Constraining Dark Energy with Clusters: Complementarity with Other Probes

The Figure of Merit Science Working Group (FoMSWG) recently forecast the constraints on dark energy that will be achieved prior to the Joint Dark Energy Mission (JDEM) by ground-based experiments that exploit baryon acoustic oscillations, type Ia supernovae, and weak gravitational lensing. We show that cluster counts from on-going and near-future surveys should provide robust, complementary dark energy constraints. In particular, we find that optimally combined optical and Sunyaev-Zel'dovich effect cluster surveys should improve the Dark Energy Task Force (DETF) figure of merit for pre-JDEM projects by a factor of two even without prior knowledge of the nuisance parameters in the cluster mass-observable relation. Comparable improvements are achieved in the forecast precision of parameters specifying the principal component description of the dark energy equation of state parameter as well as in the growth index gamma. These results indicate that cluster counts can play an important complementary role in constraining dark energy and modified gravity even if the associated systematic errors are not strongly controlled.Comment: 6 pages, 3 figures, accepted to Phys. Rev. D. Discussion section adde

High-resolution temporal constraints on the dynamics of dark energy

We use the recent type Ia supernova, cosmic microwave background and large-scale structure data to shed light on the temporal evolution of the dark energy equation of state $w(z)$ out to redshift one. We constrain the most flexible parametrization of dark energy to date, and include the dark energy perturbations consistently throughout. Interpreting our results via the principal component analysis, we find no significant evidence for dynamical dark energy: the cosmological constant model is consistent with data everywhere between redshift zero and one at 95% C.L.Comment: 5 pages, 2 figures Version for PRD (Rapid Communications

Cosmology from supernova magnification maps

High-z Type Ia supernovae are expected to be gravitationally lensed by the foreground distribution of large-scale structure. The resulting magnification of supernovae is statistically measurable, and the angular correlation of the magnification pattern directly probes the integrated mass density along the line of sight. Measurements of cosmic magnification of supernovae therefore complements galaxy shear measurements in providing a direct measure of clustering of the dark matter. As the number of supernovae is typically much smaller than the number of sheared galaxies, the two-point correlation function of lensed Type Ia supernovae suffers from significantly increased shot noise. Neverthless, we find that the magnification map of a large sample of supernovae, such as that expected from next generation dedicated searches, will be easily measurable and provide an important cosmological tool. For example, a search over 20 sq. deg. over five years leading to a sample of ~ 10,000 supernovae would measure the angular power spectrum of cosmic magnification with a cumulative signal-to-noise ratio of ~20. This detection can be further improved once the supernova distance measurements are cross-correlated with measurements of the foreground galaxy distribution. The magnification maps made using supernovae can be used for important cross-checks with traditional lensing shear statistics obtained in the same fields, as well as help to control systematics. We discuss two applications of supernova magnification maps: the breaking of the mass-sheet degeneracy when estimating masses of shear-detected clusters, and constraining the second-order corrections to weak lensing observables.Comment: 4 pages, 2 figures, ApJL submitted; "Signal" discussed here is the extra covariance in astro-ph/050958

Problems with Pencils: Lensing Covariance of Supernova Distance Measurements

While luminosity distances from Type Ia supernovae (SNe) provide a powerful probe of cosmological parameters, the accuracy with which these distances can be measured is limited by cosmic magnification due to gravitational lensing by the intervening large-scale structure. Spatial clustering of foreground mass fluctuations leads to correlated errors in distance estimates from SNe. By including the full covariance matrix of supernova distance measurements, we show that a future survey covering more than a few square degrees on the sky, and assuming a total of ~2000 SNe, will be largely unaffected by covariance noise. ``Pencil beam'' surveys with small fields of view, however, will be prone to the lensing covariance, leading to potentially significant degradations in cosmological parameter estimates. For a survey with 30 arcmin mean separation between SNe, lensing covariance leads to a ~45% increase in the expected errors in dark energy parameters compared to fully neglecting lensing, and a ~20% increase compared to including just the lensing variance. Given that the lensing covariance is cosmology dependent and cannot be mapped out sufficiently accurately with direct weak lensing observations, surveys with small mean SN separation must incorporate the effects of lensing covariance, including its dependence on the cosmological parameters.Comment: 4 pages, 2 figures, PRL submitted; "Noise" discussed here is the "signal" in astro-ph/050957

Parameterization of Dark-Energy Properties: a Principal-Component Approach

Considerable work has been devoted to the question of how to best parameterize the properties of dark energy, in particular its equation of state w. We argue that, in the absence of a compelling model for dark energy, the parameterizations of functions about which we have no prior knowledge, such as w(z), should be determined by the data rather than by our ingrained beliefs or familiar series expansions. We find the complete basis of orthonormal eigenfunctions in which the principal components (weights of w(z)) that are determined most accurately are separated from those determined most poorly. Furthermore, we show that keeping a few of the best-measured modes can be an effective way of obtaining information about w(z).Comment: Unfeasibility of a truly model-independent reconstruction of w at z>1 illustrated. f(z) left out, and w(z) discussed in more detail. Matches the PRL versio

Interference of Fock states in a single measurement

We study analytically the structure of an arbitrary order correlation function for a pair of Fock states and prove without any approximations that in a single measurement of particle positions interference effects must occur as experimentally observed with Bose-Einstein condensates. We also show that the noise level present in the statistics is slightly lower than for a respective measurement of phase states.Comment: 4 page

Dynamical behavior of generic quintessence potentials: constraints on key dark energy observables

We perform a comprehensive study of a class of dark energy models - scalar field models where the effective potential can be described by a polynomial series - exploring their dynamical behavior using the method of flow equations that has previously been applied to inflationary models. Using supernova, baryon oscillation, CMB and Hubble constant data, and an implicit theoretical prior imposed by the scalar field dynamics, we find that the LCDM model provides an excellent fit to the data. Constraints on the generic scalar field potential parameters are presented, along with the reconstructed w(z) histories consistent with the data and the theoretical prior. We propose and pursue computationally feasible algorithms to obtain estimates of the principal components of the equation of state, as well as parameters w_0 and w_a. Further, we use the Monte Carlo Markov Chain machinery to simulate future data based on the Joint Dark Energy Mission, Planck and baryon acoustic oscillation surveys and find that the inverse area figure of merit improves nearly by an order of magnitude. Therefore, most scalar field models that are currently consistent with data can be potentially ruled out by future experiments. We also comment on the classification of dark energy models into "thawing'" and "freezing" in light of the more diverse evolution histories allowed by this general class of potentials.Comment: 22 pages and 12 figures, minor clarifications and a new Figure (#9) added in v3, matches the published PRD version. Chains and high-res figures are available at http://kicp.uchicago.edu/~dhuterer/DE_FLOWROLL/de_flowroll.htm

Gravitational Lensing as a Probe of Quintessence

A large number of cosmological studies now suggest that roughly two-thirds of the critical energy density of the Universe exists in a component with negative pressure. If the equation of state of such an energy component varies with time, it should in principle be possible to identify such a variation using cosmological probes over a wide range in redshift. Proper detection of any time variation, however, requires cosmological probes beyond the currently studied range in redshift of $\sim$ 0.1 to 1. We extend our analysis to gravitational lensing statistics at high redshift and suggest that a reliable sample of lensed sources, out to a redshift of $\sim$ 5, can be used to constrain the variation of the equation of state, provided that both the redshift distribution of lensed sources and the selection function involved with the lensed source discovery process are known. An exciting opportunity to catalog an adequate sample of lensed sources (quasars) to probe quintessence is now available with the ongoing Sloan Digital Sky Survey. Writing $w(z)\approx w_0 + z (dw/dz)_0$, we study the expected accuracy to which the equation of state today $w_0$ and its rate of change $(dw/dz)_0$ can simultaneously be constrained. Such a determination can rule out some missing-energy candidates, such as classes of quintessence models or a cosmological constant.Comment: Accepted for publication in ApJ Letters (4 pages, including 4 figures