Primordial non-Gaussianity, scale-dependent bias, and the bispectrum of
  galaxies
  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, we show that the galaxy bispectrum contains five physically
distinct pieces: (i) non-linear gravitational evolution, (ii) non-linear galaxy
bias, (iii) f_nl, (iv) f_nl^2, and (v) \gnl. While (i), (ii), and a part of
(iii) have been derived in the literature, (iv) and (v) are derived in this
paper for the first time. 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 \fnl^2 can be interpreted as \tau_nl, which allows us to test
multi-field inflation models. The usual terms from Gaussian initial conditions,
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.
