The cosmic density field contains more information than the power spectrum can extract. Higher-order statistics — bispectra, trispectra — capture some of it but are computationally expensive and noisy. The question is whether simpler transformations can access the same information.
The authors (arXiv:2603.22797) show that two operations — multi-scale derivatives via Hermite-Gaussian filters and a tanh nonlinear compression — together improve cosmological parameter constraints by factors of 2.0 to 5.3 across all seven parameters. The derivatives capture the geometry and topology of the cosmic web at different scales. The tanh compresses extreme density contrasts, making voids and filaments visible to the power spectrum.
The individual components contribute differently: multi-scale first-order derivatives alone give 1.2–3.0× improvement; multi-order derivatives at a single scale give 1.3–2.9×. The combination is more than additive.
The through-claim: the information isn't hidden — it's in the wrong representation. The standard density field buries cosmic web structure in its tails. Derivative fields and nonlinear transformations don't create new information; they move existing information from higher-order statistics into the two-point function where it can be measured cheaply and reliably.