Effective $\Lambda$CDM model emerging from $f(Q,T)$ under a special EOS limit in symmetric cosmology with Bayesian and ANN observational constraints

Abstract

In this work, we investigate the cosmological consequences of an effective $\Lambda$CDM model emerging from the more general $f(Q,T)$ gravity theory under the special equation-of-state condition $\rho + p = 0$. Under this limit, the field equations yield the constraint $F(Q,T)H(t)=C$, implying that the function $F=f_Q$ becomes purely dependent on the non-metricity scalar $Q$, and the background evolution mimics that of the standard $\Lambda$CDM model. We derive the resulting functional forms of $f(Q)$, obtain the corresponding effective cosmological constant, and analyze the physical nature of this reduction. To test the model against observations, we perform a background-level parameter estimation for $H_{0}$ and $\Omega_{m}$, and evaluate the derived parameter $S_{8}$ (anchored to the Planck baseline $\sigma_8$) using cosmic chronometers (CC), baryon acoustic oscillations (BAO), and Pantheon+ SN Ia datasets. A dual-pipeline analysis is carried out using conventional Bayesian Markov Chain Monte Carlo (MCMC) sampling alongside a machine-learning based Artificial Neural Network (ANN) emulator deployed as a complementary consistency check. We demonstrate that the ANN approach successfully emulates the continuous parameter space with high computational efficiency, yielding results in close agreement with the standard MCMC likelihood framework. Because the background evolution strictly mimics the standard $\Lambda$CDM paradigm, the model successfully reproduces recent observational trends and recovers standard parameter constraints without dynamically resolving the baseline $H_{0}$ and $S_{8}$ tensions. Our results indicate that effective $\Lambda$CDM scenarios derived from $f(Q,T)$ gravity provide a viable and consistent with recent observational data.