### Abstract

The three-point correlation function of cosmological fluctuations is a sensitive probe of the physics of inflation. We calculate the bispectrum, B _{g} (k _{1}, k _{2}, k _{3}), Fourier transform of the three-point function of density peaks (e.g., galaxies), using two different methods: the Matarrese-Lucchin-Bonometto formula and the locality of galaxy bias. The bispectrum of peaks is not only sensitive to that of the underlying matter density fluctuations, but also to the four-point function. For a physically motivated, local form of primordial non-Gaussianity in the curvature perturbation, Φ = φ + f _{NL}φ^{2} + g _{NL}φ^{3}, where φ is a Gaussian field, we show that the galaxy bispectrum contains five physically distinct pieces: (1) non-linear gravitational evolution, (2) non-linear galaxy bias, (3) f _{NL}, (4) f ^{2} _{NL}, and (5) g _{NL}. While (1), (2), and a part of (3) have been derived in the literature, (4) and (5) are derived in this paper for the first time. We also find that, in the high-density peak limit, (3) receives an enhancement of a factor of 15 relative to the previous calculation for the squeezed triangles (k _{1} k _{2} ≫ k _{3}). Our finding suggests that the galaxy bispectrum is more sensitive to f _{NL} than previously recognized, and is also sensitive to a new term, g _{NL}. For a more general form of local-type non-Gaussianity, the coefficient f ^{2} _{NL} can be interpreted as τ_{NL}, which allows us to test multi-field inflation models using the relation between the three- and four-point functions. The usual terms from Gaussian initial conditions, (1) and (2), have the smallest signals in the squeezed configurations, while the others have the largest signals; thus, we can distinguish them easily. We cannot interpret the effects of f _{NL} on B_{g} (k _{1}, k _{2}, k _{3}) as a scale-dependent bias, and thus replacing the linear bias in the galaxy bispectrum with the scale-dependent bias known for the power spectrum results in an incorrect prediction. As the importance of primordial non-Gaussianity relative to the non-linear gravity evolution and galaxy bias increases toward higher redshifts, galaxy surveys probing a high-redshift universe are particularly useful for probing the primordial non-Gaussianity.

Original language | English (US) |
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Pages (from-to) | 1230-1248 |

Number of pages | 19 |

Journal | Astrophysical Journal |

Volume | 703 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2009 |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Astrophysical Journal*,

*703*(2), 1230-1248. https://doi.org/10.1088/0004-637X/703/2/1230