xTras: a field-theory inspired xAct package for Mathematica

We present the tensor computer algebra package xTras, which provides functions and methods frequently needed when doing (classical) field theory. Amongst others, it can compute contractions, make Ans\"atze, and solve tensorial equations. It is built upon the tensor computer algebra system xAct, a collection of packages for Mathematica.Comment: 29 pages. The package can be downloaded from http://www.xact.es/xtras

Euclid preparation:VI. Verifying the performance of cosmic shear experiments

Aims: Our aim is to quantify the impact of systematic effects on the inference of cosmological parameters from cosmic shear. Methods: We present an "end-to-end" approach that introduces sources of bias in a modelled weak lensing survey on a galaxy-by-galaxy level. We propagated residual biases through a pipeline from galaxy properties at one end to cosmic shear power spectra and cosmological parameter estimates at the other end. We did this to quantify how imperfect knowledge of the pipeline changes the maximum likelihood values of dark energy parameters. Results: We quantify the impact of an imperfect correction for charge transfer inefficiency and modelling uncertainties of the point spread function for Euclid, and find that the biases introduced can be corrected to acceptable levels

Euclid:Cosmology forecasts from the void-galaxy cross-correlation function with reconstruction

We have investigated the cosmological constraints that can be expected from measurement of the cross-correlation of galaxies with cosmic voids identified in the Euclid spectroscopic survey, which will include spectroscopic information for tens of millions of galaxies over 15 000 deg2 of the sky in the redshift range 0.9 ≤ z &lt; 1.8. We have done this using simulated measurements obtained from the Flagship mock catalogue, the official Euclid mock that closely matches the expected properties of the spectroscopic dataset. To mitigate anisotropic selection-bias effects, we have used a velocity field reconstruction method to remove large-scale redshift-space distortions from the galaxy field before void-finding. This allowed us to accurately model contributions to the observed anisotropy of the cross-correlation function arising from galaxy velocities around voids as well as from the Alcock-Paczynski effect, and we studied the dependence of constraints on the efficiency of reconstruction. We find that Euclid voids will be able to constrain the ratio of the transverse comoving distance DM and Hubble distance DH to a relative precision of about 0:3%, and the growth rate fσ8 to a precision of between 5% and 8% in each of the four redshift bins covering the full redshift range. In the standard cosmological model, this translates to a statistical uncertainty δωm = ±0.0028 on the matter density parameter from voids, which is better than what can be achieved from either Euclid galaxy clustering and weak lensing individually. We also find that voids alone can measure the dark energy equation of state to a 6% precision.</p

Managing the Euclid Data Model

The Euclid common data model is central in, and essential to, the Euclid science ground segment. It defines the format of all data exchanged between the pipelines and stored in the Euclid Archive, and ensures all components can communicate with each other. But with more than 25 active contributors, managing the data model has been a challenge. Care must be taken that changes in the XML of the data model do not break its Python, C++, or database bindings. We describe recent progress in tackling these problems. The former problem has been mitigated with a new data model validator tool run during continuous integration. The latter has partially been solved via git management rules. Both approaches have only been possible after the migration of SVN to git, allowing the introduction of modern tooling

Euclid preparation:XXVIII. Modelling of the weak lensing angular power spectrum

This work considers which higher-order effects in modelling the cosmic shear angular power spectra must be taken into account for Euclid. We identify which terms are of concern, and quantify their individual and cumulative impact on cosmological parameter inference from Euclid. We compute the values of these higher-order effects using analytic expressions, and calculate the impact on cosmological parameter estimation using the Fisher matrix formalism. We review 24 effects and find the following potentially need to be accounted for: the reduced shear approximation, magnification bias, source-lens clustering, source obscuration, local Universe effects, and the flat Universe assumption. Upon computing these explicitly, and calculating their cosmological parameter biases, using a maximum multipole of $\ell=5000$, we find that the magnification bias, source-lens clustering, source obscuration, and local Universe terms individually produce significant (\,>0.25\sigma) cosmological biases in one or more parameters, and accordingly must be accounted for. In total, over all effects, we find biases in $\Omega_{\rm m}$, $\Omega_{\rm b}$, $h$, and $\sigma_{8}$ of $0.73\sigma$, $0.28\sigma$, $0.25\sigma$, and $-0.79\sigma$, respectively, for flat $\Lambda$CDM. For the $w_0w_a$CDM case, we find biases in $\Omega_{\rm m}$, $\Omega_{\rm b}$, $h$, $n_{\rm s}$, $\sigma_{8}$, and $w_a$ of $1.49\sigma$, $0.35\sigma$, $-1.36\sigma$, $1.31\sigma$, $-0.84\sigma$, and $-0.35\sigma$, respectively; which are increased relative to the $\Lambda$CDM due to additional degeneracies as a function of redshift and scale

Euclid preparation:XXVIII. Modelling of the weak lensing angular power spectrum

This work considers which higher-order effects in modelling the cosmic shear angular power spectra must be taken into account for Euclid. We identify which terms are of concern, and quantify their individual and cumulative impact on cosmological parameter inference from Euclid. We compute the values of these higher-order effects using analytic expressions, and calculate the impact on cosmological parameter estimation using the Fisher matrix formalism. We review 24 effects and find the following potentially need to be accounted for: the reduced shear approximation, magnification bias, source-lens clustering, source obscuration, local Universe effects, and the flat Universe assumption. Upon computing these explicitly, and calculating their cosmological parameter biases, using a maximum multipole of $\ell=5000$, we find that the magnification bias, source-lens clustering, source obscuration, and local Universe terms individually produce significant (\,>0.25\sigma) cosmological biases in one or more parameters, and accordingly must be accounted for. In total, over all effects, we find biases in $\Omega_{\rm m}$, $\Omega_{\rm b}$, $h$, and $\sigma_{8}$ of $0.73\sigma$, $0.28\sigma$, $0.25\sigma$, and $-0.79\sigma$, respectively, for flat $\Lambda$CDM. For the $w_0w_a$CDM case, we find biases in $\Omega_{\rm m}$, $\Omega_{\rm b}$, $h$, $n_{\rm s}$, $\sigma_{8}$, and $w_a$ of $1.49\sigma$, $0.35\sigma$, $-1.36\sigma$, $1.31\sigma$, $-0.84\sigma$, and $-0.35\sigma$, respectively; which are increased relative to the $\Lambda$CDM due to additional degeneracies as a function of redshift and scale

Euclid preparation. XXX. Evaluating the weak lensing cluster mass biases using the Three Hundred Project hydrodynamical simulations

The photometric catalogue of galaxy clusters extracted from ESA Euclid data is expected to be very competitive for cosmological studies. Using state-of-the-art hydrodynamical simulations, we present systematic analyses simulating the expected weak lensing profiles from clusters in a variety of dynamic states and at wide range of redshifts. In order to derive cluster masses, we use a model consistent with the implementation within the Euclid Consortium of the dedicated processing function and find that, when jointly modelling mass and the concentration parameter of the Navarro-Frenk-White halo profile, the weak lensing masses tend to be, on average, biased low with respect to the true mass. Using a fixed value for the concentration, the mass bias is diminished along with its relative uncertainty. Simulating the weak lensing signal by projecting along the directions of the axes of the moment of inertia tensor ellipsoid, we find that orientation matters: when clusters are oriented along the major axis the lensing signal is boosted, and the recovered weak lensing mass is correspondingly overestimated. Typically, the weak lensing mass bias of individual clusters is modulated by the weak lensing signal-to-noise ratio, and the negative mass bias tends to be larger toward higher redshifts. However, when we use a fixed value of the concentration parameter the redshift evolution trend is reduced. These results provide a solid basis for the weak-lensing mass calibration required by the cosmological application of future cluster surveys from Euclid and Rubin