Constraining Exponential f(Q) Gravity with Cosmic Chronometers and Supernovae: A Data-Driven Analysis

TL;DR

This work tests an exponential modification of symmetric teleparallel gravity, f(Q) = Q + η1 Q0(1 - e^{-η2 sqrt(Q/Q0)}), with Q0 = 6H0^2, against cosmic chronometers and Type Ia supernovae (Pantheon and Pantheon+) using MCMC to constrain (H0, Ωm0, η1, η2). The analysis shows a robust late-time acceleration that is in broad agreement with ΛCDM for background evolution, and it detects subtle high-z deviations while maintaining consistency with observational data. Statefinder and Om(z) diagnostics indicate convergence toward the ΛCDM fixed point, and the model yields plausible cosmic ages compatible with Planck, while SEC is violated at low redshift as expected for acceleration. Although ΛCDM is statistically preferred by AIC/BIC, the exponential f(Q) model remains a viable, theoretically motivated alternative with a smooth GR limit and potential to unify early inflation with late-time acceleration, justifying further exploration of non-metricity-based gravity. The multi-probe approach strengthens parameter constraints and highlights the value of combining CC with Pantheon datasets to tighten the expansion history constraints and test modified gravity scenarios.

Abstract

The current paper reports an investigation of the cosmological implications of symmetric teleparallel gravity within a modified $f(Q)$ theory. We construct a specific exponential $f(Q)$ model as $f(Q) = Q + η_1 Q_0\left(1 - e^{-η_2 \sqrt{Q/Q_0}}\right)$, designed to smoothly deviate from General Relativity and accommodate both early-time inflation and late-time accelerated expansion. By employing Markov Chain Monte Carlo (MCMC) methods, we constrain the model parameters $η_1$, $η_2$, $H_0$, and $Ω_{m_0}$ using a combination of cosmic chronometers (CC), Pantheon, and Pantheon$^+$ Supernovae datasets. Our analysis demonstrates that the model consistently supports a late-time acceleration scenario and is in good agreement with current cosmological observations. We extensively analyze the dynamical behavior of the model using key cosmological diagnostics, including the deceleration parameter, equation of state, energy density parameters, Statefinder, and Om diagnostics. The reconstructed Hubble parameter $H(z)$ and distance modulus $μ(z)$ show strong consistency with $Λ$CDM and observational data, while subtle deviations at higher redshifts highlight the value of multi-probe observations. In addition, the examination of energy conditions shows that, in accordance with cosmic acceleration, the Strong Energy Condition (SEC) is broken at lower redshifts while the Dominant Energy Condition (DEC) and Null Energy Condition (NEC) are satisfied. Cosmic age estimates from the model are consistently in agreement with Planck constraints. Our results indicate the viability of exponential $f(Q)$ gravity. A comparative statistical analysis reveals that while $Λ$CDM remains statistically preferred based on AIC and BIC criteria, the exponential $f(Q)$ model yields comparable fits and remains a theoretically motivated and viable alternative for describing cosmic acceleration.

Figures (13)

• Figure 1: Corner plot showing the marginalized posterior distributions with 68% and 98% confidence contours for the model parameters $H_0$, $\Omega_{m_0}$, $\eta_1$ and $\eta_2$. The contours are obtained for CC (black), CC+Pantheon (red), CC+Pantheon$^+$(blue).
• Figure 2: Correlation matrices for the model parameters $H_0$, $\Omega_{m_0}$, $\eta_1$, and $\eta_2$, obtained from the CC, CC+Pantheon, and CC+Pantheon$^+$ dataset combinations.
• Figure 3: Whisker plot showing the constraints on cosmological parameters ($H_0$, $\Omega_{m0}$, $\eta_1$, and $\eta_2$) from different datasets (CC, CC+Pantheon, and CC+Pantheon$^+$).
• Figure 4: Comparison of the Hubble parameter $H(z)$ from different observational datasets with theoretical predictions. The upper panel shows $H(z)$ measurements from CC, CC combined with Pantheon Supernovae, and CC + Pantheon$^+$, overlaid with the $\Lambda$CDM model. The lower panel displays the residuals for each dataset, highlighting deviations from the observation across redshift. Error bars represent standard uncertainties.
• Figure 5: Corner plot showing the marginalized posterior distributions with 68% and 98% confidence contours for the parameters $H_0$ and $\Omega_{m_0}$ of the $\Lambda$CDM model. The contours are obtained for CC (green), CC+Pantheon (blue), and CC+Pantheon$^+$ (maroon).