Optimal cosmology from gravitational lensing: utilising the magnification and shear signals

Abstract

Gravitational lensing studies the distortions of a distant galaxy’s observed size, shape or flux due to the tidal bending of photons by matter between the source and observer. Such distortions can be used to infer knowledge on the mass distribution of the intervening matter, such as the dark matter halos in which clusters of individual galaxies may reside, or on cosmology through the statistics of the matter density of large scale structure and geometrical factors. In particular, gravitational lensing has the advantage that it is insensitive to the nature of the lensing matter. However, contamination of the signal by correlations between galaxy shape or size and local environment complicate a lensing analysis. Further, measurement of traditional lensing estimators is made more difficult by limitations on observations, in the form of atmospheric distortions or optical limits of the telescope itself. As a result, there has been a large effort within the lensing community to develop methods to either reduce or remove these contaminants, motivated largely by stringent science requirements for current and forthcoming surveys such as CFHTLenS, DES, LSST, HSC, Euclid and others. With the wealth of data from these wide-field surveys, it is more important than ever to understand the full range of independent probes of cosmology at our disposal. In particular, it is desirable to understand how each probe may be used, individually and in conjunction, to maximise the information of a lensing analysis and minimise or mitigate the systematics of each. With this in mind, I investigate the use of galaxy clustering measurements using photometric redshift information, including a contribution from flux magnification, as a probe of cosmology. I present cosmological forecasts when clustering data alone are used, and when clustering is combined with a cosmic shear analysis. I consider two types of clustering analysis: firstly, clustering with only redshift auto-correlations in tomographic redshift bins; secondly, clustering using all available redshift bin correlations. Finally, I consider how inferred cosmological parameters may be biased using each analysis when flux magnification is neglected. Results are presented for a Stage–III ground-based survey, and a Stage–IV space-based survey modelled with photometric redshift errors, and values for the slope of the luminosity function inferred from CFHTLenS catalogues. I find that combining clustering information with shear gives significant improvement on cosmological parameter constraints, with the largest improvement found when all redshift bins are included in the analysis. The addition of galaxy-galaxy lensing gives further improvement, with a full combined analysis improving constraints on dark energy parameters by a factor of > 3. The presence of flux magnification in a clustering analysis does not significantly affect the precision of cosmological constraints when combined with cosmic shear and galaxy-galaxy lensing. However if magnification is neglected, inferred cosmological parameter values are biased, with biases in some cosmological parameters found to be larger than statistical errors. We find that a combination of clustering, cosmic shear and galaxy-galaxy lensing can provide a significant reduction in statistical errors from each analysis individually, however care must be taken to measure and model flux magnification. Finally, I consider how measurements of galaxy size and flux may be used to constrain the dark matter profile of a foreground lens, such as galaxy- or galaxy-cluster-dark matter halos. I present a method of constructing probability distributions for halo profile free parameters using Bayes’ Theorem, provided the intrinsic size-magnitude distribution may be measured from data. I investigate the use of this method on mock clusters, with an aim of investigating the precision and accuracy of returned parameter constraints under certain conditions. As part of this analysis, I quantify the size and significance of inaccuracies in the dark matter reconstruction as a result of limitations in the data from which the sample and size-magnitude distribution is obtained. This method is applied to public data from the Space Telescope A901/902 Galaxy Evolution Survey (STAGES), and results are presented for the four STAGES clusters using measurements of source galaxy size and magnitude, and a combination of both. I find consistent results with existing shear measurements using measurements of galaxy magnitudes, but interesting inconsistent results when galaxy size measurements are used. The simplifying assumptions and limitations of the analysis are discussed, and extensions to the method presented.