= Absence of primordial scale-dependent halo bias in single-clock inflation
In an attractor with one adiabatic clock, the leading squeezed <primordial bispectrum> is the response to a coordinate dilation. Holding a halo's physical mass and smoothing scale fixed cancels this dilation in its abundance response. Thus the consistency-relation term does not generate the physical $k^{-2}$ <scale-dependent halo bias from local non-Gaussianity>. For example, a <top-hat filter> of fixed physical radius has coordinate radius $R_c=e^{-\zeta_L}R_0$, while the short <density contrast> is $\delta_s(\mathbf x)=\delta_s^{(0)}(e^{\zeta_L}\mathbf x)$. The substitution $\mathbf y=e^{\zeta_L}\mathbf x$ shows that its normalized average over $|\mathbf x|<R_c$ equals the original average over $|\mathbf y|<R_0$. Genuine local effects start at two spatial derivatives of the long mode. Non-attractor backgrounds or nonstandard initial states need not satisfy this argument.
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