General Relativistic corrections in density-shear correlations

Abstract

We investigate the corrections which relativistic light-cone computations induce on the correlation of the tangential shear with galaxy number counts, also known as galaxy-galaxy lensing. The standard-approach to galaxy-galaxy lensing treats the number density of sources in a foreground bin as observable, whereas it is in reality unobservable due to the presence of relativistic corrections. We find that already in the redshift range covered by the DES first year data, these currently neglected relativistic terms lead to a systematic correction of up to 50% in the density-shear correlation function for the highest redshift bins. This correction is dominated by the the fact that a redshift bin of number counts does not only lens sources in a background bin, but is itself again lensed by all masses between the observer and the counted source population. Relativistic corrections are currently ignored in the standard galaxy-galaxy analyses, and the additional lensing of a counted source populations is only included in the error budget (via the covariance matrix). At increasingly higher redshifts and larger scales, these relativistic and lensing corrections become however increasingly more important, and we here argue that it is then more efficient, and also cleaner, to account for these corrections in the density-shear correlations.

version published in JCAP

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• The observable $E_g$ statistics
• Intrinsic and extrinsic correlations of galaxy shapes and sizes in weak lensing data
• A new observable for cosmic shear
• Impact of lensing magnification on the analysis of galaxy clustering in redshift space
• Testing General Relativity through the $E_G$ Statistic Using the Weyl Potential and Galaxy Velocities
• Cosmological Simulations of Number Counts