Cosmic Expansion in f(Q,C) Gravity: Observational Constraints and Geometric Diagnostics

Abstract

We investigate the late-time expansion history of the Universe within the framework of $f(Q, C)$ gravity by adopting a linear parametrization of the deceleration parameter $q(z) = α+βH$, where $Q$ denotes the non-metricity scalar and $C$ represents the associated boundary term satisfying the geometrical relation $\mathring{R}= Q+C$. The adopted parametrization provides a phenomenological description of the cosmic expansion while retaining analytical tractability, allowing the transition from decelerated to accelerated expansion to be examined directly. An exact integration of the corresponding differential equation yields the closed-form Hubble function, $H(z)=\frac{1}{β\left[F_0-\ln(1+z)\right]},$ thereby providing an explicit description of the expansion history in terms of redshift. Here $F=\frac{1}β\sqrt{2βt+b}$ and $F_0$ specifies the value of $F$ at the present epoch. The model parameters are constrained using recent Cosmic Chronometer (CC) measurements, DESI DR2 Baryon Acoustic Oscillation (BAO) observations, Pantheon+SH0ES Type Ia supernovae, and the Union3 observations through Bayesian Markov Chain Monte Carlo (MCMC) analysis. Individual and combined datasets are compared to assess the model's consistency, while its cosmic evolution is examined using the deceleration, the equation-of-state parameter, the state-finder pair ${r,s}$, and the $Om$ diagnostic.