Primordial Non-gaussianity, Scale-dependent Bias, and the Bispectrum of Galaxies

The three-point correlation function of cosmological fluctuations is a sensitive probe of the physics of inflation. We calculate the bispectrum, Bg(k1, k2, k3), Fourier transform of the three-point function of density peaks (e.g., galaxies), using the Matarrese-Lucchin-Bonometto formula. 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 form of primordial non-Gaussianity in the curvature perturbation, Φ = φ+fNLφ +gNLφ , where φ is a Gaussian field, we show that the galaxy bispectrum contains five physically distinct pieces: (i) non-linear gravitational evolution, (ii) non-linear galaxy bias, (iii) fNL, (iv) f 2 NL, and (v) gNL. While (i), (ii), and (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 fNL than previously recognized, and is also sensitive to a new term, gNL. The usual terms from Gaussian initial conditions, (i) and (ii), have the smallest signals in the squeezed configurations (k1 ≈ k2 ≫ k3), while the others have the largest signals; thus, we can distinguish them easily. We cannot interpret the effects of fNL on Bg(k1, k2, k3) 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. Subject headings: cosmology : theory — large-scale structure of universe