Background solutions to the Hubble tension in $f(Q)$ gravity and consistency with BAO measurements

Abstract: We test whether $f(Q)$ symmetric teleparallel theories of gravity are capable of solving the Hubble tension while producing consistency with DESI DR2 BAO. We consider three different forms for the $f(Q)$ function: logarithmic, exponential, and hyperbolic tangent. We also consider extensions of these models by adding the Cosmological constant, and compare to phenomenological models with a flexible double exponential addition to the standard $\Lambda$CDM $H(z)$. We test these models against DESI DR2 BAO, Planck 2018, Local $H_0$, and Cosmic Chronometers data. The logarithmic and hyperbolic tangent models do not provide an adequate solution, while the exponential model gives a reasonable solution, though it faces mild tension with the BAO data. The models assisted by the cosmological constant perform slightly better than the exponential, at the cost of reduced theoretical motivation. This highlights the difficulties of finding a theoretically motivated solution to the Hubble tension while producing BAO consistency. The phenomenological models are able to achieve a good fit to all data, giving guidelines for what a background solution to the Hubble tension would look like in general.