Redshift requirements for cosmic shear with intrinsic alignment

Abstract

Intrinsic alignment (IA) modelling and photometric redshift estimation are two of the main sources of systematic uncertainty in weak lensing surveys. We investigate the impact of redshift errors and their interplay with different IA models. Generally, errors on the mean δz and on the width σz of the redshift bins can both lead to biases in cosmological constraints. We find that such biases can, however, only be partially resolved by marginalizing over δz and σz . For Stage-III surveys, δz and σz cannot be well constrained due to limited statistics. The resulting biases are thus sensitive to prior volume effects. For Stage-IV surveys, we observe that marginalizing over the redshift parameters has an impact and reduces the bias. We derive requirements on the uncertainty of σz and δz for both Stage-III and Stage-IV surveys. We assume that the redshift systematic errors on S 8 should be less than half of the statistical errors, and the median bias should be smaller than 0.25σ. We find that the uncertainty on δz has to be ≲ 0.025 for the NLA IA model with a Stage-III survey. We find no requirement threshold for σz since the requirements are met even for our maximum prior width of 0.3. For the TATT IA model, the uncertainty on δz has to be ≲ 0.02 and the uncertainty on σz has to be ≲ 0.2. Current redshift precision of Stage-III surveys is therefore high enough to meet these requirements. For Stage-IV surveys, systematic effects will be more important due to the higher statistical precision. In this case, the uncertainty on δz has to be ≲ 0.005 and the uncertainty on σz should be ≲ 0.1, with no significant dependence on the IA model. This required high precision will be a challenge for the redshift calibration of these future surveys. Finally, we investigate whether the interplay between redshift systematics and IA modelling can explain the S 8-tension between cosmic shear results and CMB measurements. We find that this is unlikely to explain the current S 8-tension. The code that was used to conduct this analysis is publicly available.[refrigerator: https://cosmo-gitlab.phys.ethz.ch/cosmo_public/refrigerator.]

12 × 2 pt combined probes: pipeline, neutrino mass, and data compression

“…This is done by representing the mapping from input parameters to function output as a series of non-linear transfer function operations. These are increasingly used in cosmology due to the significant speed gains over traditional methods (see [80][81][82][83][84][85][86][87]). Another advantage is that emulators are by default fully differentiable enabling robust numerical predictions of dC ℓ /d ⃗ θ using automatic differentiation (AD).…”

“…The second technique, PCA, allows us to find a new set of coordinates that can efficiently represent the data by choosing the modes giving rise to the highest variance across a dataset. In the present case, we perform a PCA compression on the emulator training set to find the vectors that capture the most variance as we span the parameter space within the priors (following an approach similar to [83,122]). PCA is a useful comparison to MOPED as one is free to keep as many PCA components (N PCA ) as desired.…”

“…Job arrays were submitted using esub-epipe [122,149]. Corner plots were created with trianglechain [8,83]. We used emcee [128] to run our MCMC chains.…”

Simulation-based inference of deep fields: galaxy population model and redshift distributions

“…This has proven to be a challenging task, especially since the relationship between redshift and colour in a limited wavelength range is subject to degeneracies [8]. The characterization of photometric redshift (photo-z) distributions is one of the key systematics affecting cosmic shear measurements since errors in the calibration of redshift distributions and their uncertainties can lead to biases in the retrieved cosmological parameters [8][9][10][11][12][13][14][15]. Traditional photo-z approaches include template fitting (for example LePhare [16,17], BPZ [18], ZEBRA [19] and EAZY [20]) and machine learning methods (for example ANNz [21], ANNz2 [22,23] and DNF [24]).…”

“…In previous work the α i were constrained at redshifts z = 0 and z = 1; we now use z = 3 since the functional form is fixed (so that we do not need to have a large sample of galaxies at z = 3 to pose limits on the parameters' values) and this allows us to enforce prior bounds at higher redshifts. Previously, the prior on this distribution was also a Dirichlet variable with unity weights, multiplied by a uniform number between [5,15], which accounted for the variance. This way, the α i parameters were affecting both the mean and variance of the Dirichlet variable.…”