Model-independent Reconstruction of f(T) Gravity from Gaussian Processes

Abstract

We apply Gaussian processes and Hubble function data in f ( T ) cosmology to reconstruct for the first time the f ( T ) form in a model-independent way. In particular, using H ( z ) data sets coming from cosmic chronometers as well as from the method of radial baryon acoustic oscillations, alongside the latest released local value of H 0  = 73.52 ± 1.62 km s −1 Mpc −1 , we reconstruct H ( z ) and its derivatives, resulting eventually in a reconstructed region for f ( T ), without any assumption. Although the cosmological constant lies in the central part of the reconstructed region, the obtained mean curve follows a quadratic function. Inspired by this we propose a new f ( T ) parameterization, i.e., f ( T ) = −2Λ +  ξT 2 , with ξ the sole free parameter that quantifies the deviation from ΛCDM cosmology. Additionally, we confront three viable one-parameter f ( T ) models from the literature, which are the power-law, the square-root exponential, and the exponential models, with the reconstructed f ( T ) region, and then we extract significantly improved constraints for their model parameters, comparing to the constraints that arise from the usual observational analysis. Finally, we argue that since we are using the direct Hubble measurements and the local value for H 0 in our analysis, the H 0 tension can be efficiently alleviated with the above reconstruction of f ( T ).