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 (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 $H^{\prime }(z)$, $H^{\prime \prime }(z)$, which resulting lead us to reconstruct region of $f(Q)$, without any assumptions. The obtained mean curve along $\Lambda$CDM constant in the reconstructed region follows a quadratic behavior. This motivates us to propose a new $f(Q)$ parametrization, i.e., $f(Q)=-2\Lambda +\epsilon Q^2$, with the single parameter $\epsilon$, which signifies the deviations from $\Lambda$CDM 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.

Accepted to Publication of Astrophysical Journal (ApJ)

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• Statistical and Observation Comparison of Weyl-Type $f(Q,T)$ Models with the $\Lambda$CDM Paradigm
• Reconstruction of the scalar field potential in nonmetricity gravity through Gaussian processes
• Cosmological dynamics of interacting dark energy and dark matter in $f(Q)$ gravity
• Observational constraints on cosmological parameters in the Bianchi type III Universe with f(R,T) gravity theory
• A comprehensive dynamical and phenomenological analysis of structure growth in curvature-modulated coupled quintessence scenario
• Polytropic $f(Q)$ cosmology and its implications for the $H_0$ tension
• Reconstruction of a dark energy model for the Dirac-Born-Infeld scalar field with the Hubble and DESI data via Gaussian process
• Phase space analysis of Bianchi III Universe with $f(R,T)$ gravity theory
• Observational and Thermodynamic aspects of one-dimensional Dark Energy EoS parametrization models