No abstract

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.

The upcoming generation of galaxy surveys will probe the distribution of matter in the universe with unprecedented accuracy. Measurements of the matter power spectrum at different scales and redshifts will provide stringent constraints on the cosmological parameters. However, on non-linear scales this will require an accurate evaluation of the covariance matrix. Here, we compute the covariance matrix of the 3D matter density power spectrum for the concordance ΛCDM cosmology from an ensemble of N-body simulations of the Dark Energy Universe Simulation -Parallel Universe Runs (DEUS-PUR). This consists of 12288 realisations of a (656 h −1 Mpc) 3 simulation box with 256 3 particles. We combine this set with an auxiliary sample of 96 simulations of the same volume with 1024 3 particles. We find N-body mass resolution effect to be an important source of systematic errors on the covariance at high redshift and small intermediate scales. We correct for this effect by introducing an empirical statistical method which provide an accurate determination of the covariance matrix over a wide range of scales including the Baryon Oscillations interval. Contrary to previous studies that used smaller N-body ensembles, we find the power spectrum distribution to significantly deviate from expectations of a Gaussian random density field at k 0.25 h Mpc −1 and z < 0.5. This suggests that in the case of finite volume surveys an unbiased estimate of the ensemble averaged band power at these scales and redshifts may require a careful assessment of non-Gaussian errors more than previously considered.