Euclid : Optimising tomographic redshift binning for 3 × 2 pt power spectrum constraints on dark energy

The tomographic approach to analysing the 3 × 2 pt signal involves dividing the observed galaxy sample into a configuration of redshift bins. We present a simulation-based method to explore the optimum tomographic binning strategy for Euclid , focussing on the expected configuration of its first major data release (DR1). To do so, we 1) simulated a Euclid -like observation and generated mock shear catalogues from multiple realisations of the 3 × 2 pt fields on the sky; and 2) measured the 3 × 2 pt Pseudo- C ℓ power spectra for a given tomographic configuration and derived the constraints they place on the standard dark energy equation-of-state parameters, ( w 0 , w a ). For a simulation including Gaussian-distributed photometric redshift uncertainties and shape noise under a ΛCDM cosmology, we find that bins that are equipopulated with galaxies yield the best constraints on ( w 0 , w a ) for an analysis of the full 3 × 2 pt signal or the angular clustering component only. For the cosmic shear component, the optimum ( w 0 , w a ) constraints can be achieved by bins equally spaced in fiducial comoving distance. However, the advantage with respect to alternative binning choices is only of a few per cent in the size of the 1 σ ( w 0 , w a ) contour and we conclude that the cosmic shear is relatively insensitive to the binning methodology. We find that the information gain extracted on ( w 0 , w a ) for any 3 × 2 pt component starts to become saturated beyond roughly seven or eight bins. Any marginal gains resulting from a greater number of bins are likely to be limited by additional uncertainties present in a real measurement and the increasing demand for accuracy of the covariance matrix. Finally, we considered a 5% contamination from catastrophic photometric redshift outliers and found that if these errors are not mitigated in the analysis, the bias induced in the 3 × 2 pt signal for ten equipopulated bins results in dark energy constraints that are inconsistent with the fiducial ΛCDM cosmology at ≳3 σ .