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A bias expansion relates the density of selected tracers to the matter distribution using allowed combinations of density contrast, tidal effects, spatial derivatives and stochastic contributions. For example, ${\delta }_g=b_1\delta +\frac{1}{2}{b}_2({\delta }^2-⟨{\delta }^2⟩)+\cdots$ illustrates a local part. The coefficients encode tracer-formation physics. Including further allowed operators makes the expansion systematically improvable on sufficiently large scales.^[ref]

Galaxy bias describes the statistical relation between fluctuations in galaxy counts and the underlying matter density contrast. In the simplest large-scale limit, ${\delta }_g=b_1{\delta }_m$, so the corresponding deterministic power spectrum is $b_1^2{P}_m$. Different selections can have different $b_1$ because they sample different formation environments. More generally, the bias expansion includes nonlinear, tidal and stochastic terms, so a single multiplicative constant is an approximation.^[ref]