Insights into f(Q) gravity: Modeling through deceleration parameter

Abstract

In this paper, we have reconstructed $f\left(Q\right)$ gravity cosmological models with the novel forms of the deceleration parameter. The parameters are constrained by incorporating the cosmological datasets from Hubble parameter, Type Ia Supernovae and Baryon Acoustic Oscillations. We have examined two parametrizations of the deceleration parameter and fit them into the models through Monte Carlo Markov Chain (MCMC) analysis, one with the power-law function and the other one with the logarithmic function. The Power-law model exhibits strong agreement with higher $H_0$ values, aligning well with recent $H_0$ measurements, whereas the logarithmic model achieves lower matter density constraints. Both the models successfully recover observationally consistent estimates for the Hubble constant $H_0$ and matter density ${\Omega }_{m_0}$, though with varying degrees of precision and alignment with the ΛCDM as a limit. These two models are used to reconstruct the $f\left(Q\right)$ function for each case, yielding analytical expressions that closely align with the numerical solutions. Statistical comparisons using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) reveal a competitive performance with the ΛCDM model and positioning these $f\left(Q\right)$ models as promising alternatives to explain late time cosmic phenomena.