Constraints on the gravitational potential from DESI DR2 BAO and its implications for the local void scenario

Abstract

We constrain the difference in gravitational potential between our location and sources at $z \gtrsim 0.3$ 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 $z_0$ due to our location on a potential hill. This $z_0$ model has various subtle effects that were not previously considered, including a hotter CMB and reduced BAO $r_{\rm d}$. We test whether $z_0$ can have the previously expected value of 0.84\%, which was based on fitting void parameters to galaxy number counts and local $H_0$ measurements. Combining BBN, CMB, BAO, and CC datasets at $z > 0.5$, we find that $z_0$ = $-0.4 \pm 0.9\%$, which rises to $0.0^{+0.6}_{-0.7}\%$ when extending our analysis down to $z > 0.29$. Although the results prefer the standard value of $z_0 = 0$, the best-fitting model with $z_0 = 0.84\%$ fits the data almost as well as $Λ$CDM, with $Δχ^2 < 2$. We find that $Λ$CDM faces a $2.81σ$ BAO anomaly in the standard $(H_0 r_{\rm d}, Ω_{\rm m})$ parameter space, where different regions are preferred by BAO and non-BAO datasets from $z > 0.29$. Fixing $z_0 = 0.84\%$ reduces this to $2.39σ$. This suggests that a local void large enough to solve the Hubble tension cannot be ruled out by higher-redshift datasets despite its novel impact on them.