Probing primordial non-Gaussianity by reconstructing the initial conditions

We propose to constrain the primordial (local-type) non-Gaussianity signal by first reconstructing the initial density field to remove the late time non-Gaussianities introduced by gravitational evolution. Our reconstruction algorithm combines perturbation theory on large scales with a convolutional neural network on small scales. We reconstruct the squared potential (that sources the non-Gaussian signal) out to $k=0.2\ h$/Mpc to an accuracy of 99.8%. We cross-correlate this squared potential field with the reconstructed density field and verify that this computationally inexpensive estimator has the same information content as the full matter bispectrum. As a proof of concept, our approach can yield up to a factor of three improvement in the $f_{\rm NL}$ constraints, although it does not yet include the complications of galaxy bias or imperfections in the reconstruction. These potential improvements make it a promising alternative to current approaches to constraining primordial non-Gaussianity.