Euclid preparation

Abstract

Aims. The Euclid space telescope will measure the shapes and redshifts of galaxies to reconstruct the expansion history of the Universe and the growth of cosmic structures. The estimation of the expected performance of the experiment, in terms of predicted constraints on cosmological parameters, has so far relied on various individual methodologies and numerical implementations, which were developed for different observational probes and for the combination thereof. In this paper we present validated forecasts, which combine both theoretical and observational ingredients for different cosmological probes. This work is presented to provide the community with reliable numerical codes and methods for Euclid cosmological forecasts. Methods. We describe in detail the methods adopted for Fisher matrix forecasts, which were applied to galaxy clustering, weak lensing, and the combination thereof. We estimated the required accuracy for Euclid forecasts and outline a methodology for their development. We then compare and improve different numerical implementations, reaching uncertainties on the errors of cosmological parameters that are less than the required precision in all cases. Furthermore, we provide details on the validated implementations, some of which are made publicly available, in different programming languages, together with a reference training-set of input and output matrices for a set of specific models. These can be used by the reader to validate their own implementations if required. Results. We present new cosmological forecasts for Euclid. We find that results depend on the specific cosmological model and remaining freedom in each setting, for example flat or non-flat spatial cosmologies, or different cuts at non-linear scales. The numerical implementations are now reliable for these settings. We present the results for an optimistic and a pessimistic choice for these types of settings. We demonstrate that the impact of cross-correlations is particularly relevant for models beyond a cosmological constant and may allow us to increase the dark energy figure of merit by at least a factor of three.

Cosmological parameter biases from Doppler-shifted weak lensing in stage IV experiments

“…We study the effect of neglecting Doppler shift on upcoming weak lensing surveys by utilizing the forecasting specifications of a Euclid-like survey [14] to represent stage IV cosmic shear experiments. Accordingly, we consider the case where l modes up to l max ¼ 5000 are included in the survey, as this is a requirement for such an experiment to achieve its precision goals with weak lensing.…”

“…where f sky is the fraction of sky observed, Δl is the bandwidth of l modes sampled, these blocks in l are summed over, and τ and ζ denote the current parameters of interest, θ τ and θ ζ , respectively. A more detailed calculation of this expression can be found in [14]. For a given parameter, we are then able to predict the uncertainty using the expression…”

“…In this work, we use the Fisher matrix formalism to predict the cosmological parameter biases from a Euclid-like survey, when one such effect is neglected: the Doppler shift of measured source redshifts due to their peculiar velocities and the inhomogeneity of the Universe. While the second-order correction for this effect is known [12,13], its impact at the angular power spectrum level, on intrinsic alignments (IAs), and on cosmological parameter inference for the specifications of an Euclid-like survey [14], and under the Limber approximation, has not been explicitly evaluated.…”

Cosmological parameter forecasts by a joint 2D tomographic approach to CMB and galaxy clustering

“…The Euclid-like spectroscopic survey (hereafter, Euclidsp-like) will measure the galaxy clustering from ∼30 million Hα emitters. According to the updated predictions obtained by [42,76,77], the Euclid-like wide single-grism survey will reach a flux limit F Hα > 2 × 10 −16 erg cm −2 s −1 and will cover a redshift range 0.9 ≤ z ≤ 1.8. The sky coverage is also 15000 deg 2 , and the expected number density of objects will ben g ≃ 2000 sources per deg 2 .…”

“…As galaxy surveys, we consider Euclid-like and Vera C. Rubin Observatory as examples for photometric surveys, Euclid-like spectroscopic as an example for a pure spectroscopic survey, SPHEREx as an example for a spectrophotometric survey, and EMU [40] and SKA in Phase 1 (SKA1) as examples for radio continuum surveys. Note that in this paper, we consider only the 2D tomographic clustering from Euclid-like photometric and spectroscopic surveys separately, and we refer to [41] for the combination and cross-correlation of the full Euclid capabilities [42] with the CMB fields. This analysis is performed for the current concordance ΛCDM model and some of its important extensions, such as (i) the w 0 ; w a parametrization for a dark energy component with a parameter of state dependent on the redshift, (ii) a neutrino sector in which N eff and Σm ν are allowed to vary, (iii) primordial perturbations, which allow the running of the spectral index, and a local non-Gaussianity parameter, which leads to a scale dependence for the galaxy bias.…”