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

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 $f(Q) = Q + \eta_1 Q_0\left(1 - e^{-\eta_2 \sqrt{Q/Q_0}}\right)$, 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 $\eta_1$, $\eta_2$, $H_0$, and $\Omega_{m_0}$ 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 $\mu(z)$ show strong consistency with $\Lambda$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 $\Lambda$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.