Verify distance-ratio cancellation in curved cosmological backgrounds

Determine whether the cancellation that makes the CMB distance-free ratios insensitive to late-time modifications of gravity survives at the percent level in a spatially curved cosmological background.

Background

The paper’s comparison of the gravitational constant at recombination with its laboratory value relies on distance-free ratios such as the damping multipole divided by the acoustic scale. This argument assumes spatial flatness, under which the comoving distance can be identified with the appropriately scaled angular-diameter distance.

The authors explicitly state that they have not verified whether the cancellation remains valid at percent-level accuracy when spatial curvature is allowed. Establishing the robustness of the ratio-based inference in curved backgrounds is therefore left unresolved.

References

Second, spatial flatness is assumed, since it is what lets $D_c$ be identified with $(1+z)D_A$; we have not verified that the cancellation survives at the percent level in a curved background.

— The gravitational constant and the cosmic microwave background  (2610.22128 - Lamine et al., 15 Oct 2026) in Section 11, “Discussion,” paragraph beginning “That statement rests on four assumptions”