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Register a new userCosmological constraints with deep learning from KiDS-450 weak lensing maps
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Convolutional Neural Networks (CNN) have recently been demonstrated on synthetic data to improve upon the precision of cosmological inference. In particular they have the potential to yield more precise cosmological constraints from weak lensing mass maps than the two-point functions. We present the cosmological results with a CNN from the KiDS-450 tomographic weak lensing dataset, constraining the total matter density $Omega_m$, the fluctuation amplitude $sigma_8$, and the intrinsic alignment amplitude $A_{rm{IA}}$. We use a grid of N-body simulations to generate a training set of tomographic weak lensing maps. We test the robustness of the expected constraints to various effects, such as baryonic feedback, simulation accuracy, different value of $H_0$, or the lightcone projection technique. We train a set of ResNet-based CNNs with varying depths to analyze sets of tomographic KiDS mass maps divided into 20 flat regions, with applied Gaussian smoothing of $sigma=2.34$ arcmin. The uncertainties on shear calibration and $n(z)$ error are marginalized in the likelihood pipeline. Following a blinding scheme, we derive constraints of $S_8 = sigma_8 (Omega_m/0.3)^{0.5} = 0.777^{+0.038}_{-0.036}$ with our CNN analysis, with $A_{rm{IA}}=1.398^{+0.779}_{-0.724}$. We compare this result to the power spectrum analysis on the same maps and likelihood pipeline and find an improvement of about $30%$ for the CNN. We discuss how our results offer excellent prospects for the use of deep learning in future cosmological data analysis.
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We present cosmological parameter constraints from a tomographic weak gravitational lensing analysis of ~450deg$^2$ of imaging data from the Kilo Degree Survey (KiDS). For a flat $Lambda$CDM cosmology with a prior on $H_0$ that encompasses the most recent direct measurements, we find $S_8equivsigma_8sqrt{Omega_{rm m}/0.3}=0.745pm0.039$. This result is in good agreement with other low redshift probes of large scale structure, including recent cosmic shear results, along with pre-Planck cosmic microwave background constraints. A $2.3$-$sigma$ tension in $S_8$ and `substantial discordance in the full parameter space is found with respect to the Planck 2015 results. We use shear measurements for nearly 15 million galaxies, determined with a new improved `self-calibrating version of $lens$fit validated using an extensive suite of image simulations. Four-band $ugri$ photometric redshifts are calibrated directly with deep spectroscopic surveys. The redshift calibration is confirmed using two independent techniques based on angular cross-correlations and the properties of the photometric redshift probability distributions. Our covariance matrix is determined using an analytical approach, verified numerically with large mock galaxy catalogues. We account for uncertainties in the modelling of intrinsic galaxy alignments and the impact of baryon feedback on the shape of the non-linear matter power spectrum, in addition to the small residual uncertainties in the shear and redshift calibration. The cosmology analysis was performed blind. Our high-level data products, including shear correlation functions, covariance matrices, redshift distributions, and Monte Carlo Markov Chains are available at http://kids.strw.leidenuniv.nl.
We present measurements of the weak gravitational lensing shear power spectrum based on $450$ sq. deg. of imaging data from the Kilo Degree Survey. We employ a quadratic estimator in two and three redshift bins and extract band powers of redshift auto-correlation and cross-correlation spectra in the multipole range $76 leq ell leq 1310$. The cosmological interpretation of the measured shear power spectra is performed in a Bayesian framework assuming a $Lambda$CDM model with spatially flat geometry, while accounting for small residual uncertainties in the shear calibration and redshift distributions as well as marginalising over intrinsic alignments, baryon feedback and an excess-noise power model. Moreover, massive neutrinos are included in the modelling. The cosmological main result is expressed in terms of the parameter combination $S_8 equiv sigma_8 sqrt{Omega_{rm m}/0.3}$ yielding $S_8 = 0.651 pm 0.058$ (3 z-bins), confirming the recently reported tension in this parameter with constraints from Planck at $3.2sigma$ (3 z-bins). We cross-check the results of the 3 z-bin analysis with the weaker constraints from the 2 z-bin analysis and find them to be consistent. The high-level data products of this analysis, such as the band power measurements, covariance matrices, redshift distributions, and likelihood evaluation chains are available at http://kids.strw.leidenuniv.nl/
We study the statistics of peaks in a weak lensing reconstructed mass map of the first 450 square degrees of the Kilo Degree Survey. The map is computed with aperture masses directly applied to the shear field with an NFW-like compensated filter. We compare the peak statistics in the observations with that of simulations for various cosmologies to constrain the cosmological parameter $S_8 = sigma_8 sqrt{Omega_{rm m}/0.3}$, which probes the ($Omega_{rm m}, sigma_8$) plane perpendicularly to its main degeneracy. We estimate $S_8=0.750pm0.059$, using peaks in the signal-to-noise range $0 leq {rm S/N} leq 4$, and accounting for various systematics, such as multiplicative shear bias, mean redshift bias, baryon feedback, intrinsic alignment, and shear-position coupling. These constraints are $sim25%$ tighter than the constraints from the high significance peaks alone ($3 leq {rm S/N} leq 4$) which typically trace single-massive halos. This demonstrates the gain of information from low-S/N peaks. However we find that including ${rm S/N} < 0$ peaks does not add further information. Our results are in good agreement with the tomographic shear two-point correlation function measurement in KiDS-450. Combining shear peaks with non-tomographic measurements of the shear two-point correlation functions yields a $sim20%$ improvement in the uncertainty on $S_8$ compared to the shear two-point correlation functions alone, highlighting the great potential of peaks as a cosmological probe.
We perform a combined analysis of cosmic shear tomography, galaxy-galaxy lensing tomography, and redshift-space multipole power spectra (monopole and quadrupole) using 450 deg$^2$ of imaging data by the Kilo Degree Survey (KiDS) overlapping with two spectroscopic surveys: the 2-degree Field Lensing Survey (2dFLenS) and the Baryon Oscillation Spectroscopic Survey (BOSS). We restrict the galaxy-galaxy lensing and multipole power spectrum measurements to the overlapping regions with KiDS, and self-consistently compute the full covariance between the different observables using a large suite of $N$-body simulations. We methodically analyze different combinations of the observables, finding that galaxy-galaxy lensing measurements are particularly useful in improving the constraint on the intrinsic alignment amplitude (by 30%, positive at $3.5sigma$ in the fiducial data analysis), while the multipole power spectra are useful in tightening the constraints along the lensing degeneracy direction (e.g. factor of two stronger matter density constraint in the fiducial analysis). The fully combined constraint on $S_8 equiv sigma_8 sqrt{Omega_{rm m}/0.3} = 0.742 pm 0.035$, which is an improvement by 20% compared to KiDS alone, corresponds to a $2.6sigma$ discordance with Planck, and is not significantly affected by fitting to a more conservative set of scales. Given the tightening of the parameter space, we are unable to resolve the discordance with an extended cosmology that is simultaneously favored in a model selection sense, including the sum of neutrino masses, curvature, evolving dark energy, and modified gravity. The complementarity of our observables allows for constraints on modified gravity degrees of freedom that are not simultaneously bounded with either probe alone, and up to a factor of three improvement in the $S_8$ constraint in the extended cosmology compared to KiDS alone.
This paper is the first of a series of papers constraining cosmological parameters with weak lensing peak statistics using $sim 450~rm deg^2$ of imaging data from the Kilo Degree Survey (KiDS-450). We measure high signal-to-noise ratio (SNR: $ u$) weak lensing convergence peaks in the range of $3< u<5$, and employ theoretical models to derive expected values. These models are validated using a suite of simulations. We take into account two major systematic effects, the boost factor and the effect of baryons on the mass-concentration relation of dark matter haloes. In addition, we investigate the impacts of other potential astrophysical systematics including the projection effects of large scale structures, intrinsic galaxy alignments, as well as residual measurement uncertainties in the shear and redshift calibration. Assuming a flat $Lambda$CDM model, we find constraints for $S_{rm 8}=sigma_{rm 8}(Omega_{rm m}/0.3)^{0.5}=0.746^{+0.046}_{-0.107}$ according to the degeneracy direction of the cosmic shear analysis and $Sigma_{rm 8}=sigma_{rm 8}(Omega_{rm m}/0.3)^{0.38}=0.696^{+0.048}_{-0.050}$ based on the derived degeneracy direction of our high-SNR peak statistics. The difference between the power index of $S_{rm 8}$ and in $Sigma_{rm 8}$ indicates that combining the two probes has the potential to break the degeneracy in $sigma_{rm 8}$ and $Omega_{rm m}$. Our results are consistent with the cosmic shear tomographic correlation analysis of the same dataset and $sim 2sigma$ lower than the Planck 2016 results.
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