Matching exact cosmological solutions in linear and nonlinear f(Q) gravity with cosmological data

We investigate the cosmological implications of two analytically solvable f ( Q ) gravity models within the framework of symmetric teleparallel gravity. The first model corresponds to the linear case f ( Q ) = α Q + β , which is dynamically equivalent to general relativity with a cosmological constant, while the second model introduces a nonlinear correction f ( Q ) = α Q + β / Q . By assuming pressureless matter, we derive exact background solutions for both models, allowing the Hubble expansion rate, the matter energy density, and the deceleration parameter to be expressed in terms of the redshift. Then, we constrain the model parameters using a Bayesian Markov Chain Monte Carlo analysis based on H ( z ) cosmic chronometer measurements, the Pantheon+SH0ES Type Ia supernova compilation, and DESI baryon acoustic oscillation data. The results show that the linear model reproduces the standard ΛCDM background dynamics, whereas the nonlinear model leads to modified cosmological evolution while remaining consistent with observational data. Moreover, the reconstructed deceleration parameter indicates a transition from an early matter-dominated decelerating phase to the present accelerated expansion. In addition, the Om ( z ) diagnostic reveals that Model I behaves identically to ΛCDM, while Model II exhibits a redshift-dependent behavior indicative of a phantom-like effective regime. We conclude that symmetric teleparallel f ( Q ) gravity presents a viable geometric framework for describing the late-time acceleration of the universe.