Non-Gaussian Halo Bias Beyond the Squeezed Limit

Primordial non-Gaussianity, in particular the coupling of modes with widely different wavelengths, can have a strong impact on the large-scale clustering of tracers through a scale-dependent bias with respect to matter. We demonstrate that the standard derivation of this non-Gaussian scale-dependent bias is in general valid only in the extreme squeezed limit of the primordial bispectrum, i.e. for clustering over very large scales. We further show how the treatment can be generalized to describe the scale-dependent bias on smaller scales, without making any assumptions on the nature of tracers apart from a dependence on the small-scale fluctuations within a finite region. If the leading scale-dependent bias \Delta b \propto k^{\alpha}, then the first subleading term will scale as k^{\alpha+2}. This correction typically becomes relevant as one considers clustering over scales k >~ 0.01 h Mpc^{-1}.