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Published March 15, 2000 | Published
Journal Article Open

Cosmic microwave background bispectrum and inflation


We derive an expression for the non-Gaussian cosmic microwave background (CMB) statistic Il3 defined recently by Ferreira, Magueijo, and Górski in terms of the slow-roll-inflation parameters ε and η. This result shows that a nonzero value of Il3 in COBE would rule out single-field slow-roll inflation. A sharp change in the slope of the inflaton potential could increase the predicted value of Il3, but not significantly. This further suggests that it will be difficult to account for such a detection in multiple-field models in which density perturbations are produced by quantum fluctuations in the scalar field driving inflation. An Appendix shows how to evaluate an integral that is needed in our calculation as well as in more general calculations of CMB bispectra.

Additional Information

© 2000 The American Physical Society. Received 5 August 1999; published 22 February 2000. We thank R. Friedberg for suggesting the recursive technique for evaluating integrals with oscillatory integrands. We thank K. Gorski, A. Kosowsky, J. Lesgourges, J. Magueijo, and L. Verde for useful comments and discussions. This work was supported by the DOE Outstanding Junior Investigator program, DE-FG02-92ER40699, NASA grant NAG5-3091, and the Alfred P. Sloan Foundation.

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