Neural Network Reconstructions for the Hubble Parameter, Growth Rate and Distance Modulus

In this paper we propose a method to perform non-parametric reconstructions using artificial neural networks based solely on cosmological data without any previous theoretical assumptions. Data modelling using neural networks makes it possible to increase the amount of information from small observational data sets and, in some cases, to find new features. In particular, we focus on data sets with cosmic chronometers, fσ 8 measurements, and the distance modulus of the Type Ia supernovae. Furthermore, we introduce a first approach to generate synthetic covariance matrices through a variational autoencoder, for which we use the systematic error covariance matrix of the type Ia supernova compilation. The power of our proposal is exploited if the neural network models generates synthetic data which can be used within a Bayesian inference procedure; we have employed some dark energy models to show the usefulness of our method. Our findings point out slight deviations from the ΛCDM standard model and they are statistically consistent with the results obtained using the original datasets