KiDS-450: The tomographic weak lensing power spectrum and constraints on cosmological parameters (1706.02892v2)

Abstract: 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 $3.2\sigma$ (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/

Essay on "KiDS-450: The Tomographic Weak Lensing Power Spectrum and Constraints on Cosmological Parameters"

The paper "KiDS-450: The Tomographic Weak Lensing Power Spectrum and Constraints on Cosmological Parameters" presents a comprehensive analysis of weak gravitational lensing using data from the Kilo Degree Survey (KiDS-450), which encompasses 450 square degrees of imaging data. The paper aims to measure the shear power spectrum—a crucial observational artifact caused by the bending of light from distant galaxies by intervening mass—which is used to infer cosmological parameters. The methodology integrates a quadratic estimator approach across multiple redshift bins to extract shear power spectra, applying advanced Bayesian techniques for cosmological interpretation.

Methodology and Approach

The authors employ a quadratic estimator method, which is a statistical tool adept at handling large datasets with complex survey geometry without correlation issues that can arise in real-space correlation function approaches. This framework efficiently measures the shear power spectrum in both two and three tomographic redshift bins. The paper includes detailed theoretical background necessary for interpreting the weak lensing power spectra and emphasizes the integration of massive neutrino models and known systematics such as intrinsic alignments and baryon feedback into their model.

Numerical Results

The paper reports a measured value for the parameter combination $S_8 \equiv \sigma_8 \sqrt{\Omega_{\rm m}/0.3}$, which amounts to $S_8 = 0.651 \pm 0.058$ for the three redshift bins. This result is insightful as it confirms a considerable tension—at the level of $3.2\sigma$—with measurements from the Planck satellite, which is a pivotal finding in cosmology. Such tensions potentially point to nuances in the underlying assumptions or the physics of the standard model of cosmology ($\Lambda$CDM).

Implications and Future Developments

The implications of this analysis touch upon both observational and theoretical cosmology. Firstly, the tension with the Planck measurements could suggest deviations from the standard $\Lambda$CDM model, warranting further examination into extensions that incorporate new physics such as varying neutrino masses or alternative dark energy models. Secondly, the methodology itself could set a precedent for analyzing future surveys, such as LSST or Euclid, offering a robust alternative to correlation function techniques.

Robustness and Systematics

The paper meticulously addresses various sources of systematic uncertainties. The authors implement cross-checks using different redshift bin settings and account for multiplicative shear biases. Notably, the treatment of potential excess noise illustrates the operational rigor in ensuring measurement fidelity. The paper sets strong grounds for confidence in the extracted cosmological insights, despite the identified systematic concerns which are diligently managed.

Speculation on Future AI Role

Looking forward, advances in AI might revolutionize the data processing and analysis paradigms employed in weak lensing surveys. Machine learning algorithms could enhance the calibration of systematic effects or automate the detection and interpretation of power spectrum anomalies, thereby refining the accuracy of cosmological inferences drawn from such surveys.

In conclusion, K\"ohlinger et al.'s paper represents a significant contribution to the domain of cosmic shear studies and cosmological parameter estimation. It thoughtfully integrates sophisticated statistical methods and robust systematic mitigation strategies, offering insights that challenge prevailing cosmological models and guide future observational strategies.