Reconstructing teleparallel gravity with cosmic structure growth and expansion rate data

We consider the application of a machine learning technique to growth and expansion rate data in the context of teleparallel gravity (TG). We do this by using a combined approach of Hubble data together with redshift-space-distortion $f\sigma_8$ data which together are used to reconstruct the TG Lagrangian via Gaussian processes (GP), where the Hubble data mainly comes from cosmic chronometer and supernova type Ia data from the Pantheon release. In this work, we consider two main GP covariance functions, namely the squared-exponential and Cauchy kernels in order to show consistency (to within 1$\sigma$ uncertainties). The core results of this work are the numerical constructions of the TG Lagrangian from GP reconstructed Hubble and growth data. We take different possible combinations of the datasets and kernels to show any potential differences in this regard. We show that nontrivial cosmology beyond $\Lambda$CDM falls within the uncertainties of the reconstruction from growth data.