Reconstructing teleparallel gravity with cosmic structure growth and expansion rate data

In this work, we use a combined approach of Hubble parameter data together with redshift-space-distortion $(f\sigma_8)$ data, which together are used to reconstruct the teleparallel gravity (TG) Lagrangian via Gaussian processes (GP). The adopted Hubble data mainly comes from cosmic chronometers, while for the Type Ia supernovae data we use the latest jointly calibrated Pantheon compilation. Moreover, 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 reconstructions of the TG Lagrangian from GP reconstructed Hubble and growth data. We take different possible combinations of the datasets and kernels to illustrate any potential differences in this regard. We show that nontrivial cosmology beyond $\Lambda$CDM falls within the uncertainties of the reconstructions from growth data, which therefore indicates no significant departure from the concordance cosmological model.