We present a new power spectrum emulator named EuclidEmulator that estimates the nonlinear correction to the linear dark matter power spectrum depending on the six cosmological parameters ω b , ω m , n s , h, w 0 , and σ 8. It is constructed using the uncertainty quantification software UQLab using a spectral decomposition method called polynomial chaos expansion. All steps in its construction have been tested and optimized: the large highresolution N-body simulations carried out with PKDGRAV3 were validated using a simulation from the Euclid Flagship campaign and demonstrated to have converged up to wavenumbers k ≈ 5 h Mpc −1 for redshifts z ≤ 5. The emulator is based on 100 input cosmologies simulated in boxes of (1250 Mpc/h) 3 using 2048 3 particles. We show that by creating mock emulators it is possible to successfully predict and optimize the performance of the final emulator prior to performing any N-body simulations. The absolute accuracy of the final nonlinear power spectrum is as good as one obtained with N-body simulations, conservatively, ∼1 per cent for k 1 h Mpc −1 and z 1. This enables efficient forward modelling in the nonlinear regime, allowing for estimation of cosmological parameters using Markov Chain Monte Carlo methods. EuclidEmulator has been compared to HALOFIT, CosmicEmu, and NGenHalofit, and shown to be more accurate than these other approaches. This work paves a new way for optimal construction of future emulators that also consider other cosmological observables, use higher resolution input simulations, and investigate higher dimensional cosmological parameter spaces.

Baryonic feedback effects lead to a suppression of the weak lensing angular power spectrum on small scales. The poorly constrained shape and amplitude of this suppression is an important source of uncertainties for upcoming cosmological weak-lensing surveys such as Euclid or LSST. In this first paper in a series of two, we use simulations to build a Euclidlike tomographic mock data-set for the cosmic shear power spectrum and the corresponding covariance matrix, which are both corrected for baryons following the baryonification method of Schneider et al. [1]. In addition, we develop an emulator to obtain fast predictions of the baryonic suppression effects, allowing us to perform a likelihood inference analysis for a standard ΛCDM cosmology with both cosmological and astrophysical parameters. Our main findings are the following: (i) ignoring baryonic effects leads to a greater than 5σ bias on the cosmological parameters Ω m and σ 8 ; (ii) restricting the analysis to the largest scales, that are mostly unaffected by baryons, makes the bias disappear, but results in a blow-up of the Ω m -σ 8 contour area by more than a factor of 10; (iii) ignoring baryonic effects on

We present a new, updated version of the EuclidEmulator (called EuclidEmulator2), a fast and accurate predictor for the nonlinear correction of the matter power spectrum. 2 per cent-level accurate emulation is now supported in the eight-dimensional parameter space of w0waCDM+∑mν models between redshift z = 0 and z = 3 for spatial scales within the range 0.01 h Mpc−1 ≤ k ≤ 10 h Mpc−1. In order to achieve this level of accuracy, we have had to improve the quality of the underlying N-body simulations used as training data: (i) we use self-consistent linear evolution of non-dark matter species such as massive neutrinos, photons, dark energy and the metric field, (ii) we perform the simulations in the so-called N-body gauge, which allows one to interpret the results in the framework of general relativity, (iii) we run over 250 high-resolution simulations with 30003 particles in boxes of 1(h−1 Gpc)3 volumes based on paired-and-fixed initial conditions and (iv) we provide a resolution correction that can be applied to emulated results as a post-processing step in order to drastically reduce systematic biases on small scales due to residual resolution effects in the simulations. We find that the inclusion of the dynamical dark energy parameter wa significantly increases the complexity and expense of creating the emulator. The high fidelity of EuclidEmulator2 is tested in various comparisons against N-body simulations as well as alternative fast predictors like HALOFIT, HMCode and CosmicEmu. A blind test is successfully performed against the Euclid Flagship v2.0 simulation. Nonlinear correction factors emulated with EuclidEmulator2 are accurate at the level of $1{{\ \rm per\ cent}}$ or better for 0.01 h Mpc−1 ≤ k ≤ 10 h Mpc−1 and z ≤ 3 compared to high-resolution dark matter only simulations. EuclidEmulator2 is publicly available at https://github.com/miknab/EuclidEmulator2.

An accurate modelling of baryonic feedback effects is required to exploit the full potential of future weak-lensing surveys such as Euclid or LSST. In this second paper in a series of two, we combine Euclid-like mock data of the cosmic shear power spectrum with an eROSITA X-ray mock of the cluster gas fraction to run a combined likelihood analysis including both cosmological and baryonic parameters. Following the first paper of this series, the baryonic effects (based on the baryonic correction model of Ref.[1]) are included in both the tomographic power spectrum and the covariance matrix. However, this time we assume the more realistic case of a ΛCDM cosmology with massive neutrinos and we consider several extensions of the currently favoured cosmological model. For the standard ΛCDM case, we show that including X-ray data reduces the uncertainties on the sum of the neutrino mass by ∼ 30 percent, while there is only a mild improvement on other parameters such as Ω m and σ 8 . As extensions of ΛCDM, we consider the cases of a dynamical dark energy model (wCDM), a f (R) gravity model (fRCDM), and a mixed dark matter model (ΛMDM) with both a cold and a warm/hot dark matter component. We find that combining weak-lensing with X-ray data only leads to a mild improvement of the constraints on the additional parameters of wCDM, while the improvement is more substantial for both fRCDM and ΛMDM. Ignoring baryonic effects in the analysis pipeline leads significant false-detections of either phantom dark energy or a light subdominant dark matter component. Overall we conclude that for all cosmologies considered, a general parametrisation of baryonic effects is both necessary and sufficient to obtain tight constraints on cosmological parameters.

We present N -body simulations which are fully compatible with general relativity, with dark energy consistently included at both the background and perturbation level. We test our approach for dark energy parameterised as both a fluid, and using the parameterised post-Friedmann (PPF) formalism. In most cases, dark energy is very smooth relative to dark matter so that its leading effect on structure formation is the change to the background expansion rate. This can be easily incorporated into Newtonian N -body simulations by changing the Friedmann equation. However, dark energy perturbations and relativistic corrections can lead to differences relative to Newtonian N -body simulations at the tens of percent level for scales k < (10 −3 -10 −2 ) Mpc −1 , and given the accuracy of upcoming large scale structure surveys such effects must be included. In this paper we will study both effects in detail and highlight the conditions under which they are important. We also show that our N -body simulations exactly reproduce the results of the Boltzmann solver class for all scales which remain linear. arXiv:1904.05210v1 [astro-ph.CO]