KiDS-450: Cosmological parameter constraints from tomographic weak gravitational lensing (1606.05338v2)

Abstract: 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 $S_8\equiv\sigma_8\sqrt{\Omega_{\rm m}/0.3}=0.745\pm0.039$. 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 improvedself-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.

• The paper employs a tomographic approach dividing nearly 15 million galaxies into redshift bins to constrain cosmological parameters within a flat ΛCDM model.
• The study refines shear measurements using an improved lensfit calibration combined with multiple photometric redshift methods.
• The analysis reports S8 = 0.745 ± 0.039, highlighting a 2.3σ tension with Planck results and emphasizing the challenges of systematic uncertainties.

Cosmological Parameter Constraints from KiDS-450 Using Tomographic Weak Gravitational Lensing

The research presented in this paper explores the cosmological constraints derived from the weak gravitational lensing analysis of the Kilo Degree Survey (KiDS) 450-square-degree dataset. The authors employ a tomographic approach, utilizing imaging data to examine the large-scale structure of the universe over several redshift bins. This analysis aims to refine our understanding of key cosmological parameters within the context of a flat ΛCDM model.

Methodology and Analysis

Key to this paper is the use of tomographic techniques to divide the source galaxies into four redshift bins, providing a more detailed three-dimensional map of the mass distribution in the universe. The weak lensing effect, which causes small distortions in the shapes of background galaxies due to foreground mass concentrations, is quantified using the ellipticity measurements from nearly 15 million galaxies. These measurements are corrected for systematic biases using a refined version of the lensfit algorithm, which incorporates a new self-calibrating method validated against image simulations.

The cosmological parameters are derived from the two-point shear correlation functions, which are sensitive to the amplitude and growth of structure in the universe. The shear correlation function is decomposed into contributions from cosmic shear (E-mode), intrinsic alignments (II and GI modes), and potential systematic B-mode contributions. The analysis accounts for various systematic errors, including the influence of photometric redshift errors, intrinsic galaxy alignments, and the impact of baryon feedback on the non-linear matter power spectrum.

Key Results

This paper yields a measurement of the parameter combination $$S_8 \equiv \sigma_8 \sqrt{\Omega_{\rm m}/0.3} = 0.745 \pm 0.039$$. The result indicates a significant tension with the Planck 2015 results, standing at 2.3 standard deviations. This tension continues the discrepancy seen in similar studies, such as those with CFHTLenS and other low-redshift probes. However, the results align well with other recent lensing constraints and pre-Planck CMB results.

The analysis highlights several systematic investigations, including three photometric redshift calibration methods—weighted direct calibration (DIR), angular cross-correlations (CC), and re-calibration of photometric $P(z)$ (BOR). All methods yield consistent cosmological constraints, suggesting robustness against systematic uncertainties in the redshift calibration. Additionally, the impact of intrinsic alignments is constrained to $A_{\rm IA} = 1.10 \pm 0.64$, contrasting with earlier studies reporting a negative amplitude.

Implications and Future Directions

These findings provide an essential contribution to ongoing cosmological research, underscoring the need for further insights into the tension between cosmic shear surveys and Planck's CMB measurements. The paper also emphasizes the importance of accounting for systematic errors, particularly in photometric redshift calibration, to achieve reliable cosmological insights.

As the KiDS survey continues, with further data acquisitions and enhancements in photometric calibration through the inclusion of VIKING data, more precise and detailed results can be anticipated. These improvements will help refine the cosmic shear technique and address systematic challenges, including the source of residual B-modes. Ultimately, such advancements will be crucial for elucidating whether the current tension with Planck is due to systematic errors, or if it points towards new physics beyond the standard cosmological model.

Moreover, this work sets the stage for future collaborations between large-scale structure surveys, CMB observations, and other cosmological probes. Such concerted efforts will be vital to unravel the mysteries of the universe's composition and evolution, helping to achieve a more coherent cosmological framework.