Cosmic Structure Growth and Dark Energy

TL;DR

This study investigates how dark energy with a time-varying equation of state, w(z), influences both the expansion history and the growth of cosmic structures. It combines analytic linear perturbation theory, including weak gravitational lensing, with a large-volume N-body simulation in a SUGRA-inspired quintessence model to quantify deviations from constant-w scenarios. The results show that a positive time derivative of the EOS, w'>0, yields significant differences in linear growth relative to ΛCDM and that weak lensing and SN+CMB data provide complementary constraints; nonlinear structure formation is well captured by the Jenkins universal mass function (J01) even for evolving w, enabling reliable predictions for cluster counts and lensing probes. Overall, the work lays a practical foundation for using both expansion history and growth history to constrain dark energy in upcoming large-scale structure surveys.

Abstract

Dark energy has a dramatic effect on the dynamics of the universe, causing the recently discovered acceleration of the expansion. The dynamics are also central to the behavior of the growth of large scale structure, offering the possibility that observations of structure formation provide a sensitive probe of the cosmology and dark energy characteristics. In particular, dark energy with a time varying equation of state can have an influence on structure formation stretching back well into the matter dominated epoch. We analyze this impact, first calculating the linear perturbation results, including those for weak gravitational lensing. These dynamical models possess definite observable differences from constant equation of state models. Then we present a large scale numerical simulation of structure formation, including the largest volume to date involving a time varying equation of state. We find the halo mass function is well described by the Jenkins et al. mass function formula. We also show how to interpret modifications of the Friedmann equation in terms of a time variable equation of state. The results presented here provide steps toward realistic computation of the effect of dark energy in cosmological probes involving large scale structure, such as cluster counts, Sunyaev-Zel'dovich effect, or weak gravitational lensing.

Figures (9)

• Figure 1: Growth factor of linear density perturbations plotted vs. scale factor $a=(1+z)^{-1}$ for six dark energy models with $\Omega_m=0.3$. Dotted curves show the effect of changing $\Omega_m$ by $\pm0.02$ for the cosmological constant case. Curves labeled $w_{eff}$ use the constant equation of state that gives the same distance to the last scattering surface as the bracketed models, and hence are degenerate with respect to the CMB.
• Figure 2: Same as Fig. \ref{['fig.lingrow']} but with the growth factors normalized by their values today. The present growth, related to the mass variance $\sigma_8$, is not yet precisely known, however.
• Figure 3: Logarithmic sensitivity of the growth factor to the cosmological parameters, perturbed around the cosmological constant model, as a function of redshift. Such a plot is useful in finding lower bounds to parameter estimation errors and in indicating degeneracies between parameters.
• Figure 4: Parameter estimations (68% confidence level) of the present equation of state and its time variation, marginalizing over the matter density $\Omega_m$ with a prior of $\sigma(\Omega_m)=0.03$. Dotted curves use the growth factor normalized to its value today. The growth factor alone (not shown) is poor in constraining the cosmological model, and offers little complementary leverage for the proposed SNAP supernova survey, and none in addition to SNAP plus the Planck CMB survey.
• Figure 5: Same as Fig. \ref{['fig.sngr']} but for dark energy following the SUGRA model, with present equation of state $w_0=-0.82$ and time variation $w_a=0.58$. In this case, information on the linear growth factor adds valuable constraints.