzmann code including quintessence models and the computation of weak lensing observables, we determine several two-point shear statistics. The non-linear regime is described by two different mappings. The likelihood analysis is based on a grid method. The data include the "gold set" of supernovae Ia, the WMAP-1 year data and the VIRMOS-Descart and CFHTLS-deep and -wide data for weak lensing. This is the first analysis of high-energy motivated dark energy models that uses weak lensing data. We explore larger angular scales, using a synthetic realization of the complete CFHTLS-wide survey as well as next space-based missions surveys. Two classes of cosmological parameters are discussed: i) those accounting for quintessence affect mainly geometrical factors; ii) cosmological parameters specifying the primordial universe strongly depend on the description of the non-linear regime. This dependence is addressed using wide surveys, by discarding the smaller angular scales to reduce the dependence on the non-linear regime. Special care is payed to the comparison of these physical models with parameterizations of the equation of state. For a flat universe and a quintessence inverse power law potential with slope alpha, we obtain alpha < 1 and Omega_Q=0.75^{+0.03}_{-0.04} at 95% confidence level, whereas alpha=2^{+18}_{-2}, Omega_Q=0.74^{+0.03}_{-0.05} when including supergravity corrections.

Figures (13)

• Figure 1: Evolution of the equation of state $w$ and of the sound speed $c_s$ with the redshift for an inverse power law quintessence model with $\alpha=6$, including or not the supergravity correction. We recover, from high to low redshift, the kinetic, slow-rolling and tracking phases described in the text.
• Figure 2: Deviation of quintessence equation of state for Ratra-Peebles (solid) and SUGRA (dotted) models with $\alpha=6$ from the generalized parameterization, Eq. (\ref{['eq:para4']}), setting $z_\mathrm{pivot} = 0$ (thick) or $z_\mathrm{pivot} = 0.5$ (thin). Fitting the previous one up to $z\lesssim 0.3$, a deviation larger than 2% occurs at $z\simeq 1$ for Ratra-Peebles models while at $z\simeq 0.5$ for SUGRA models.
• Figure 3: Contour plots of the quintessence equation of state. We compare the equation of state of two quintessence models with the parameterization (\ref{['eq:genLinder']}) for two values of the pivot redshift: $z_\mathrm{pivot}=0$ (left) and $z_\mathrm{pivot}=0.5$ (right). Solid lines correspond to level contours for $w_\mathrm{pivot}$ while dotted lines correspond to level contours of $w_a$. We have chosen the spacing of all the contour lines to be $\Delta w=0.1$, except for the plots in the upper line, where $\Delta w_a=0.02$. The upper line corresponds to Ratra-Peebles models, Eq. (\ref{['eq:RP']}), while the lower line corresponds to SUGRA models, Eq. (\ref{['eq:SUGRA']}). Due to the exponential correction, $w_0$ is always smaller for SUGRA models because the potential is flatter and the field is rolling slower. Also, the value of $w_\mathrm{pivot}$ and $w_a$ are more sensitive to the choice of $z_\mathrm{pivot}$ for SUGRA models than for Ratra-Peebles models.
• Figure 4: Dynamics of the two quintessence models in the plane $(w,w')$. The shaded regions correspond to the constraints (\ref{['eq:wpw1']}) in light gray and (\ref{['eq:wpw2']}) in dark grey. We have considered a Ratra-Peebles (solid) and SUGRA (dash) models with $\alpha=6$ (thick/red) and $\alpha=11$ (thin/blue). Only in the tracking regime the models are compatible with Eq. (\ref{['eq:wpw2']}).
• Figure 5: Pipeline implemented for this work. Presently, we restrict to three free cosmological parameters, $\{\Omega_{\mathrm{Q} 0},\alpha, n_s \}$, keeping fixed the others. The lensing code manipulates both background's and perturbations quantities computed by the CMB code, using a sources distribution $n(z)$ depending on the used dataset. In particular, the source redshift parameter $z_\mathrm{s}$ is left to vary and marginalized over afterwards. Finally, the likelihood is computed using (either real or synthetic) cosmic shear and Sn Ia data, both separately and jointly. The temperature CMB data are used to fix the amplitude $A$ of the power spectrum at decoupling, and to put (conservative) constraints on the $(\Omega_{\mathrm{Q} 0},\alpha)$ parameters sub-space using the location of the first peak. In the CMB section of the pipeline, we indicate by $\delta_\mathrm{m}$ and $\delta_\mathrm{Q}$ energy density fluctuations in matter and quintessence components, respectively, while $\Phi(k,z)$ and $\Psi(k,z)$ are the scalar perturbations of the metric (Bardeen potentials) in Fourier space. In the lensing section, we denote by $k_\mathrm{NL}$ the scale at which the power spectrum becomes non-linear, $P(k_\mathrm{NL},z)\sim 1$. See § \ref{['sec3']} for details.