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Register a new userAccessing the high-$ell$ frontier under the Reduced Shear Approximation with $k$-cut Cosmic Shear
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The precision of Stage IV cosmic shear surveys will enable us to probe smaller physical scales than ever before, however, model uncertainties from baryonic physics and non-linear structure formation will become a significant concern. The $k$-cut method -- applying a redshift-dependent $ell$-cut after making the Bernardeau-Nishimichi-Taruya transform -- can reduce sensitivity to baryonic physics; allowing Stage IV surveys to include information from increasingly higher $ell$-modes. Here we address the question of whether it can also mitigate the impact of making the reduced shear approximation; which is also important in the high-$kappa$, small-scale regime. The standard procedure for relaxing this approximation requires the repeated evaluation of the convergence bispectrum, and consequently can be prohibitively computationally expensive when included in Monte Carlo analyses. We find that the $k$-cut cosmic shear procedure suppresses the $w_0w_a$CDM cosmological parameter biases expected from the reduced shear approximation for Stage IV experiments, when $ell$-modes up to $5000$ are probed. The maximum cut required for biases from the reduced shear approximation to be below the threshold of significance is at $k = 5.37 , h{rm Mpc}^{-1}$. With this cut, the predicted $1sigma$ constraints increase, relative to the case where the correction is directly computed, by less than $10%$ for all parameters. This represents a significant improvement in constraints compared to the more conservative case where only $ell$-modes up to 1500 are probed, and no $k$-cut is used. We also repeat this analysis for a hypothetical, comparable kinematic weak lensing survey. The key parts of code used for this analysis are made publicly available.
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Stage IV weak lensing experiments will offer more than an order of magnitude leap in precision. We must therefore ensure that our analyses remain accurate in this new era. Accordingly, previously ignored systematic effects must be addressed. In this work, we evaluate the impact of the reduced shear approximation and magnification bias, on the information obtained from the angular power spectrum. To first-order, the statistics of reduced shear, a combination of shear and convergence, are taken to be equal to those of shear. However, this approximation can induce a bias in the cosmological parameters that can no longer be neglected. A separate bias arises from the statistics of shear being altered by the preferential selection of galaxies and the dilution of their surface densities, in high-magnification regions. The corrections for these systematic effects take similar forms, allowing them to be treated together. We calculated the impact of neglecting these effects on the cosmological parameters that would be determined from Euclid, using cosmic shear tomography. To do so, we employed the Fisher matrix formalism, and included the impact of the super-sample covariance. We also demonstrate how the reduced shear correction can be calculated using a lognormal field forward modelling approach. These effects cause significant biases in Omega_m, sigma_8, n_s, Omega_DE, w_0, and w_a of -0.53 sigma, 0.43 sigma, -0.34 sigma, 1.36 sigma, -0.68 sigma, and 1.21 sigma, respectively. We then show that these lensing biases interact with another systematic: the intrinsic alignment of galaxies. Accordingly, we develop the formalism for an intrinsic alignment-enhanced lensing bias correction. Applying this to Euclid, we find that the additional terms introduced by this correction are sub-dominant.
If left unchecked modeling uncertainties at small scales, due to poorly understood baryonic physics and non-linear structure formation, will significantly bias Stage IV cosmic shear two-point statistic parameter constraints. While it is perhaps possible to run N-body or hydrodynamical simulations to determine the impact of these effects this approach is computationally expensive; especially to test a large number of theories of gravity. Instead we propose directly removing sensitivity to small-scale structure from the lensing spectrum, creating a statistic that is robust to these uncertainties. We do this by taking a redshift-dependent l-cut after applying the Bernardeau-Nishimichi-Taruya (BNT) nulling scheme. This reorganizes the information in the lensing spectrum to make the relationship between the angular scale, l, and the structure scale, k, much clearer compared to standard cosmic shear power spectra -- for which no direct relationship exists. We quantify the effectiveness of this method at removing sensitivity to small scales and compute the predicted Fisher error on the dark energy equation of state, w0, for different k-cuts in the matter power spectrum.
We introduce the Generalised Lensing and Shear Spectra GLaSS code which is available for download from https://github.com/astro-informatics/GLaSS It is a fast and flexible public code, written in Python, that computes generalized spherical cosmic shear spectra. The commonly used tomographic and spherical Bessel lensing spectra come as built-in run-mode options. GLaSS is integrated into the Cosmosis modular cosmological pipeline package. We outline several computational choices that accelerate the computation of cosmic shear power spectra. Using GLaSS, we test whether the assumption that using the lensing and projection kernels for a spatially-flat universe -- in a universe with a small amount of spatial curvature -- negligibly impacts the lensing spectrum. We refer to this assumption as The Spatially-Flat Universe Approximation, that has been implicitly assumed in all cosmic shear studies to date. We confirm that The Spatially-Flat Universe Approximation has a negligible impact on Stage IV cosmic shear experiments.
Using Subaru Hyper Suprime-Cam (HSC) year 1 data, we perform the first $k$-cut cosmic shear analysis constraining both $Lambda$CDM and $f(R)$ Hu-Sawicki modified gravity. To generate the $f(R)$ cosmic shear theory vector, we use the matter power spectrum emulator trained on COLA (COmoving Lagrangian Acceleration) simulations. The $k$-cut method is used to significantly down-weight sensitivity to small scale ($k > 1 h {rm Mpc }^{-1}$) modes in the matter power spectrum where the emulator is less accurate, while simultaneously ensuring our results are robust to baryonic feedback model uncertainty. We have also developed a test to ensure that the effects of poorly modeled small scales are nulled as intended. For $Lambda$CDM we find $S_8 = sigma_8 (Omega_m / 0.3) ^ {0.5} = 0.789 ^{+0.039}_{-0.022}$, while the constraints on the $f(R)$ modified gravity parameters are prior dominated. In the future, the $k$-cut method could be used to constrain a large number of theories of gravity where computational limitations make it infeasible to model the matter power spectrum down to extremely small scales.
With the advent of large-scale weak lensing surveys there is a need to understand how realistic, scale-dependent systematics bias cosmic shear and dark energy measurements, and how they can be removed. Here we describe how spatial variations in the amplitude and orientation of realistic image distortions convolve with the measured shear field, mixing the even-parity convergence and odd-parity modes, and bias the shear power spectrum. Many of these biases can be removed by calibration to external data, the survey itself, or by modelling in simulations. The uncertainty in the calibration must be marginalised over and we calculate how this propagates into parameter estimation, degrading the dark energy Figure-of-Merit. We find that noise-like biases affect dark energy measurements the most, while spikes in the bias power have the least impact, reflecting their correlation with the effect of cosmological parameters. We argue that in order to remove systematic biases in cosmic shear surveys and maintain statistical power effort should be put into improving the accuracy of the bias calibration rather than minimising the size of the bias. In general, this appears to be a weaker condition for bias removal. We also investigate how to minimise the size of the calibration set for a fixed reduction in the Figure-of-Merit. These results can be used to model the effect of biases and calibration on a cosmic shear survey accurately, assess their impact on the measurement of modified gravity and dark energy models, and to optimise surveys and calibration requirements.
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