Weak lensing refers to the statistically correlated image distortions of background galaxies due to the foreground matter distribution, also known as “cosmic shear”.  Weak lensing has the advantage of being sensitive to the clustering of matter, which can potentially allow us to differentiate between dark energy and modified gravity. However, if the clustering of matter is not accurately measured, the uncertainty is propagated into the measurement of dark energy parameters. If the systematic effects are properly modeled, a weak lensing survey can potentially allow us to differentiate between dark energy and modified gravity.

Weak lensing can be used to probe dark energy in two different ways: weak lensing tomography, or weak lensing cross-correlation cosmography (also known as “the geometric method”). Much of the effort has been focused on using the geometric weak lensing method to probe dark energy to minimize the sensitivity to the clustering of matter (which can be a source of systematic uncertainty).

Illustration of weak lensing of a galaxy. Image Credit: Jason Rhodes (JPL).

The basic idea of the geometric weak lensing method is to construct a map of the foreground galaxies, from which an estimated map of the foreground mass can be made. This foreground mass slice induces shear on all the galaxies in the background. The amplitude of the induced shear as a function of the background redshift is measured, from which a weighted sum of the ratios of angular diameter distances between the source slice and lens slice, and between the lens slice and observer is estimated. Note that this marks an important difference of the weak lensing method from the supernova and baryon acoustic oscillation methods: the weak lensing method gives correlated measurements of the cosmic expansion history H(z), in redshift bins, while the supernova and baryon acoustic oscillation methods can give uncorrelated measurements of H(z).

In the geometric weak lensing method, photometric redshifts are used to divide galaxies into redshift bins. The centroids of the photometric redshifts must be know to the accuracy of around 0.1% in order to avoid significant degradation of dark energy constraints. In addition to the uncertainty in the centroids of photometric redshift bins, there are other systematic uncertainties in the use of weak lensing as dark energy probe. These include point spread function (PSF) correction, bias in the selection of the galaxy sample, and the intrinsic distortion signal due to the intrinsic alignment of galaxies.

Euclid will carry out a ~15,000 square degree weak lensing survey, measuring the shapes of ~1.5 billion galaxies down to a magnitude of 24.5 over a wavelength range of 550-900nm, and obtain images of the same galaxies in three NIR filters (Y, J, and H). The NIR imaging of the galaxies will be combined with ground-based data to obtain precise and accurate photometric redshifts.