Position-dependent power asks a sharp question: does the small-scale clustering amplitude measured inside a patch of the universe depend on the large-scale density of that patch in the way Gaussian initial conditions plus gravity predict? The separate-universe formalism makes the standard answer precise, a long-wavelength overdensity acts like a slightly closed background that boosts local growth by a calculable response function, so dividing a survey into sub-volumes and correlating local power with mean density tests the model's mode-coupling machinery directly (Chiang et al. 2014; Barreira et al. 2019).
The measured coupling misbehaves at the margins. Position-dependent power analyses find local small-scale power varying more strongly with large-scale environment, direction, or location than the Gaussian-plus-linear-bias response supplies, pointing at enhanced super-sample effects, primordial non-Gaussian couplings, or large-scale structure the standard inventory does not contain. Within ΛCDM the response function is not adjustable; it follows from the growth equations in a homogeneous background, so a genuine excess means either the initial conditions carried extra couplings or the growth itself is not the same everywhere.
The standing is a precision frontier rather than a headline anomaly: the deviations are modest and methodology-sensitive, but the statistic is exactly the kind that next-generation volume will sharpen. DESI, Euclid, and SPHEREx will measure the position-dependent power response across environments and directions with enough sub-volumes to separate a real environmental growth signal from sample variance.