Exploring f(Q) gravity through model-independent reconstruction with genetic algorithms

Abstract

In this paper, we use a machine learning technique, specifically genetic algorithms, to reconstruct the functional form of $f\left(Q\right)$ gravity in a model-independent manner. To achieve this, we use Hubble measurements derived from cosmic chronometers and radial baryon acoustic oscillations, including the latest Dark Energy Spectroscopic Instrument (DESI) BAO data. For the cosmic chronometers, we estimate the covariance matrix for 31 data points, considering both statistical and systematic errors. To the best of our knowledge, this is the first time that this estimation has been carried out, providing a robust and reliable foundation for reconstructing the functional form of $f\left(Q\right)$ gravity. We reconstruct the Hubble parameter $H\left(z\right)$ without assuming any specific dark energy model or a flat Universe, which allows us to derive $f\left(Q\right)$ gravity without prior assumptions. In this reconstruction, we use the current value of $H_0$ derived from genetic algorithms. The reconstructed $f\left(Q\right)$ function aligns well with the ΛCDM model, suggesting only minor deviations at high redshift values that remain within the 1σ confidence region. Our approach is fully model-independent and does not rely on any a priori assumptions about the cosmological model, providing a powerful tool to describe the accelerated expansion of the Universe.