Alizadeh, Esfandiar and Hirata, Christopher M. (2012) How to detect gravitational waves through the cross correlation of the galaxy distribution with the CMB polarization. Physical Review D, 85 (12). Art. No. 123540. ISSN 1550-7998 http://resolver.caltech.edu/CaltechAUTHORS:20120723-120732250
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Thompson scattering of cosmic microwave background (CMB) photons off of free electrons during the reionization epoch induces a correlation between the distribution of galaxies and the polarization pattern of the CMB, the magnitude of which is proportional to the quadrupole moment of radiation at the time of scattering. Since the quadrupole moment generated by gravitational waves (GWs) gives rise to a different polarization pattern than that produced by scalar modes, one can put interesting constraints on the strength of GWs on large scales by cross correlating the small scale galaxy distribution and CMB polarization. We use this method together with Fisher analysis to predict how well future surveys can measure the tensor-to-scalar ratio r. We find that with a future CMB experiment with detector noise Δ_P = 2 µK-arcmin and a beam width θ_(FWHM) = 2' and a future galaxy survey with limiting magnitude I < 25.6 one can measure the tensor-to-scalar ratio with an error σ_r ≃ 0.09. To measure r ≈ 0.01, however, one needs Δ_P ≃ 0.5 µK-arcmin and θ_(FWHM) ≃ 1'. We also investigate a few systematic effects, none of which turn out to add any biases to our estimators, but they increase the error bars by adding to the cosmic variance. The incomplete sky coverage has the most dramatic effect on our constraints on r for large sky cuts, with a reduction in signal-to-noise smaller than one would expect from the naive estimate (S/N)^2 ∝ f_(sky). Specifically, we find a degradation factor of f_(deg) = 0.32 ± 0.01 for a sky cut of |b| > 10° (f_(sky) = 0.83) and f_(deg) = 0.056 ± 0.004 for a sky cut of |b| > 20° (f_(sky) = 0.66). Nonetheless, given that our method has different systematics than the more conventional method of observing the large scale B modes directly, it may be used as an important check in the case of a detection.
|Additional Information:||© 2012 American Physical Society. Received 29 February 2012; published 26 June 2012. E. A. and C.H. were supported by the U.S. Department of Energy (DE-FG03-92-ER40701). C.H. is also supported by the National Science Foundation (AST-0807337) and David & Lucile Packard Foundation. E.A. acknowledges support from the National Science Foundation (Grant No. AST 07-08849) during part of this work. He thanks Laura Book and BenWandelt for their help and Avi Loeb and John Kovac for useful conversations.|
|Classification Code:||PACS: 98.80.-k; 95.85.Sz; 98.70.Vc|
|Official Citation:||Alizadeh, E. and C. M. Hirata (2012). "How to detect gravitational waves through the cross correlation of the galaxy distribution with the CMB polarization." Physical Review D 85(12): 123540.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Aucoeur Ngo|
|Deposited On:||23 Jul 2012 20:22|
|Last Modified:||26 Dec 2012 15:41|
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