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A sufficiently long adiabatic tensor mode acts locally as an anisotropic change of spatial coordinates. Write the spatial metric as $a^2(e^{\gamma }{)}_{ij}$, with ${\gamma }_{ij}={ϵ}_{ij}^s{\gamma }^s$ transverse and trace-free. Removing a constant long mode maps the short wavevector to ${\tilde{k}}_i=k_i-{\gamma }_{ij}{k}_j/2$ at first order. The trace-free deformation has no first-order volume Jacobian, so its effect on an isotropic scalar power spectrum isCorrelating this response with the long graviton givesThe prime removes the momentum-conserving $(2\pi {)}^3{\delta }^3(\sum \mathbf{k})$, and $P_{\gamma }$ is the power of the same polarization amplitude used in ${\gamma }_{ij}={\sum }_s{ϵ}_{ij}^s{\gamma }^s$. Thus polarization normalization must be consistent on both sides.^[ref]

This consistency relation concerns a squeezed bispectrum configuration: it relates a three-point correlation function to a coordinate response of a two-point function. It requires the long tensor to be adiabatic and the state/dynamics to respect that response. Additional physical long-wavelength effects or incompatible initial-state assumptions cannot simply be replaced by this identity.

Juan Maldacena calculated three-point correlations of primordial scalar and tensor fluctuations in single-field cosmic inflation. His 2003 analysis gave explicit leading slow-roll predictions for primordial non-Gaussianity and showed that certain squeezed limits are fixed by the scale dependence of the two-point spectrum.^[ref]

A squeezed bispectrum configuration compares one long wavelength with two short ones. In the applicable single-field regime, the long fluctuation acts locally as a coordinate rescaling, producing the single-field inflation squeezed-limit consistency relation. The statement depends on the inflationary model and limiting assumptions, rather than applying to every primordial three-point function.