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Large Scale Structure Reconstruction with Short-Wavelength Modes

Large scale density modes are difficult to measure because they are sensitive to systematic observational errors in galaxy surveys, but we can study them indirectly by observing their impact on small scale perturbations. Cosmological perturbation theory predicts that second-order density inhomogeneities are a convolution of a short- and a long-wavelength mode. This arises physically because small scale structures grow at different rates depending on the large scale environment in which they reside. This induces an off-diagonal term in the two-point statistics in Fourier space that we use as the basis for a quadratic estimator for the large scale field. We demonstrate that this quadratic estimator works well on an N-body simulation of size (2.5 h^{-1} Gpc)^3. In particular, the quadratic estimator successfully reconstructs the long-wavelength modes using only small-scale information. This opens up novel opportunities to study structure on the largest observable scales.