= Scale-dependent halo bias from local non-Gaussianity
{title2=$\Delta b(k)=2f_{\rm NL}\delta_c b_L/\alpha(k)$}
For a universal abundance depending on <halo peak height>, the <peak-background split> gives a potential-response coefficient $b_\varphi=2f_{\rm NL}\delta_c b_L$, with $b_L$ the <linear Lagrangian halo bias>. If $\delta=\alpha(k)\varphi$, the corresponding deterministic <galaxy bias> correction is $\Delta b=b_\varphi/\alpha(k)$, proportional to $k^{-2}$ on sufficiently large scales. For a physical Eulerian tracer, $b_E=1+b_L$, so $b_\varphi=2f_{\rm NL}\delta_c(b_E-1)$. The deterministic tracer <power spectrum> is $(b_E+\Delta b)^2P_m$; it remains nonnegative even if a negative correction changes the sign of the tracer-matter correlation.
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