Nonparametric cosmology with cosmic shear

Abstract

We present a method to measure the growth of structure and the background geometry of the Universewith no a priori assumption about the underlying cosmological model. Using Canada-France-Hawaii Lensing Survey (CFHTLenS) shear data, we simultaneously reconstruct the lensing amplitude, the linear intrinsic alignment amplitude, the redshift evolving matter power spectrum, Pðk; zÞ, and the comoving distance, rðzÞ. We find that lensing predominately constrains a single global power spectrum amplitude and several comoving distance bins. Our approach can localize the precise scales (k-modes in the matter power spectrum) and redshifts where lambda-cold dark matter (LCDM) fails-if any. We find that below z ¼ 0.4, the measured comoving distance rðzÞ is higher than that expected from the Planck LCDM cosmology by ∼1.5σ, while at higher redshifts, our reconstruction is fully consistent. To validate our reconstruction, we compare LCDM parameter constraints from the standard cosmic shear likelihood analysis to those found by fitting to the nonparametric information and we find good agreement.

Euclid: Impact of non-linear and baryonic feedback prescriptions on cosmological parameter estimation from weak lensing cosmic shear

“…Over this range, the argument k (z) of the matter power spectrum P δδ (k, z) feeding the integral is larger than k max for z < 0.84 so that which non-linear recipe is adopted still matters. Such an argument can be repeated for all the bins combinations and the multipoles thus explaining why the FoM is still dependent on the non-linear recipe even with these very conservative scale cuts, a result in agreement with what was discussed in Taylor et al (2018a). Therefore, in order to remove completely the dependence on the non-linear description from the analysis, different approaches are needed, for example using band powers rather than a C ( ) analysis (Joachimi et al 2021).…”

Euclid preparation

“…The linear power spectrum of Eq. ( 28) is able to match the one measured from numerical simulations only over a limited range in k. For cosmic shear, one needs to model the matter power spectrum deep into the non-linear, high-k, regime that corresponds to projected angular modes in C i j ( ) up to multipoles ∼ 1000, and in fact already important at ∼ 100 (Taylor et al 2018a). A common approach to model the non-linear matter power spectrum is to define it as a general function of the linear power spectrum, P lin,δδ (k, z), that translates it into the full, non-linear power spectrum P δδ (k, z).…”

“…While the cosmological signal with which we are concerned is the additional ellipticity caused by the lensing of the large-scale structure, that we summarise in the cosmic shear power spectrum, we also wish to model the primary astrophysical systematics. We consider five main quantities that must be modelled in order to recover the observable cosmic shear power spectrum: Firstly, the (theoretical) cosmic shear power spectrum, namely the primary cosmological power spectrum; secondly, the intrinsic alignment power spectrum, modelling the local alignment of galaxies, representing the main astrophysical systematics; as a third quantity, we consider the small-scale part of the matter power spectrum, including a halo model describing the clustering of dark matter on small scales beyond linear theory (k < 7 h Mpc −1 ) to which the cosmic shear power spectrum is particularly sensitive (Taylor et al 2018a), which includes the impact of baryonic feedback (e.g. Semboloni et al 2011;Copeland et al 2018); the fourth item includes photometric redshifts and number density, which model the inferred uncertainty in galaxy positions due to the broad-band estimates of the redshifts, where the redshift distribution affects the signal part of the cosmic shear power spectrum but the total number of galaxies does not; as fifth, and last point, the shot noise due to Poisson sampling by galaxy positions of the shear field, which is affected by the total number of galaxies observed.…”

“…The standard cosmic shear power spectrum is sensitive to k-modes in the range 0 < k ≤ 7 h Mpc −1 (Taylor et al 2018a), which therefore necessitates a modelling of high-k behaviour of the matter power spectrum. Whilst it is possible to exclude some high-k information by performing a cut in -mode this procedure is not a "clean" way to remove modes and is inefficient, particularly at low redshift.…”

“…A second area of attention has been in the appreciation of the impact of the small-scale (high k-mode) matter power spectrum on WL two-point statistics (e.g. Taylor et al 2018a;Copeland et al 2018). This has led to improved models of the impact of baryonic feedback, neutrino mass, and non-linear clustering on small scales.…”