Optimal ISW detection and joint likelihood for cosmological parameter estimation

Abstract

We analyse the local variance effect in the standard method for detecting the integrated Sachs-Wolfe effect (ISW) via cross-correlating the cosmic microwave background (CMB) with the large-scale structure (LSS). Local variance is defined as the systematic noise in the ISW detection that originates in the realisation of the matter distribution in the observed Universe. We show that the local variance contributes about 11 per cent to the total variance in the standard method, if a perfect and complete LSS survey up to z ~ 2 is assumed. Due to local variance, the estimated detection significance and cosmological parameter constraints in the standard method are biased. In this work, we present an optimal method of how to reduce the local variance effect in the ISW detection by working conditional on the LSS-data. The variance of the optimal method, and hence the signal-to-noise ratio, depends on the actual realisation of the matter distribution in the observed Universe. We show that for an ideal galaxy survey, the average signal-to-noise ratio is enhanced by about 7 per cent in the optimal method, as compared to the standard method. Furthermore, in the optimal method there is no need to estimate the covariance matrix by Monte Carlo simulations as in the standard method, which saves time and increases the accuracy. Finally, we derive the correct joint likelihood function for cosmological parameters given CMB- and LSS-data within the linear LSS formation regime, which includes a small coupling of the two datasets due to the ISW effect.

Proof added to appendix. Minor changes to text and formulae. Results and figures unchanged. Matches published MNRAS version

References in corpus (39)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Efficient Computation of CMB anisotropies in closed FRW models
• Cosmological parameters from SDSS and WMAP
• The 2dF Galaxy Redshift Survey: Power-spectrum analysis of the final dataset and cosmological implications
• A Line of Sight Approach to Cosmic Microwave Background Anisotropies
• The Sixth Data Release of the Sloan Digital Sky Survey
• 2MASS Extended Source Catalog: Overview and Algorithms
• Mass Reconstruction with CMB Polarization
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Parameter Estimation Methodology
• A correlation of the cosmic microwave sky with large scale structure
• Correlation of CMB with large-scale structure: I. ISW Tomography and Cosmological Implications
• Looking for $\Lambda$ with the Rees-Sciama Effect
• Detection of the ISW and SZ effects from the CMB-Galaxy correlation
• Wiener Reconstruction of The Large Scale Structure
• Cross-Correlation of the Cosmic Microwave Background with the 2MASS Galaxy Survey: Signatures of Dark Energy, Hot Gas, and Point Sources
• The 2dF Galaxy Redshift Survey: Spherical Harmonics analysis of fluctuations in the final catalogue
• Integrated Sachs-Wolfe effect from the cross correlation of WMAP3 year and the NRAO VLA sky survey data: New results and constraints on dark energy
• Differentiating between Modified Gravity and Dark Energy
• Testing Gravity Against Early Time Integrated Sachs-Wolfe Effect
• Mapping the Dark Matter through the CMB Damping Tail
• Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization
• Measurement of the gravitational potential evolution from the cross-correlation between WMAP and the APM Galaxy survey
• Cross-correlation of the CMB and radio galaxies in real, harmonic and wavelet spaces: detection of the integrated Sachs-Wolfe effect and dark energy constraints
• Wiener Reconstruction of Density, Velocity, and Potential Fields from All-Sky Galaxy Redshift Surveys
• Integrated Sachs-Wolfe effect in Cross-Correlation: The Observer's Manual
• Error analysis in cross-correlation of sky maps: application to the ISW detection
• Detection of the ISW effect and corresponding dark energy constraints
• Detection of the ISW effect and corresponding dark energy constraints made with directional spherical wavelets
• The 2dF Galaxy Redshift Survey: Wiener Reconstruction of the Cosmic Web
• A reassessment of the evidence of the Integrated Sachs-Wolfe effect through the WMAP-NVSS correlation
• The integrated Sachs-Wolfe Effect -- Large Scale Structure Correlation
• Tracking Dark Energy with the ISW effect: short and long-term predictions
• Correlations Between the Cosmic X-ray and Microwave Backgrounds: Constraints on a Cosmological Constant
• A Detection of the Integrated Sachs-Wolfe Effect
• Magnification-Temperature Correlation: the Dark Side of ISW Measurements
• Detectability of a phantom-like braneworld model with the integrated Sachs-Wolfe effect
• Implementation of a Fourier Matched Filter in CMB Analyses. Application to ISW Studies
• Isolating the decay rate of cosmological gravitational potential
• Cross-Correlation analysis of WMAP and EGRET in Wavelet Space

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