Constraints on the Gravitational Potential from DESI DR2 BAO and Its Implications for the Local Void Scenario

We constrain the difference in gravitational potential between our location and sources at z≳0.3 using datasets at those redshifts. Our motivation is that the Hubble tension might be caused by a local void, as suggested by galaxy number counts. This would increase the redshift through outflow and gravitational redshift (GR). Only the latter is important at high redshift, where a void contributes a fixed additional GR contribution of z0 due to our location on a potential hill. This z0 model has various subtle effects that were not previously considered, including a hotter CMB and reduced BAO scale rd. We test whether z0 can have the previously expected value of 0.84%, which was based on the fitting of void parameters to galaxy number counts and local H0 measurements. Combining BBN, CMB, BAO, and CC datasets at z>0.5, we find that z0 = −0.4−0.9+0.8%, which rises to −0.1±0.7% when extending our analysis down to z>0.29. Although the results prefer the standard value of z0=0, the best-fitting model with z0=0.84% fits the data almost as well as ΛCDM, with Δχ2<2. We find that ΛCDM faces a 3.07σ BAO anomaly in the standard (H0rd,Ωm) parameter space, where different regions are preferred by BAO and non-BAO datasets from z>0.29. Fixing z0=0.84% reduces this to 2.79σ. This suggests that a local void large enough to solve the Hubble tension cannot be ruled out by higher-redshift datasets, despite its novel impacts on them.