Cosmological reconstruction from galaxy light: neural network based light-matter connection

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We present a method to reconstruct the initial conditions of the universe using observed galaxy positions and luminosities under the assumption that the luminosities can be calibrated with weak lensing to give the mean halo mass. Our method relies on following the gradients of forward model and since the standard way to identify halos is non-differentiable and results in a discrete sample of objects, we propose a framework to model the halo position and mass field starting from the non-linear matter field using Neural Networks (NN), which are differentiable, yet can produce very pointlike maps. We evaluate the performance of our model with multiple metrics and find that our model is more than 95% correlated with the halo-mass fields up to k∼ 0.7 h/Mpc, and significantly reduces the stochasticity over the Poisson shot noise. We develop a data likelihood model that takes our modeling error and intrinsic scatter in the halo mass-light relation into account and show that a displaced log-normal model is a good approximation to it. We optimize over the corresponding loss function to reconstruct the initial density field of the dark matter starting from the halo mass field. To speed up and improve the convergence, we develop an annealing procedure for several parameters in the loss function, such as smoothing the likelihood starting with large smoothing and gradually decreasing it. We apply the method to halo number densities of n̄ = 2.5× 10−4 − 10−3(h/Mpc)3, typical of current and future redshift surveys, and recover a Gaussian initial density field, mapping all the higher order information in the data into the power spectrum of the linear reconstructed field. We show that our reconstruction improves over the standard reconstruction. For baryonic acoustic oscillations (BAO) the gains are relatively modest because BAO is dominated by large scales where standard reconstruction suffices. We improve upon it by ∼ 15–20% in terms of error on BAO peak as estimated by Fisher analysis at z=0. We expect larger gains will be achieved when applying this method to the broadband linear power spectrum reconstruction on smaller scales.