= Galaxy bispectrum
{title2=$B_g(k_1,k_2,k_3)$}
The <galaxy bispectrum> measures the connected three-point correlation of the <Fourier modes> of the <galaxy density contrast>. For a mean-zero field, <statistical homogeneity> gives
$$
\langle\delta_g(\mathbf k_1)\delta_g(\mathbf k_2)\delta_g(\mathbf k_3)\rangle_c
=(2\pi)^3\delta^{(3)}(\mathbf k_1+\mathbf k_2+\mathbf k_3)
B_g(\mathbf k_1,\mathbf k_2,\mathbf k_3).
$$
The delta function enforces a closed <wavevector> triangle. With the additional assumption of <statistical isotropy>, one can write $B_g(k_1,k_2,k_3)$ as a function of triangle size and shape. <Statistical homogeneity> alone leaves possible orientation dependence.
The <galaxy bispectrum> adds information beyond the <power spectrum>. For example, take a zero-mean <Gaussian random field> $\delta$ and a local tracer model $\delta_g=b_1\delta+(b_2/2)(\delta^2-\langle\delta^2\rangle)$. Two <Wick contractions> at each quadratic insertion cancel its factor of two, yielding at leading order
$$
B_g=b_1^2b_2[P(k_1)P(k_2)+P(k_2)P(k_3)+P(k_3)P(k_1)].
$$
Thus nonlinear <galaxy bias> can generate a three-point signal even from Gaussian matter fluctuations. Nonlinear gravitational evolution supplies a further matter-bispectrum contribution. Both effects must be modeled before interpreting a measured <galaxy> three-point signal as <primordial non-Gaussianity>.<Large-Scale Structure of the Universe and Cosmological Perturbation Theory by F. Bernardeau and others>[Sections 3.2.4, 4.1.3 and 7.1: higher correlations, gravity-induced bispectrum and bias]{ref}
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