Evidence for the accelerated expansion of the Universe from weak lensing tomography with COSMOS

TL;DR

This work presents a tomographic weak-lensing analysis of the COSMOS field using a state-of-the-art PSF and CTI correction scheme, PCA-based PSF modeling, and photometric redshifts to partition galaxies into redshift bins. By deriving a covariance from 288 Millennium Simulation realizations and calibrating non-linear power corrections, the authors obtain robust 3D cosmological constraints that are consistent with WMAP-5, including a flat LCDM result of $\sigma_8(\Omega_m/0.3)^{0.51}=0.75\pm0.08$ and joint parameters $\Omega_m=0.266^{+0.025}_{-0.023}$, $\sigma_8=0.802^{+0.028}_{-0.029}$. In a general non-flat LCDM analysis they find $q_0<0$ at $\sim94$–$96\%$ confidence, providing independent evidence for accelerated expansion; in flat $w$CDM they constrain $w<-0.41$ at 90% conf. While limited by COSMOS area, the study demonstrates the viability and power of space-based tomographic weak lensing for probing dark energy and cosmic acceleration, and highlights the need for improved non-linear and baryonic corrections for future surveys. The results are reinforced by cross-checks showing vanishing B-modes and strong agreement with external cosmological probes.

Abstract

We present a tomographic cosmological weak lensing analysis of the HST COSMOS Survey. Applying our lensing-optimized data reduction, principal component interpolation for the ACS PSF, and improved modelling of charge-transfer inefficiency, we measure a lensing signal which is consistent with pure gravitational modes and no significant shape systematics. We carefully estimate the statistical uncertainty from simulated COSMOS-like fields obtained from ray-tracing through the Millennium Simulation. We test our pipeline on simulated space-based data, recalibrate non-linear power spectrum corrections using the ray-tracing, employ photometric redshifts to reduce potential contamination by intrinsic galaxy alignments, and marginalize over systematic uncertainties. We find that the lensing signal scales with redshift as expected from General Relativity for a concordance LCDM cosmology, including the full cross-correlations between different redshift bins. For a flat LCDM cosmology, we measure sigma_8(Omega_m/0.3)^0.51=0.75+-0.08 from lensing, in perfect agreement with WMAP-5, yielding joint constraints Omega_m=0.266+0.025-0.023, sigma_8=0.802+0.028-0.029 (all 68% conf.). Dropping the assumption of flatness and using HST Key Project and BBN priors only, we find a negative deceleration parameter q_0 at 94.3% conf. from the tomographic lensing analysis, providing independent evidence for the accelerated expansion of the Universe. For a flat wCDM cosmology and prior w in [-2,0], we obtain w<-0.41 (90% conf.). Our dark energy constraints are still relatively weak solely due to the limited area of COSMOS. However, they provide an important demonstration for the usefulness of tomographic weak lensing measurements from space. (abridged)

Figures (25)

• Figure 1: Relation between the mean photometric redshift and $i_{814}$ magnitude for COSMOS, HUDF, and HDF-N, where the error-bars indicate the error of the mean assuming Gaussian scatter and neglecting sampling variance. The best fit (\ref{['eq:zmag']}) to the COSMOS data from $i_{814}<25$ is shown as the bold line, whereas the thin lines indicate the conservative $10\%$ uncertainty considered for the extrapolation in the cosmological analysis. The HDF-N data agree with the relation very well, whereas the mean redshifts are higher in the HUDF both for $i_{814}<25$ and $i_{814}>25$, demonstrating the influence of sampling variance in such small fields.
• Figure 2: Redshift histogram for galaxies in our shear catalogue with COSMOS-30 photo-$z$s (dotted), split into four magnitude bins. The solid curves show the fit according to (\ref{['eq:zmag']}) and (\ref{['eq:zdist_tim']}), which is capable to describe both the peak and high redshift tail.
• Figure 3: Combined redshift histogram for the HDF-N and HUDF photo-$z$s, split into two magnitude bins. The solid curves show the prediction according to (\ref{['eq:zmag']}), (\ref{['eq:zdist_tim']}) and the galaxy magnitude distribution. The good agreement for $25<i_{814}<27$ galaxies confirms the applicability of the model in this magnitude regime.
• Figure 4: Decomposition of the shear field into E- and B-modes using the shear correlation function $\xi_{E/B}$ (left), aperture mass dispersion $\langle M_\mathrm{ap/\perp}^2 \rangle$ (middle), and ring statistics $\langle\mathcal{R} \mathcal{R} \rangle_{E/B}$ (right). Error-bars have been computed from 300 bootstrap resamples of the shear catalogue, accounting for shape and shot noise, but not for sampling variance. The solid curves indicate model predictions for $\sigma_8=(0.7,0.8)$. In all cases the B-mode is consistent with zero, confirming the success of our correction for instrumental effects. For $\xi_{E/B}$ the E/B-mode decomposition is model-dependent, where we have assumed $\sigma_8=0.8$ for the points, while the dashed curves have been computed for $\sigma_8=(0.7,0.9)$. The dotted curves indicate the signal if the residual ellipticity correction discussed in App.\ref{['se:wl:galcor']} is not applied, yielding nearly unchanged results. Note that the correlation between points is strongest for $\xi_{E/B}$ and weakest for $\langle\mathcal{R} \mathcal{R} \rangle_{E/B}$.
• Figure 5: Cross-correlation between galaxy shear estimates and uncorrected stellar ellipticities as defined in (\ref{['eq:xisys']}). The signal is consistent with zero if the residual ellipticity correction discussed in App.\ref{['se:wl:galcor']} is applied (circles). Even without this correction (triangles) it is at a level negligible compared to the expected cosmological signal (dotted curves), except for the largest scales, where the error-budget is anyway dominated by sampling variance.