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

Abstract

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, which allows us to eliminate this issue in an f ( Q ) model-independent way. In particular, we use the 58 Hubble measurements coming from cosmic chronometers and the radial Baryon acoustic oscillations to reconstruct H ( z ) and its derivatives $H^{\prime} (z)$ and H ″( z ), which leads us to reconstruct the region of f ( Q ), without any assumptions. The obtained mean curve along the Lambda Cold Dark Matter (ΛCDM) constant in the reconstructed region follows a quadratic behavior. This motivates us to propose a new f ( Q ) parameterization, 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.

Keywords

• Dark energy