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Density-estimation likelihood-free inference (DELFI) has recently been proposed as an efficient method for simulation-based cosmological parameter inference. Compared to the standard likelihood-based Markov Chain Monte Carlo (MCMC) approach, DELFI has several advantages: it is highly parallelizable, there is no need to assume a possibly incorrect functional form for the likelihood and complicated effects (e.g the mask and detector systematics) are easier to handle with forward models. In light of this, we present two DELFI pipelines to perform weak lensing parameter inference with lognormal realizations of the tomographic shear field -- using the C_l summary statistic. The first pipeline accounts for the non-Gaussianities of the shear field, intrinsic alignments and photometric-redshift error. We validate that it is accurate enough for Stage III experiments and estimate that O(1000) simulations are needed to perform inference on Stage IV data. By comparing the second DELFI pipeline, which makes no assumption about the functional form of the likelihood, with the standard MCMC approach, which assumes a Gaussian likelihood, we test the impact of the Gaussian likelihood approximation in the MCMC analysis. We find it has a negligible impact on Stage IV parameter constraints. Our pipeline is a step towards seamlessly propagating all data-processing, instrumental, theoretical and astrophysical systematics through to the final parameter constraints.
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Cosmic shear is sensitive to fluctuations in the cosmological matter density field, including on small physical scales, where matter clustering is affected by baryonic physics in galaxies and galaxy clusters, such as star formation, supernovae feedback and AGN feedback. While muddying any cosmological information that is contained in small scale cosmic shear measurements, this does mean that cosmic shear has the potential to constrain baryonic physics and galaxy formation. We perform an analysis of the Dark Energy Survey (DES) Science Verification (SV) cosmic shear measurements, now extended to smaller scales, and using the Mead et al. 2015 halo model to account for baryonic feedback. While the SV data has limited statistical power, we demonstrate using a simulated likelihood analysis that the final DES data will have the statistical power to differentiate among baryonic feedback scenarios. We also explore some of the difficulties in interpreting the small scales in cosmic shear measurements, presenting estimates of the size of several other systematic effects that make inference from small scales difficult, including uncertainty in the modelling of intrinsic alignment on nonlinear scales, `lensing bias, and shape measurement selection effects. For the latter two, we make use of novel image simulations. While future cosmic shear datasets have the statistical power to constrain baryonic feedback scenarios, there are several systematic effects that require improved treatments, in order to make robust conclusions about baryonic feedback.
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.
While baryonic feedback is one of the most important astrophysical systematics that we need to address in order to achieve precision cosmology, few weak lensing studies have directly measured its impact on the matter power spectrum. We report measurement of the baryonic feedback parameter with the constraints on its lower and upper limits from cosmic shear. We use the public data from the Kilo-Degree Survey and the VISTA Kilo-Degree Infrared Galaxy Survey spanning 450 deg$^2$. Estimating both cosmological and feedback parameters simultaneously, we obtain $A_{rm b}=1.01_{-0.85}^{+0.80}$, which shows a consistency with the dark matter-only (DMO) case at the $sim1.2~sigma$ level and a tendency toward positive feedback; the $A_{rm b}=0$ ($0.81$) value corresponds to the DMO (OWLS AGN) case. Despite this full constraint of the feedback parameter, our $S_8~(equiv sigma_8 sqrt{Omega_m / 0.3})$ measurement ($0.739^{+0.036}_{- 0.035}$) shifts by only $sim6$% of the statistical error, compared to the previous measurement. When we assume the flat $Lambda$CDM cosmology favored by the Nine-Year Wilkinson Microwave Anisotropy Probe (Planck) result, the feedback parameter is constrained to be $A_{rm b}=1.21_{-0.54}^{+0.61}$ ($1.60_{-0.52}^{+0.53}$), which excludes the DMO case at the $sim2.2~sigma$ ($sim3.1~sigma$) level.
One of the most pernicious theoretical systematics facing upcoming gravitational lensing surveys is the uncertainty introduced by the effects of baryons on the power spectrum of the convergence field. One method that has been proposed to account for these effects is to allow several additional parameters (that characterize dark matter halos) to vary and to fit lensing data to these halo parameters concurrently with the standard set of cosmological parameters. We test this method. In particular, we use this technique to model convergence power spectrum predictions from a set of cosmological simulations. We estimate biases in dark energy equation of state parameters that would be incurred if one were to fit the spectra predicted by the simulations either with no model for baryons, or with the proposed method. We show that neglecting baryonic effect leads to biases in dark energy parameters that are several times the statistical errors for a survey like the Dark Energy Survey. The proposed method to correct for baryonic effects renders the residual biases in dark energy equation of state parameters smaller than the statistical errors. These results suggest that this mitigation method may be applied to analyze convergence spectra from a survey like the Dark Energy Survey. For significantly larger surveys, such as will be carried out by the Large Synoptic Survey Telescope, the biases introduced by baryonic effects are much more significant. We show that this mitigation technique significantly reduces the biases for such larger surveys, but that a more effective mitigation strategy will need to be developed in order ensure that the residual biases in these surveys fall below the statistical errors.
We present the first constraints on cosmology from the Dark Energy Survey (DES), using weak lensing measurements from the preliminary Science Verification (SV) data. We use 139 square degrees of SV data, which is less than 3% of the full DES survey area. Using cosmic shear 2-point measurements over three redshift bins we find $sigma_8 (Omega_{rm m}/0.3)^{0.5} = 0.81 pm 0.06$ (68% confidence), after marginalising over 7 systematics parameters and 3 other cosmological parameters. We examine the robustness of our results to the choice of data vector and systematics assumed, and find them to be stable. About $20$% of our error bar comes from marginalising over shear and photometric redshift calibration uncertainties. The current state-of-the-art cosmic shear measurements from CFHTLenS are mildly discrepant with the cosmological constraints from Planck CMB data; our results are consistent with both datasets. Our uncertainties are $sim$30% larger than those from CFHTLenS when we carry out a comparable analysis of the two datasets, which we attribute largely to the lower number density of our shear catalogue. We investigate constraints on dark energy and find that, with this small fraction of the full survey, the DES SV constraints make negligible impact on the Planck constraints. The moderate disagreement between the CFHTLenS and Planck values of $sigma_8 (Omega_{rm m}/0.3)^{0.5}$ is present regardless of the value of $w$.
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