Gaussian Process Approach for Model-Independent Reconstruction of f(Q) Gravity with Direct Hubble Measurements

The increase of discrepancy in the standard procedure to choose the arbitrary functional form of the Lagrangian f(Q) motivates us to solve this issue in modified theories of gravity. In this regard, we investigate the Gaussian process (GP), which allows us to eliminate this issue in a f(Q) model-independent way. In particular, we use the 57 Hubble measurements coming from cosmic chronometers and the radial Baryon acoustic oscillations (BAO) to reconstruct H(z) and its derivatives H'(z), H”(z), which resulting lead us to reconstruct region of f(Q), without any assumptions. The obtained mean curve along ΛCDM constant in the reconstructed region follows a quadratic behavior. This motivates us to propose a new f(Q) parametrization, i.e., f(Q)= -2Λ+ ϵ Q^2, with the single parameter ϵ, which signifies the deviations from ΛCDM cosmology. Further, we probe the widely studied power-law and exponential f(Q) models against the reconstructed region and can improve the parameter spaces significantly compared with observational analysis. In addition, the direct Hubble measurements, along with the reconstructed f(Q) function, allow the H_0 tension to be alleviated.