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Weak gravitational lensing is a powerful probe, which is used to constrain the standard cosmological model and its extensions. With the enhanced statistical precision of current and upcoming surveys, high-accuracy predictions for weak lensing statistics are needed to limit the impact of theoretical uncertainties on cosmological parameter constraints. For this purpose, we present a comparison of the theoretical predictions for the non-linear matter and weak lensing power spectra, based on the widely used fitting functions (⁠|$\texttt {mead}$| and |$\texttt {rev-halofit}$|), emulators (⁠|$\texttt {EuclidEmulator}$| , |$\texttt {EuclidEmulator2}$| , |$\texttt {BaccoEmulator}$| , and |$\texttt {CosmicEmulator}$|), and N -body simulations (pkdgrav3). We consider the forecasted constraints on the |$\Lambda \texttt {CDM}$| and |$\texttt {wCDM}$| models from weak lensing for stage III and stage IV surveys. We study the relative bias on the constraints and their dependence on the assumed prescriptions. Assuming a |$\Lambda \texttt {CDM}$| cosmology, we find that the relative agreement on the S 8 parameter is between 0.2 and 0.3σ for a stage III-like survey between the above predictors. For a stage IV-like survey the agreement becomes 1.4–3.0σ. In the |$\texttt {wCDM}$| scenario, we find broader S 8 constraints, and agreements of 0.18–0.26σ and 0.7–1.7σ for stage III and stage IV surveys, respectively. The accuracies of the above predictors therefore appear adequate for stage III surveys, whereas the fitting functions would need improvements for future stage IV surveys. Furthermore, we find that, of the fitting functions, |$\texttt {mead}$| provides the best agreement with the emulators. We discuss the implication of these findings for the preparation of future weak lensing surveys, and the relative impact of theoretical uncertainties to other systematics. [ABSTRACT FROM AUTHOR]

Cosmic shear is a powerful probe of cosmological parameters, but its potential can be fully utilized only if galaxy shapes are measured with great accuracy. Two major effects have been identified which are likely to account for most of the bias seen for maximum likelihood methods in recent shear measurement challenges. Model bias occurs when the true galaxy shape is not well represented by the fitted model. Noise bias occurs due to the non-linear relationship between image pixels and galaxy shape. In this paper we investigate the potential interplay between these two effects when an imperfect model is used in the presence of high noise. We present analytical expressions for this bias, which depends on the residual difference between the model and real data. They can lead to biases not accounted for in previous calibration schemes. By measuring the model bias, noise bias and their interaction, we provide a complete statistical framework for measuring galaxy shapes with model fitting methods from GRavitational lEnsing Accuracy Testing (GREAT)-like images. We demonstrate the noise and model interaction bias using a simple toy model, which indicates that this effect can potentially be significant. Using real galaxy images from the Cosmological Evolution Survey (COSMOS) we quantify the strength of the model bias, noise bias and their interaction. We find that the interaction term is often of a similar size to the model bias term, and is smaller than the requirements of current and near future galaxy surveys. [ABSTRACT FROM AUTHOR]

ABSTRACT Weak gravitational lensing has the potential to constrain cosmological parameters to high precision. However, as shown by the Shear Testing Programmes and Gravitational lensing Accuracy Testing challenges, measuring galaxy shears is a non-trivial task: various methods introduce different systematic biases which have to be accounted for. We investigate how pixel noise on the image affects the bias on shear estimates from a maximum likelihood forward model-fitting approach using a sum of co-elliptical Sérsic profiles, in complement to the theoretical approach of an associated paper. We evaluate the bias using a simple but realistic galaxy model and find that the effects of noise alone can cause biases of the order of 1-10 per cent on measured shears, which is significant for current and future lensing surveys. We evaluate a simulation-based calibration method to create a bias model as a function of galaxy properties and observing conditions. This model is then used to correct the simulated measurements. We demonstrate that, for the simple case in which the correct range of galaxy models is used in the fit, the calibration method can reduce noise bias to the level required for estimating cosmic shear in upcoming lensing surveys. [ABSTRACT FROM AUTHOR]

ABSTRACT Weak lensing experiments are a powerful probe into cosmology through their measurement of the mass distribution of the universe. A challenge for this technique is to control systematic errors that occur when measuring the shapes of distant galaxies. In this paper, we investigate noise bias, a systematic error that arises from second-order noise terms in the shape measurement process. We first derive analytical expressions for the bias of general maximum-likelihood estimators in the presence of additive noise. We then find analytical expressions for a simplified toy model in which galaxies are modelled and fitted with a Gaussian with its size as a single free parameter. Even for this very simple case we find a significant effect. We also extend our analysis to a more realistic six-parameter elliptical Gaussian model. We find that the noise bias is generically of the order of the inverse-squared signal-to-noise ratio (SNR) of the galaxies and is thus of the order of a percent for galaxies of SNR 10, i.e. comparable to the weak lensing shear signal. This is nearly two orders of magnitude greater than the systematic requirements for future all-sky weak lensing surveys. We discuss possible ways to circumvent this effect, including a calibration method using simulations discussed in an associated paper. [ABSTRACT FROM AUTHOR]