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Cluster abundances are oddly insensitive to canonical early dark energy. Early dark energy with sound speed equal to the speed of light cannot be distinguished from a quintessence model with the equivalent expansion history for $z<2$ but negligible early dark energy density, despite the different early growth rate. However, cold early dark energy, with a sound speed much smaller than the speed of light, can give a detectable signature. Combining cluster abundances with cosmic microwave background power spectra can determine the early dark energy fraction to 0.3 % and distinguish a true sound speed of 0.1 from 1 at 99 % confidence. We project constraints on early dark energy from the Euclid cluster survey, as well as the Dark Energy Survey, using both current and projected Planck CMB data, and assess the impact of cluster mass systematics. We also quantify the importance of dark energy perturbations, and the role of sound speed during a crossing of $w=-1$.
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We measure the clustering of DES Year 1 galaxies that are intended to be combined with weak lensing samples in order to produce precise cosmological constraints from the joint analysis of large-scale structure and lensing correlations. Two-point correlation functions are measured for a sample of $6.6 times 10^{5}$ luminous red galaxies selected using the textsc{redMaGiC} algorithm over an area of $1321$ square degrees, in the redshift range $0.15 < z < 0.9$, split into five tomographic redshift bins. The sample has a mean redshift uncertainty of $sigma_{z}/(1+z) = 0.017$. We quantify and correct spurious correlations induced by spatially variable survey properties, testing their impact on the clustering measurements and covariance. We demonstrate the samples robustness by testing for stellar contamination, for potential biases that could arise from the systematic correction, and for the consistency between the two-point auto- and cross-correlation functions. We show that the corrections we apply have a significant impact on the resultant measurement of cosmological parameters, but that the results are robust against arbitrary choices in the correction method. We find the linear galaxy bias in each redshift bin in a fiducial cosmology to be $b(z$=$0.24)=1.40 pm 0.08$, $b(z$=$0.38)=1.61 pm 0.05$, $b(z$=$0.53)=1.60 pm 0.04$ for galaxies with luminosities $L/L_*>$$0.5$, $b(z$=$0.68)=1.93 pm 0.05$ for $L/L_*>$$1$ and $b(z$=$0.83)=1.99 pm 0.07$ for $L/L_*$$>1.5$, broadly consistent with expectations for the redshift and luminosity dependence of the bias of red galaxies. We show these measurements to be consistent with the linear bias obtained from tangential shear measurements.
This document presents the results from the Distances subgroup of the Cosmic Frontier Community Planning Study (Snowmass 2013). We summarize the current state of the field as well as future prospects and challenges. In addition to the established probes using Type IA supernovae and baryon acoustic oscillations, we also consider prospective methods based on clusters, active galactic nuclei, gravitational wave sirens and strong lensing time delays.
Within the standard paradigm, dark energy is taken as a homogeneous fluid that drives the accelerated expansion of the universe and does not contribute to the mass of collapsed objects such as galaxies and galaxy clusters. The abundance of galaxy clusters -- measured through a variety of channels -- has been extensively used to constrain the normalization of the power spectrum: it is an important probe as it allows us to test if the standard $Lambda$CDM model can indeed accurately describe the evolution of structures across billions of years. It is then quite significant that the Planck satellite has detected, via the Sunyaev-Zeldovich effect, less clusters than expected according to the primary CMB anisotropies. One of the simplest generalizations that could reconcile these observations is to consider models in which dark energy is allowed to cluster, i.e., allowing its sound speed to vary. In this case, however, the standard methods to compute the abundance of galaxy clusters need to be adapted to account for the contributions of dark energy. In particular, we examine the case of clustering dark energy -- a dark energy fluid with negligible sound speed -- with a redshift-dependent equation of state. We carefully study how the halo mass function is modified in this scenario, highlighting corrections that have not been considered before in the literature. We address modifications in the growth function, collapse threshold, virialization densities and also changes in the comoving scale of collapse and mass function normalization. Our results show that clustering dark energy can impact halo abundances at the level of 10%--30%, depending on the halo mass, and that cluster counts are modified by about 30% at a redshift of unity.
We compare current and forecasted constraints on dynamical dark energy models from Type Ia supernovae and the cosmic microwave background using figures of merit based on the volume of the allowed dark energy parameter space. For a two-parameter dark energy equation of state that varies linearly with the scale factor, and assuming a flat universe, the area of the error ellipse can be reduced by a factor of ~10 relative to current constraints by future space-based supernova data and CMB measurements from the Planck satellite. If the dark energy equation of state is described by a more general basis of principal components, the expected improvement in volume-based figures of merit is much greater. While the forecasted precision for any single parameter is only a factor of 2-5 smaller than current uncertainties, the constraints on dark energy models bounded by -1<w<1 improve for approximately 6 independent dark energy parameters resulting in a reduction of the total allowed volume of principal component parameter space by a factor of ~100. Typical quintessence models can be adequately described by just 2-3 of these parameters even given the precision of future data, leading to a more modest but still significant improvement. In addition to advances in supernova and CMB data, percent-level measurement of absolute distance and/or the expansion rate is required to ensure that dark energy constraints remain robust to variations in spatial curvature.
The rate of structure formation in the Universe is different in homogeneous and clustered dark energy models. The degree of dark energy clustering depends on the magnitude of its effective sound speed $c^{2}_{rm eff}$ and for $c_{rm eff}=0$ dark energy clusters in a similar fashion to dark matter while for $c_{rm eff}=1$ it stays (approximately) homogeneous. In this paper we consider two distinct equations of state for the dark energy component, $w_{rm d}=const$ and $w_{rm d}=w_0+w_1left(frac{z}{1+z}right)$ with $c_{rm eff}$ as a free parameter and we try to constrain the dark energy effective sound speed using current available data including SnIa, Baryon Acoustic Oscillation, CMB shift parameter ({em Planck} and {em WMAP}), Hubble parameter, Big Bang Nucleosynthesis and the growth rate of structures $fsigma_{8}(z)$. At first we derive the most general form of the equations governing dark matter and dark energy clustering under the assumption that $c_{rm eff}=const$. Finally, performing an overall likelihood analysis we find that the likelihood function peaks at $c_{rm eff}=0$, however the dark energy sound speed is degenerate with respect to the cosmological parameters, namely $Omega_{rm m}$ and $w_{rm d}$.
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