Observational viability of generalized Chaplygin gas in \(f(Q, L_{m})\) gravity

Abstract

Our analysis focuses on the Generalized Chaplygin Gas (GCG) model within the \(f(Q, L_{m})\) gravity framework, assuming \(f(Q,L_{m})=\beta Q+\delta L_{m}\) with \(L_{m}=-\rho \). Using the GCG equation of state \(p=-\frac{A}{\rho ^{\alpha }}\), we derive expressions for energy density \(\rho (z)\) and the Hubble parameter \(H(z)\). Constraining parameters through MCMC analysis with 31 cosmic chronometers, 15 BAO points, recent DESI DR2 BAO points and 1701 Pantheon+, we find best-fit values \(H_{0}=74.026^{+3.332}_{-3.317}\) km/s/Mpc, \(A_{s}=0.880^{+0.019}_{-0.020}\) and \(\alpha =-0.001^{+0.053}_{-0.052}\) which are consistent with local measurements. The deceleration parameter transitions at \(z_{tr} \approx 0.79\), with present value \(q_{0}=-0.61\), while the equation of state evolves toward \(\omega =-1\) with \(\omega _{0} \approx -0.79\). Energy conditions are satisfied except for the SEC, which is violated during acceleration. The model predicts a cosmic age of 13.42 Gyr and shows freezing quintessence behavior in the \(\omega -\omega '\) plane, confirming its potential as a viable dark energy candidate.