Halo clustering with nonlocal non-Gaussianity
We show how the peak-background split (PBS) can be generalized to predict the effect of nonlocal primordial non-Gaussianity on the clustering of halos. Our approach is applicable to arbitrary primordial bispectra. We show that the scale dependence of halo clustering predicted in the peak-background split agrees with that of the local-biasing model on large scales. On smaller scales, k ≳ 0:01h Mpc^(-1), the predictions diverge, a consequence of the assumption of separation of scales in the peak-background split. Even on large scales, PBS and local biasing do not generally agree on the amplitude of the effect outside of the high-peak limit. The scale dependence of the biasing—the effect that provides strong constraints to the local-model bispectrum—is far weaker for the equilateral and self-ordering-scalar-field models of non-Gaussianity. The bias scale dependence for the orthogonal and folded models is weaker than in the local model (~k^(-1)), but likely still strong enough to be constraining.We show that departures from scale-invariance of the primordial power spectrum may lead to order-unity corrections, relative to predictions made assuming scale-invariance—to the non-Gaussian bias in some of these nonlocal models for non-Gaussianity. An Appendix shows that a nonlocal model can produce the local-model bispectrum, a mathematical curiosity we uncovered in the course of this investigation.
Additional Information© 2010 American Physical Society. Received 6 August 2010; published 5 November 2010. We would like to thank Neal Dalal, Olivier Doré, Lam Hui, Donghui Jeong, Román Scoccimarro, and Sarah Shandera for enlightening discussions. This work was supported by DOE DE-FG03-92-ER40701, NASA NNX10AD04G, and the Gordon and Betty Moore Foundation.
Published - Schmidt2010p11991Phys_Rev_D.pdf