Reconstruction of the scalar field potential in nonmetricity gravity through Gaussian processes

Abstract: The accelerated expansion of the universe has been widely confirmed, posing challenges to the standard $\Lambda$CDM model, particularly the cosmological coincidence problem. This has motivated the exploration of modified gravity theories, including non-metricity gravity, which explains cosmic acceleration without dark energy. In this work, we incorporate a quintessence scalar field into the non-metricity framework to model both inflation and late-time acceleration. Employing the Gaussian process method with a square exponential kernel, we reconstruct the scalar field potential, $V(\phi)$, from observational Hubble data sets coming from cosmic chronometers (CC) as well as from the method of radial baryon acoustic oscillations (BAO) in a model-independent approach. This approach allows us to obtain a suitable quintessence scalar field model that aligns with the observational Hubble data under the framework of power-law non-metricity gravity. Additionally, we compare our reconstructed potential with power-law scalar field potentials, revealing that these models show better agreement with the observational data, providing new insights into the dynamics of the universe. In contrast, we find that the early dark energy has minimal effect on the present-time accelerated expansion of the universe.