## Primordial Non-Gaussianity, Scale-Dependent Bias, And The Bispectrum Of Galaxies

##### 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, Phi = phi + f(NL)phi(2) + g(NL)phi(3), where phi 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(NL)(2), 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 similar to 15 relative to the previous calculation for the squeezed triangles (k(1) approximate to k(2) approximate to 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(NL)(2) can be interpreted as tau(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.