Non-Linearity-Free prediction of the growth-rate $fσ_8$ using Convolutional Neural Networks

Abstract: The growth-rate $f\sigma_8(z)$ of the large-scale structure of the Universe is an important dynamic probe of gravity that can be used to test for deviations from General Relativity. However, for galaxy surveys to extract this key quantity from cosmological observations, two important assumptions have to be made: i) a fiducial cosmological model, typically taken to be the cosmological constant and cold dark matter ($\Lambda$CDM) model and ii) the modeling of the observed power spectrum, especially at non-linear scales, which is particularly dangerous as most models used in the literature are phenomenological at best. In this work, we propose a novel approach involving convolutional neural networks (CNNs), trained on the Quijote N-body simulations, to predict $f\sigma_8(z)$ directly and without assuming a model for the non-linear part of the power spectrum, thus avoiding the second of the assumptions above. This could serve as an initial step towards the future development of a method for parameter inference in Stage IV surveys. We find that the predictions for the value of $f\sigma_8$ from the CNN are in excellent agreement with the fiducial values since they outperform a maximum likelihood analysis and the CNN trained on the power spectrum. Therefore, we find that the CNN reconstructions provide a viable alternative to avoid the theoretical modeling of the non-linearities at small scales when extracting the growth rate.