Comparing measures of the Hubble and BAO tensions in $\Lambda$CDM and possible solutions in $f(Q)$ gravity

Abstract

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 $\Lambda$CDM $H(z)$. We test these models against DESI DR2 BAO, CMB ($Planck$ 2018 + SPT-3G + ACT DR6), local $H_0$, 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 $({\Omega }_m,H_0{r}_d)$ parameter space tension between CMB and BAO datasets to $2.56\sigma$, down from $2.65\sigma$ for $\Lambda$CDM. Although $\Lambda$CDM faces only $1.66\sigma$ tension in DESI data space, the $1\sigma$ 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 $H_0$ 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.

32 pages, 9 figures, 7 tables. Published in Galaxies special issue on the Hubble tension in this form

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• Dark Energy in the DESI Era: A Brief Review of Evidence, Beyond-$\Lambda$CDM Interpretations, and Tensions
• A Review on Resolving the Hubble Tension via Late-Universe Physics
• Constraints on the gravitational potential from DESI DR2 BAO and its implications for the local void scenario