The last stand before MAP: cosmological parameters from lensing, CMB and galaxy clustering

TL;DR

This work treats weak lensing as a first-class cosmological probe alongside CMB and galaxy clustering, performing a joint analysis with a 9-parameter grid to extract constraints from CMB, 2dF, and RCS lensing data. It computes lensing observables via $\langle M_{ m ap}^2(\theta)\rangle$ and $P_{\kappa}(\ell)$ using nonlinear $P^{\rm nl}_\delta(k,z)$ mapped from linear theory, incorporating a detailed treatment of source redshift distributions. The main result is a largely consistent flat $\Lambda$CDM picture from CMB+LSS, with hints of reionization around $z\sim 8$, but the inclusion of lensing data raises $\sigma_8$ to about $0.92$ and reduces $\Omega_\\Lambda$, generating tension between datasets and highlighting the critical role of power-spectrum normalization. The paper also scrutinizes the precision of error bars relative to Fisher predictions, suggesting the need for cross-checks and forecasting with MAP-era data to assess the realism of cosmological parameter inferences.

Abstract

Cosmic shear measurements have now improved to the point where they deserve to be treated on par with CMB and galaxy clustering data for cosmological parameter analysis, using the full measured aperture mass variance curve rather than a mere phenomenological parametrization thereof. We perform a detailed 9-parameter analysis of recent lensing (RCS), CMB (up to Archeops) and galaxy clustering (2dF) data, both separately and jointly. CMB and 2dF data are consistent with a simple flat adiabatic scale-invariant model with Omega_Lambda=0.72+/-0.09, omega_cdm=0.115+/- 0.013, omega_b=0.024+/-0.003, and a hint of reionization around z~8. Lensing helps further tighten these constraints, but reveals tension regarding the power spectrum normalization: including the RCS survey results raises sigma8 significantly and forces other parameters to uncomfortable values. Indeed, sigma8 is emerging as the currently most controversial cosmological parameter, and we discuss possible resolutions of this sigma8 problem. We also comment on the disturbing fact that many recent analyses (including this one) obtain error bars smaller than the Fisher matrix bound. We produce a CMB power spectrum combining all existing experiments, and using it for a "MAP versus world" comparison next month will provide a powerful test of how realistic the error estimates have been in the cosmology community.

Figures (10)

• Figure 1: CMB data used in our analysis. Error bars do not include calibration or beam errors which allow substantial vertical shifting and tilting for some experiments (these effects are included in our analysis).
• Figure 2: Combination of data from Figure \ref{['cmbdataFig']}. These error bars include the effects of beam and calibration uncertainties, which cause long-range correlations of order 10% over the peaks. In addition, points tend to be anti-correlated with their nearest neighbors, typically at the level of 10-20%. The curve shows our model best fitting CMB+LSS data (second last column in Table 2).
• Figure 3: 2dF galaxy power spectrum data used. We include only points leftward of the dotted line (with $k<0.3h/Mpc$) in our analysis to stay in the linear regime. The curve shows our model best fitting CMB+LSS data (second last column in Table 2).
• Figure 4: Lensing data used in our analysis. The two curves show our best fit model excluding (bottom) and including (top) lensing data.
• Figure 5: Constraints on individual parameters using only CMB information. The quoted $1-\sigma$ and $2-\sigma$ confidence limits are where each curve drops below the horizontal dashed lines $e^{-1^2/2}\approx 0.61$ and $e^{-2^2/2}\approx 0.14$, respectively.