Comparing Measures of the Hubble and BAO Tensions in ΛCDM and Possible Solutions in f(Q) Gravity

We test whether f(Q) symmetric teleparallel gravity theories can solve the Hubble tension consistently with DESI DR2 BAO. We consider three f(Q) functional forms: logarithmic, exponential, and hyperbolic tangent. We extend these models by allowing a cosmological constant, and compare to phenomenological models with a flexible exponential, hyperbolic secant, and polynomial decay addition to the standard ΛCDM H(z). We test these models against DESI DR2 BAO, CMB (Planck 2018 + SPT-3G + ACT DR6), local H0, and Cosmic Chronometer data. The logarithmic and hyperbolic tangent f(Q) models do not provide an adequate solution, but the exponential model does. Furthermore, it slightly reduces the (Ωm,H0rd) parameter space tension between CMB and BAO datasets to 2.56σ, down from 2.65σ for ΛCDM. Although ΛCDM faces only 1.66σ tension in DESI data space, the 1σ higher tension in parameter space suggests a real anomaly. The models assisted by the cosmological constant perform slightly better still, at the cost of undermined theoretical motivation. They also perform poorly once local H0 measurements are included. The phenomenological models fit all data reasonably well, yet the best-fitting models predict isotropically averaged BAO distances exceeding the DESI DR2 measurements at all redshifts. This highlights the difficulties of finding a theoretically motivated solution to the Hubble tension while remaining consistent with BAO data.