Academic literature on the topic 'Tomographic Weak Lensing'

ABSTRACT We introduce the skew-spectrum statistic for weak lensing convergence κ maps and test it against state-of-the-art high-resolution all-sky numerical simulations. We perform the analysis as a function of source redshift and smoothing angular scale for individual tomographic bins. We also analyse the cross-correlation between different tomographic bins. We compare the numerical results to fitting-functions used to model the bispectrum of the underlying density field as a function of redshift and scale. We derive a closed form expression for the skew-spectrum for gravity-induced secondary non-Gaussianity. We also compute the skew-spectrum for the projected κ inferred from cosmic microwave background (CMB) studies. As opposed to the low redshift case, we find the post-Born corrections to be important in the modelling of the skew-spectrum for such studies. We show how the presence of a mask and noise can be incorporated in the estimation of a skew-spectrum.

ABSTRACT The subject of this paper is optimization of weak lensing tomography: we carry out numerical minimization of a measure of total statistical error as a function of the redshifts of the tomographic bin edges by means of a Nelder–Mead algorithm in order to optimize the sensitivity of weak lensing with respect to different optimization targets. Working under the assumption of a Gaussian likelihood for the parameters of a w0wa CDM (cold dark matter) model and using euclid’s conservative survey specifications, we compare an equipopulated, equidistant, and optimized bin setting and find that in general the equipopulated setting is very close to the optimal one, while an equidistant setting is far from optimal and also suffers from the ad hoc choice of a maximum redshift. More importantly, we find that nearly saturated information content can be gained using already few tomographic bins. This is crucial for photometric redshift surveys with large redshift errors. We consider a large range of targets for the optimization process that can be computed from the parameter covariance (or equivalently, from the Fisher matrix), extend these studies to information entropy measures such as the Kullback–Leibler divergence and conclude that in many cases equipopulated binning yields results close to the optimum, which we support by analytical arguments.

Abstract We introduce the response function approach to model the weak lensing statistics in the context of separate universe formalism. Numerical results for the RFs are presented for various semi-analytical models that includes perturbative modelling and variants of halo models. These results extend the recent studies of the Integrated Bispectrum and Trispectrum to arbitrary order. We find that due to the line-of-sight projection effects, the expressions for RFs are not identical to the squeezed correlation functions of the same order. We compute the RFs in three-dimensions using the spherical Fourier-Bessel formalism which provides a natural framework for incorporating photometric redshifts, and relate these expressions to tomographic and projected statistics. We generalise the concept of k-cut power spectrum to k-cut response functions. In addition to response functions, we also define their counterparts in real space, since they are easier to estimate from surveys with low sky-coverage and non-trivial survey boundaries.

ABSTRACT Determining the distribution of redshifts of galaxies observed by wide-field photometric experiments like the Dark Energy Survey (DES) is an essential component to mapping the matter density field with gravitational lensing. In this work we describe the methods used to assign individual weak lensing source galaxies from the DES Year 3 Weak Lensing Source Catalogue to four tomographic bins and to estimate the redshift distributions in these bins. As the first application of these methods to data, we validate that the assumptions made apply to the DES Y3 weak lensing source galaxies and develop a full treatment of systematic uncertainties. Our method consists of combining information from three independent likelihood functions: self-organizing map p(z) (sompz), a method for constraining redshifts from galaxy photometry; clustering redshifts (WZ), constraints on redshifts from cross-correlations of galaxy density functions; and shear ratios (SRs), which provide constraints on redshifts from the ratios of the galaxy-shear correlation functions at small scales. Finally, we describe how these independent probes are combined to yield an ensemble of redshift distributions encapsulating our full uncertainty. We calibrate redshifts with combined effective uncertainties of σ〈z〉 ∼ 0.01 on the mean redshift in each tomographic bin.

ABSTRACT We study the morphology of convergence maps by perturbatively reconstructing their Minkowski functionals (MFs). We present a systematic study using a set of three generalized skew spectra as a function of source redshift and smoothing angular scale. These spectra denote the leading-order corrections to the Gaussian MFs in the quasi-linear regime. They can also be used as independent statistics to probe the bispectrum. Using an approach based on pseudo-Sℓs, we show how these spectra will allow the reconstruction of MFs in the presence of an arbitrary mask and inhomogeneous noise in an unbiased way. Our theoretical predictions are based on a recently introduced fitting function to the bispectrum. We compare our results against state-of-the-art numerical simulations and find an excellent agreement. The reconstruction can be carried out in a controlled manner as a function of angular harmonics ℓ and source redshift zs, which allows for a greater handle on any possible sources of non-Gaussianity. Our method has the advantage of estimating the topology of convergence maps directly using shear data. We also study weak lensing convergence maps inferred from cosmic microwave background observations, and we find that, though less significant at low redshift, the post-Born corrections play an important role in any modelling of the non-Gaussianity of convergence maps at higher redshift. We also study the cross-correlations of estimates from different tomographic bins.

ABSTRACT Intrinsic alignments of galaxies are recognized as one of the most important systematic in weak lensing surveys on small angular scales. In this paper, we investigate ellipticity correlation functions that are measured separately on elliptical and spiral galaxies, for which we assume the generic alignment mechanisms based on tidal shearing and tidal torquing, respectively. Including morphological information allows to find linear combinations of measured ellipticity correlation functions that suppress the gravitational lensing signal completely or which show a strongly boosted gravitational lensing signal relative to intrinsic alignments. Specifically, we find that (i) intrinsic alignment spectra can be measured in a model-independent way at a significance of Σ ≃ 60 with a wide-angle tomographic survey such as Euclid’s, (ii) the underlying intrinsic alignment model parameters can be determined at per cent-level precision, (iii) this measurement is not impeded by misclassifying galaxies and assuming a wrong alignment model, (iv) parameter estimation from a cleaned weak lensing spectrum is possible with almost no bias, and (v) the misclassification would not strongly impact parameter estimation from the boosted weak lensing spectrum.

This thesis is devoted to the study of phaenomenology within the quest for Dark Energy (DE) nature. Nowadays, thanks to the accuracy with which cosmological parameters have been constrained, Cosmology has really turned into a high precision science. In spite of their accuracy, however, data are still far from really constraining DE nature, so that this keeps perhaps the main puzzle in today’s cosmology. Constraints on DE, until now, came from measurements of the Cosmic Microwave Background (CMB), from the Hubble diagram of SupernovæIa, from deep galaxy samples and from a few other observables, as Lyα clouds, galaxy cluster distribution, etc. Such measures will be certainly extended and improved in the next decade(s) leading to more stringent constraints. Even more effective are however expected to be future weak lensing (WL) data, namely in combination with the above classical observables, marking a real turning point to Cosmology. This thesis wants to add a brick to the construction of this wide building, trying to study the impact of tomographic WL measurements on constraining dynamical and/or coupled DE models. Within this context, it will be outlined how massive neutrinos, added to the total cosmological energy balance, allow the consistency with present data of a higher DM–DE coupling. This last issue outlines how tomographic WL observables will allow to shed new light over a problem as neutrino masses, so enriching the patterns through which large scale data influence microphysical issues.

Weak gravitational lensing is a powerful astronomical tool for constraining cosmological parameters that is entering its prime. Lensing occurs because gravitational fields deflect light rays and measuring this deflection through a statistic known as cosmic shear allows us to directly measure the properties of dark matter and dark energy on large scales. In principle, gravitational lensing is a clean probe of the cosmology of the Universe, as it depends on gravity alone and not on incomplete astrophysical models or approximations. In practice, however, there are several factors that limit the accuracy and precision of lensing measurements. These include accurate measurement of galaxy shapes, correctly accounting for distortions to galaxy images due to the point spread function of the telescope, the presence of intrinsic alignments (IAs) of galaxy shapes due to physical processes, and inaccuracies in commonly-used galaxy photometric redshift information. These effects may all introduce systematic errors in lensing measurements which must be carefully accounted for to ensure that cosmological constraints from lensing are unbiased and as precise as possible. The Canada-France-Hawaii-Telescope Lensing Survey (CFHTLenS) is the largest weak lensing survey completed to date, covering 154 square degrees of the sky in 5 optical bands, with photometric redshift information for every survey galaxy. With lensing measurements from more galaxies than ever before, the statistical uncertainties on parameter estimates will be the lowest ever achieved from weak lensing. If left unaccounted for, sources of systematic error would dominate over the statistical uncertainty, potentially biasing parameter estimates catastrophically. A technique known as tomography in which galaxies are sorted into bins based on their redshift can help constrain cosmological parameters more precisely. This is because utilising the redshifts of survey galaxies retains cosmological information that would otherwise be lost, such as the behaviour of dark energy and the growth of structure over time. Tomography, however, increases the demand for systematics-free galaxy catalogues as the technique is strongly sensitive to the IA signal and photometric redshift errors. Therefore, future lensing analyses will require a more sophisticated treatment of these effects to extract maximal information from the lensing signal. A thorough understanding of the error on lensing measurements is necessary in order to produce meaningful cosmological constraints. One of the key features of cosmic shear is that it is highly correlated over di erent angular scales, meaning that error estimates must take into account the covariance of the data over different angular scales, and in the case of tomography, between different redshift bins. The behaviour and size of the (inverse) covariance matrix is one of the limiting factors in such a cosmological likelihood analysis, so constructing an accurate, unbiased estimate of the covariance matrix inverse is essential to cosmic shear analysis. This thesis presents work to optimise tomographic weak lensing analysis and achieve the tightest parameter constraints possible for a CFHTLenS-like survey. N-body simulations and Gaussian shear fields incorporating an IA model (known as the `non-linear alignment' model) with a free parameter are used to estimate fully tomographic covariance matrices of cosmic shear for CFHTLenS. We simultaneously incorporate for the first time the error contribution expected from the non-linear alignment model for IAs and realistic photometric redshift uncertainties as measured from the CFHTLenS. We find that non-Gaussian simulations that incorporate nonlinearity on small scales are needed to ensure the covariance is not underestimated, and that the covariance matrix is shot-noise dominated for almost all tomographic correlations. The number of realisations of the simulations used to estimate the covariance places a hard limit on the maximum number of tomographic bins that one can use in an analysis. Given the available number of lines of sight generated from CFHTLenS-like simulations, we find that up to ~ 15 tomographic bins may be utilised in a likelihood analysis. The estimated tomographic covariance matrices are used in a least-squares likelihood analysis in order to find the combination of both angular and tomographic bins that gives the tightest constraints on some key cosmological parameters. We find that the optimum binning is somewhat degenerate, with around 6 tomographic and 8 angular bins being optimal, and limited by the available number of realisations of the simulations used to estimate the covariance. We also investigate the bias on best- t parameter estimates that occurs if IAs or photometric redshift errors are neglected. With our choice of IA model, the effect of neglecting IAs on the best- t cosmological parameters is not significant for a CFHTLenS-like survey, although this may not be true if the IA signal differs substantially from the model, or for future wide-field surveys with much smaller statistical uncertainties. Similarly, neglecting photometric redshift errors does not result in significant bias, although we apply similar caveats. Finally, we apply the results of this optimisation to the CFHTLenS cosmic shear data, performing a preliminary analysis of the shear correlation function to produce both 2D and optimal tomographic cosmological constraints. From 6-bin tomography, we constrain the matter density parameter Ωm = 0:419+0:123-0:090, the amplitude of the matter power spectrum σ8 = 0:623+0:101 -0:084 and the amplitude parameter of the non-linear alignment model, A = -1:161+1:163 -0:597. We perform this analysis to test the validity and limitations of the optimal binning on real data and find that 6-bin tomography improves parameter constraints considerably, albeit not as much as when performed on simulated data. This analysis represents an important step in the development of techniques to optimise the recovery of lensing information and hence cosmological constraints, while simultaneously accounting for potential sources of bias in shear analysis.