Neural Network Reconstruction of $H^{\prime }(z)$ and its application in Teleparallel Gravity

Abstract

In this work, we explore the possibility of using artificial neural networks to impose constraints on teleparallel gravity and its $f(T)$ extensions. We use the available Hubble parameter observations from cosmic chronometers and baryon acoustic oscillations from different galaxy surveys. We discuss the procedure for training a network model to reconstruct the Hubble diagram. Further, we describe the procedure to obtain $H^{\prime }(z)$, the first order derivative of $H(z)$, using artificial neural networks which is a novel approach to this method of reconstruction. These analyses are complemented with further studies on the impact of two priors which we put on $H_0$ to assess their impact on the analysis, which are the local measurements by the SH0ES team ($H_0^{\text{R20}}=73.2\pm 1.3$ km Mpc${}^{-1}$ s${}^{-1}$) and the updated TRGB calibration from the Carnegie Supernova Project ($H_0^{\text{TRGB}}=69.8\pm 1.9$ km Mpc${}^{-1}$ s${}^{-1}$), respectively. Additionally, we investigate the validity of the concordance model, through some cosmological null tests with these reconstructed data sets. Finally, we reconstruct the allowed $f(T)$ functions for different combinations of the observational Hubble data sets. Results show that the $\Lambda$CDM model lies comfortably included at the 1$\sigma$ confidence level for all the examined cases.

19 pages, 11 sets of figures, version accepted in JCAP

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