Improving constraints on primordial non-Gaussianity using neural network based reconstruction

We study the use of U-Nets in reconstructing the linear dark matter density field and its consequences for constraining cosmological parameters, in particular primordial non-Gaussianity. Our network is able to reconstruct the initial conditions of redshift $z=0$ density fields from N-body simulations with $90\%$ accuracy out to $k \leq 0.4$ h/Mpc, competitive with state-of-the-art reconstruction algorithms at a fraction of the computational cost. We study the information content of the reconstructed $z=0$ density field with a Fisher analysis using the QUIJOTE simulation suite, including non-Gaussian initial conditions. Combining the pre- and post-reconstructed power spectrum and bispectrum data up to $k_{\rm max} = 0.52$ h/Mpc, we find significant improvements on all parameters. Most notably, we find a factor $3.65$ (local), $3.54$ (equilateral) and $2.90$ (orthogonal) improvement on the marginalized errors of $f_{\rm NL}$ as compared to only using the pre-reconstructed data. We show that these improvements can be attributed to a combination of reduced data covariance and parameter degeneracy. The results constitute an important step towards more optimal inference of primordial non-Gaussianity from non-linear scales.