Cosmic expansion history analysis with Hubble parametrization in $Q^n$ gravity

We propose a specialized parameterization for the Hubble parameter, inspired by $\mathrm{\Lambda }$CDM cosmology, to investigate the cosmic expansion history of the Universe. This parameterization is employed to analyze the Universe’s late-time behavior within the context of $Q^n$ gravity, where $Q$ represents non-metricity. By using data from 57 Hubble data points, 1048 supernova (SNe) data points, and 6 baryon acoustic oscillation (BAO) data points, we determine the optimal values for the model parameters. Additionally, we explore three distinct cosmological models based on the parameter $n$, specifically when it takes on the values of $0.55$, $1.5$, and $2.0$. The results of our analysis indicate that our proposed parameterization, along with the associated models for different values of $n$, predicts an accelerated cosmic expansion phase.