Testing (modified) gravity with 3D and tomographic cosmic shear
  Cosmic shear is one of the primary probes to test gravity with current and
future surveys. There are two main techniques to analyse a cosmic shear survey;
a tomographic method, where correlations between the lensing signal in
different redshift bins are used to recover redshift information, and a 3D
approach, where the full redshift information is carried through the entire
analysis. Here we compare the two methods, by forecasting cosmological
constraints for future surveys like Euclid. We extend the 3D formalism for the
first time to theories beyond the standard model, belonging to the Horndeski
class. This includes the majority of universally coupled extensions to
$\Lambda$CDM with one scalar degree of freedom in addition to the metric, still
in agreement with current observations. Given a fixed background, the evolution
of linear perturbations in Horndeski gravity is described by a set of four
functions of time only. We model their time evolution assuming proportionality
to the dark energy density fraction and place Fisher matrix constraints on the
proportionality coefficients. We find that a 3D analysis can constrain
Horndeski theories better than a tomographic one, in particular with a decrease
in the errors of the order of 20$\%$. This paper shows for the first time a
quantitative comparison on an equal footing between Fisher matrix forecasts for
both a fully 3D and a tomographic analysis of cosmic shear surveys. The
increased sensitivity of the 3D formalism comes from its ability to retain
information on the source redshifts along the entire analysis.
