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

TL;DR

This work shows that an effective ΛCDM model can arise from f(Q,T) gravity when the matter sector satisfies ρ+ p = 0, which enforces the constraint $F(Q)H=C$ and renders $F$ a function of $Q$ only. Consequently, the background evolution reduces to ΛCDM with an effective cosmological constant $ρ_Λ = B/(2κ^2)$ and a mapping $B = 6Ω_Λ H_0^2$, yielding the familiar expansion $H(z)=H_0\sqrt{Ω_m(1+z)^3+Ω_Λ}$ with $Ω_Λ=1-Ω_m$. The paper tests this setup against CC, BAO, and Pantheon+ SN Ia data using both Bayesian MCMC and an ANN emulator, finding that the ANN approach delivers tighter constraints and substantial speedups while remaining consistent with observations. The results highlight the viability of nonmetricity-based dark energy as an alternative to ΛCDM and indicate that future high-precision surveys could more sharply distinguish this framework from standard cosmology.

Abstract

In this work, we investigate the cosmological consequences of an effective $f(Q)$ model emerging from the more general $f(Q,T)$ gravity theory under the special equation-of-state condition $ρ+ p = 0$. 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 nonmetricity scalar $Q$, and the background evolution mimics that of the standard $Λ$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 constrain the parameters $H_0$, $Ω_m$, and $S_8$ using cosmic chronometers (CC), baryon acoustic oscillations (BAO), and Pantheon+ SN Ia datasets. A comparative analysis is performed using both the conventional Bayesian Markov Chain Monte Carlo (MCMC) sampling and a machine-learning based Artificial Neural Network (ANN) emulator. We find that the ANN approach yields tighter posterior constraints while significantly reducing computational time. The model successfully reproduces the observational trends of each dataset and offers insights into the persistent $H_0$ and $S_8$ tensions. Our results indicate that effective nonmetricity-based dark energy scenarios derived from $f(Q,T)$ gravity provide a viable and observationally consistent alternative to $Λ$CDM, with future high-precision surveys expected to further distinguish between these frameworks.

Figures (10)

• Figure 1: One-dimensional marginalized probability distributions and two-dimensional ($2D$) confidence contours at $1\sigma$ and $2\sigma$ levels for the derived cosmological model, using the CC dataset analyzed with the conventional MCMC approaches.
• Figure 2: One-dimensional marginalized probability distributions and two-dimensional ($2D$) confidence contours at $1\sigma$ and $2\sigma$ levels for the derived cosmological model, using the BAO dataset analyzed with the conventional MCMC approaches.
• Figure 3: One-dimensional marginalized probability distributions and two-dimensional ($2D$) confidence contours at $1\sigma$ and $2\sigma$ levels for the derived cosmological model, using the Pantheon+ SN Ia dataset analyzed with the conventional MCMC approaches.
• Figure 4: One-dimensional marginalized probability distributions and two-dimensional ($2D$) confidence contours at $1\sigma$ and $2\sigma$ levels for the derived cosmological model, using CC dataset analyzed with advanced ANN approach.
• Figure 5: One-dimensional marginalized probability distributions and two-dimensional ($2D$) confidence contours at $1\sigma$ and $2\sigma$ levels for the derived cosmological model, using the BAO dataset analyzed with advanced ANN approach.