We cross-correlate large scale structure ( LSS ) observations from a number of surveys with cosmic microwave background ( CMB ) anisotropies from the Wilkinson Microwave Anisotropy Probe ( WMAP ) to investigate the Integrated Sachs-Wolfe ( ISW ) effect as a function of redshift , covering z \sim 0.1 - 2.5 .
Our main goal is to go beyond reporting detections towards developing a reliable likelihood analysis that allows one to determine cosmological constraints from ISW observations .
With this in mind we spend a considerable amount of effort in determining the redshift-dependent bias and redshift distribution ( b ( z ) \times dN / dz ) of these samples by matching with spectroscopic observations where available , and analyzing auto-power spectra and cross-power spectra between the samples .
Due to wide redshift distributions of some of the data sets we do not assume a constant bias model , in contrast to previous work on this subject .
We only use the LSS data sets for which we can extract such information reliably and as a result the data sets we use are 2-Micron All Sky Survey ( 2MASS ) samples , Sloan Digital Sky Survey ( SDSS ) photometric Luminous Red Galaxies , SDSS photometric quasars and NRAO VLA Sky Survey ( NVSS ) radio sources .
We make a joint analysis of all samples constructing a full covariance matrix , which we subsequently use for cosmological parameter fitting .
We report a 3.7 \sigma detection of ISW combining all the datasets .
We do not find significant evidence for an ISW signal at z > 1 , in agreement with theoretical expectation in \Lambda CDM model .
We combine the ISW likelihood function with weak lensing of CMB ( hereafter Paper II ( ) ) and CMB power spectrum to constrain the equation of state of dark energy and the curvature of the Universe .
While ISW does not significantly improve the constraints in the simplest 6-parameter flat \Lambda CDM model , it improves constraints on 7-parameter models with curvature by a factor of 3.2 ( relative to WMAP alone ) to \Omega _ { K } = -0.004 ^ { +0.014 } _ { -0.020 } , and with dark energy equation of state by 15 % to w = -1.01 ^ { +0.30 } _ { -0.40 } [ posterior median with ‘ ‘ 1 \sigma ’ ’ ( 16th–84th percentile ) range ] .
A software package for calculating the ISW likelihood function can be downloaded at http : //www.astro.princeton.edu/~shirley/ISW_WL.html .