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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 givesThe 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 ${\delta }_g=b_1\delta +(b_2/2)({\delta }^2-⟨{\delta }^2⟩)$. Two Wick contractions at each quadratic insertion cancel its factor of two, yielding at leading orderThus 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.^[ref]

For nonzero momentum, the Fourier transform of the local bias expansion isThe subtracted variance contributes only at $\mathbf{k}=0$. Because $\delta$ is a Gaussian random field, its three-point function vanishes and its four-point function factorizes by Wick theorem. At leading order one of the three galaxy fields supplies the quadratic term and the other two supply linear terms. The two cross-contractions cancel the factor $1/2$, givingThus even Gaussian matter fluctuations acquire a nonzero galaxy bispectrum through local quadratic galaxy bias.