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Magnification-Temperature Correlation: the Dark Side of ISW Measurements

Integrated Sachs-Wolfe (ISW) measurements, which involve cross-correlating the CMB with the foreground large-scale structure (e.g. galaxies/quasars), have proven to be an interesting probe of dark energy. We show that magnification bias, which is the inevitable modulation of the foreground number counts by gravitational lensing, alters both the shape and amplitude of the observed ISW signal. This is true especially at high redshifts because (1) the intrinsic galaxy-temperature signal diminishes greatly back in the matter dominated era, (2) the lensing efficiency increases with redshift and (3) the number count slope generally steepens with redshift in a magnitude limited sample. At z >~ 2, the magnification-temperature correlation dominates over the intrinsic galaxy-temperature correlation and causes the observed ISW signal to increase with z, despite dark energy subdominance -- a result of the fact that magnification probes structures between the observer and the sources. Ignoring magnification bias can then lead to erroneous conclusions about dark energy. While the lensing modulation opens up an interesting high z window for ISW measurements, high z measurements are not expected to add much new information to low z ones if dark energy is the cosmological constant. This is because lensing introduces significant covariance across redshifts. The most compelling reason to pursue high z ISW measurements is to look for a potential surprise such as early dark energy domination or the signature of modified gravity. We conclude with a discussion of existing measurements, the highest z of which is at the margin of being sensitive to magnification bias. We also develop a formalism which might be of general interest: to predict biases in estimating parameters when certain physical effects are ignored in interpreting data.

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