We consider a phenomenological model for a coupling between the dark matter and dark energy fluids and investigate the sensitivity of a weak lensing measurement for constraining the size of this coupling term. Physically, the functional form of the coupling term in our model describes the decay of dark matter into dark energy. We present forecasts for tomographic measurements of the weak shear bispectrum for the DUNE experiment in a Fisher-matrix formalism, where we describe the nonlinearities in structure formation by hyper-extended perturbation theory. Physically, CDM decay tends to increase the growth rate of density perturbations due to higher values for the CDM density at early times, and amplifies the lensing signal because of stronger fluctuations in the gravitational potential. We focus on degeneracies between the dark energy equation of state properties and the CDM decay constant relevant for structure formation and weak lensing. A typical lower bound on the CDM decay time ~7.7/H_0 = 75.3 Gyr/h$ which could be provided by DUNE would imply that it would not possible to produce the dark energy content of the universe by CDM decay within the age of the Universe for a constant equation of state parameter of w close to -1.
The cosmic microwave background (CMB) bispectrum is a well-known probe of the non-Gaussianity of primordial perturbations. Just as the intervening large-scale structure modifies the CMB angular power spectrum through weak gravitational lensing, the CMB primary bispectrum generated at the last scattering surface is also modified by lensing. We discuss the lensing modification to the CMB bispectrum and show that lensing leads to an overall decrease in the amplitude of the primary bispectrum at multipoles of interest between 100 and 2000 through additional smoothing introduced by lensing. Since w…
Weak gravitational lensing of background galaxies offers an excellent opportunity to study the intervening distribution of matter. While much attention to date has focused on the two-point function of the cosmic shear, the three-point function, the {\it bispectrum}, also contains very useful cosmological information. Here, we compute three corrections to the bispectrum which are nominally of the same order as the leading term. We show that the corrections are small, so they can be ignored when analyzing present surveys. However, they will eventually have to be included for accurate parameter e…
We examine how lensing tomography with the bispectrum and power spectrum can constrain cosmological parameters and the equation of state of dark energy. Our analysis uses the full information at the two- and three-point level from angular scales of a few degrees to 5 arcminutes (50 < l < 3000), which will be probed by lensing surveys. We use all triangle configurations, cross-power spectra and bispectra constructed from up to three redshift bins with photometric redshifts, and relevant covariances in our analysis. We find that the parameter constraints from bispectrum tomography are comparable…
Weak gravitational lensing observations probe the spectrum and evolution of density fluctuations and the cosmological parameters which govern them. The non-linear evolution of large scale structure produces a non-Gaussian signal which is potentially observable in galaxy shear data. We study the three-point statistics of the convergence, specifically the bispectrum, using the dark matter halo approach which describes the density field in terms of correlations between and within dark matter halos. Our approach allows us to study the effect of the mass distribution in observed fields, in particul…
It is now well known that mode-coupling effects associated with certain secondary effects generate higher order correlations in cosmic microwave background (CMB) temperature anisotropies, beyond the two-point function. In order to extract the non-Gaussian signal at the three-point level, we suggest a two-point statistic in the form of an angular power spectrum involving correlations between squared temperature and temperature anisotropies. This power spectrum contains compressed information from the bispectrum and can be easily measured in data with the same techniques that have been considere…
We consider the CMB bispectrum signal induced by structure formation through the correlation between the Integrated Sachs-Wolfe and the weak lensing effect. We investigate how the bispectrum knowledge can improve our knowledge of the most important cosmological parameters, focusing on the dark energy ones. Preliminary results suggest a consistent improvement on the estimation of dark energy abundance and on dynamical properties of the equation of state.
By obtaining photometric redshift information, tomography allows us to cross-correlate galaxy ellipticities in different source redshift bins. The cross-correlation is non-vanishing because the different bins share much of the foreground mass distribution from which, over Gpc scales, the lensing signal is built. If the redshift bins are thick enough however, the cross-correlations are insensitive to contamination from the intrinsic alignments of galaxies since these fall off rapidly on scales larger than a few tens of Mpc. We forecast how lensing tomography using only the cross-power spectra c…
We study how CMB bispectrum, produced by weak gravitational lensing and structure formation, can constrain the redshift evolution of the dark energy equation of state independently on its present value. Analyzing the line of sight contribution to the angular CMB bispectrum, we find that the relevant redshift at which the structure formation contributes to the signal is $0.1 \lsim z \lsim 2$ for multipoles $1000 \gsim l \gsim 100$: just the epoch when the dark energy starts to dominate the cosmological expansion rate. For scenarios having the same equation of state at the present, this turns ou…
We report the weak lensing discovery, spectroscopic confirmation, and weak lensing tomography of a massive cluster of galaxies at $z=0.68$, demonstrating that shear selection of clusters works at redshifts high enough to be cosmologically interesting. The mass estimate from weak lensing, $11.1 +- 2.8 x 10^{14} (r/Mpc)$ solar masses within projected radius r, agrees with that derived from the spectroscopy ($σ_v = 980 km s^{-1}$), and with the position of an arc which is likely to be a strongly lensed background galaxy. The redshift estimate from weak lensing tomography is consistent with the sp…
Upcoming weak lensing surveys on wide fields will provide the opportunity to reconstruct the structure along the line of sight tomographically by employing photometric redshift information about the source distribution. We define power-spectrum statistics, including cross correlation between redshift bins, quantify the improvement that redshift information can make in cosmological parameter estimation, and discuss ways to optimize the redshift binning. We find that within the adiabatic cold dark matter class of models, crude tomography using two or three redshift bins is sufficient to extract …
A cross-correlation technique of lensing tomography is presented to measure the evolution of dark energy in the universe. The variation of the weak lensing shear with redshift around massive foreground objects like bright galaxies and clusters depends solely on ratios of angular diameter distances. Use of the massive foreground halos allow us to compare relatively high, linear shear values in the same part of the sky, thus largely eliminating the dominant source of systematic error in cosmological weak lensing measurements. The statistic we use does not rely on knowledge of the foreground mass…
We compute the cosmic microwave background bispectrum arising from the cross-correlation of primordial, lensing and Rees-Sciama signals. The amplitude of the bispectrum signal is sensitive to the matter density parameter, Omega_0, and the equation of state of the dark energy, which we parameterize by w_Q. We conclude that the dataset of the Atacama Cosmology Telescope, combined with MAP 2-year data or the Planck data set alone will allow us to break the degeneracy between Omega_0 and w_Q that arises from the analysis of CMB power spectrum. In particular a joint measurement of Omega_0 and w_Q w…
I discuss the use of cross correlations between galaxies with distance information and projected weak lensing dark matter maps to obtain a fully three dimensional dark matter map and power spectrum. On large scales l<100 one expects the galaxies to be biased, but not stochastic. I show that this allows a simultaneous solution of the full 3-D evolving galaxy bias and the dark matter power spectrum simultaneously. Within the photo-z information of the CFH lensing legacy survey, this allows a threefold reduction of statistical error, while a cross correlation with CLAR or other deep spectroscopic…
With increasingly large data sets, weak lensing measurements are able to measure cosmological parameters with ever greater precision. However this increased accuracy also places greater demands on the statistical tools used to extract the available information. To date, the majority of lensing analyses use the two point-statistics of the cosmic shear field. These can either be studied directly using the two-point correlation function, or in Fourier space, using the power spectrum. But analyzing weak lensing data inevitably involves the masking out of regions or example to remove bright stars f…
The current methods available to estimate gravitational shear from astronomical images of galaxies introduce systematic errors which can affect the accuracy of weak lensing cosmological constraints. We study the impact of KSB shape measurement bias on the cosmological interpretation of tomographic two-point weak lensing shear statistics. We use a set of realistic image simulations produced by the STEP collaboration to derive shape measurement bias as a function of redshift. We define biased two-point weak lensing statistics and perform a likelihood analysis for two fiducial surveys. We present…
We explore several strategies of eliminating (or nulling) the small-scale information in weak lensing convergence power spectrum measurements in order to protect against undesirable effects, for example the effects of baryonic cooling and pressure forces on the distribution of large-scale structures. We selectively throw out the small-scale information in the convergence power spectrum that is most sensitive to the unwanted bias, while trying to retain most of the sensitivity to cosmological parameters. The strategies are effective in the difficult but realistic situations when we are able to …
Lensing tomography with multi-color imaging surveys can probe dark energy and the cosmological power spectrum. However accurate photometric redshifts for tomography out to high redshift require imaging in five or more bands, which is expensive to carry out over thousands of square degrees. Since lensing makes coarse, statistical use of redshift information, we explore the prospects for tomography using limited color information from two or three band imaging. With an appropriate calibration sample, we find that it is feasible to create up to four redshift bins using imaging data in just the g,…
Two methods of constraining the properties of dark energy are weak lensing tomography and cluster counting. Uncertainties in mass calibration of clusters can be reduced by using the properties of halo clustering (the clustering of clusters). However, within a single survey, weak lensing and halo clustering probe the same density fluctuations. We explore the question of whether this information can be used twice -- once in weak lensing and then again in halo clustering to calibrate cluster masses -- or whether the combined dark energy constraints are weaker than the sum of the individual constr…
We consider the distribution of the non-Gaussian signal induced by weak lensing on the primary total intensity cosmic microwave background (CMB) anisotropies. Our study focuses on the three point statistics exploiting an harmonic analysis based on the CMB bispectrum. By considering the three multipoles as independent variables, we reveal a complex structure of peaks and valleys determined by the re-projection of the primordial acoustic oscillations through the lensing mechanism. We study the dependence of this system on the expansion rate at the epoch in which the weak lensing power injection …
Reconstructed from lensing tomography, the evolution of the dark matter density field in the well-understood linear regime can provide model-independent constraints on the growth function of structure and the evolution of the dark energy density. We examine this potential in the context that high-redshift cosmology has in the future been fixed by CMB measurements. We construct sharp tests for the existence of multiple dark matter components or a dark energy component that is not a cosmological constant. These functional constraints can be transformed into physically motivated model parameters.…
We perform a systematic analysis of the effects of photometric redshift uncertainties on weak lensing tomography. We describe the photo-z distribution with a bias and Gaussian scatter that are allowed to vary arbitrarily between intervals of dz = 0.1 in redshift.While the mere presence of bias and scatter does not substantially degrade dark energy information, uncertainties in both parameters do. For a fiducial next-generation survey each would need to be known to better than about 0.003-0.01 in redshift for each interval in order to lead to less than a factor of 1.5 increase in the dark energ…
Weak lensing surveys provide a powerful probe of dark energy through the measurement of the mass distribution of the local Universe. A number of ground-based and space-based surveys are being planned for this purpose. Here, we study the optimal strategy for these future surveys using the joint constraints on the equation of state parameter wn and its evolution wa as a figure of merit by considering power spectrum tomography. For this purpose, we first consider an `ideal' survey which is both wide and deep and exempt from systematics. We find that such a survey has great potential for dark ener…
During the past few years, secure detections of cosmic shear have been obtained, manifest in the correlation of the observed ellipticities of galaxies. Constraints have already been placed on cosmological parameters, such as the normalisation of the matter power spectrum sigma_8. One possible systematic contaminant of the lensing correlation signal arises from intrinsic galaxy alignment, which is still poorly constrained. Unlike lensing, intrinsic correlations only pertain to galaxies with small physical separations, the correlation length being a few Mpc. We present a new method that harnesse…
We study in detail the photometric redshift requirements needed for tomographic weak gravitational lensing in order to measure accurately the Dark Energy equation of state. In particular, we examine how ground-based photometry (u,g,r,i,z,y) can be complemented by space-based near-infrared (IR) photometry (J,H), e.g. on board the planned DUNE satellite. Using realistic photometric redshift simulations and an artificial neural network photo-z method we evaluate the Figure of Merit for the Dark Energy parameters $(w_0, w_a)$. We consider a DUNE-like broad optical filter supplemented with ground-b…
Brightness-temperature fluctuations in the redshifted 21-cm background from the cosmic dark ages are generated by irregularities in the gas-density distribution and can then be used to determine the statistical properties of density fluctuations in the early Universe. We first derive the most general expansion of brightness-temperature fluctuations up to second order in terms of all the possible sources of spatial fluctuations. We then focus on the three-point statistics and compute the angular bispectrum of brightness-temperature fluctuations generated prior to the epoch of hydrogen reionizat…
As pointed out in previous studies, the measurement of the skewness of the convergence field $κ$ will be useful in breaking the degeneracy among the cosmological parameters constrained from weak lensing observations. The combination of shot noise and finite survey volume implies that such a measurement is likely to be done in a range of intermediate scales ($0.5'$ to 20') where neither perturbation theory nor the hierarchical ansatz apply. Here we explore the behavior of the skewness of $κ$ at these intermediate scales, based on results for the non-linear evolution of the mass bispectrum. We c…
Surveys of weak gravitational lensing of distant galaxies will be one of the key cosmological probes in the future. We study the ability of such surveys to constrain neutrino masses and the equation of state parameter of the dark energy, focussing on how tomographic information can improve the sensitivity to these parameters. We also provide a detailed discussion of systematic effects pertinent to weak lensing surveys, and the possible degradation of sensitivity to cosmological parameters due to these effects. For future probes such as the Large Synoptic Survey Telescope survey, we find that, …
We study the potential of weak lensing surveys to detect clusters of galaxies, using a fast Particle Mesh cosmological N-body simulation algorithm specifically tailored to investigate the statistics of these mass-selected clusters. In particular, we explore the degree to which the radial positions of galaxy clusters can be determined tomographically, by using photometric redshifts of background source galaxies. We quantify the errors in the tomographic redshifts, and study their dependence on mass, redshift, detection significance, and filtering scheme. A Tomographic Matched Filtering (TMF) sc…
The weak gravitational lensing of distant galaxies by large-scale structure is expected to become a powerful probe of dark energy. By measuring the ellipticities of large numbers of background galaxies, the subtle gravitational distortion called "cosmic shear" can be measured and used to constrain dark energy parameters. The observed galaxy ellipticities, however, are induced not by shear but by reduced shear, which also accounts for slight magnifications of the images. This distinction is negligible for present weak lensing surveys, but it will become more important as we improve our ability …
We explore the effect of substructure in dark matter halos on the power spectrum and bispectrum of matter fluctuations and weak lensing shear. By experimenting with substructure in a cosmological N = 512^3 simulation, we find that when a larger fraction of the host halo mass is in subhalos, the resulting power spectrum has less power at 1 < k < 100 h Mpc^{-1} and more power at k > 100 h Mpc^{-1}. We explain this effect using an analytic halo model including subhalos, which shows that the 1 < k < 100 h Mpc^{-1} regime depends sensitively on the radial distribution of subhalo centers while the i…
We study future constraints on dark energy parameters determined from several combinations of CMB experiments, supernova data, and weak lensing surveys with and without tomography. In this analysis, we look in particular for combinations that will bring the uncertainties to a level of precision tight enough (a few percent) to answer decisively some of the dark energy questions. We probe the dark energy using two variants of its equation of state, and its energy density.We consider a set of 13 cosmological and systematic parameters, and assume reasonable priors on the lensing and supernova syst…
We consider the influence of the dark energy dynamics at the onset of cosmic acceleration on the Cosmic Microwave Background (CMB) bispectrum, through the weak lensing effect induced by structure formation. We study the line of sight behavior of the contribution to the bispectrum signal at a given angular multipole $l$: we show that it is non-zero in a narrow interval centered at a redshift $z$ satisfying the relation $l/r(z)\simeq k_{NL}(z)$, where the wavenumber corresponds to the scale entering the non-linear phase, and $r$ is the cosmological comoving distance. The relevant redshift interv…
