Determine the polarization damping-envelope response to varying gravitational constant

Establish the damping-envelope exponent for the TE and EE polarization spectra under a variation of the gravitational constant during recombination, using a suitable tail model for those spectra.

Background

The paper derives and tests the damping-envelope behavior primarily for the temperature-temperature (TT) spectrum. It argues that the TE and EE polarization spectra are governed by the same Silk-diffusion damping and visibility-function cutoff, so their response to a varying gravitational constant is expected to be related to the TT response.

However, the analysis does not construct the required tail models for TE and EE. Consequently, the polarization damping exponent remains unresolved and is explicitly outside the claims of the paper.

References

The polarization spectra carry a damping envelope driven by the same Silk diffusion and cut off by the same visibility function, so one would expect them to respond to $G$ in a closely related way, but establishing that requires a tail model for $TE$ and $EE$ which we have not built. We therefore make no claim about the polarization exponent, and every result below refers to $TT$.

— The gravitational constant and the cosmic microwave background  (2610.22128 - Lamine et al., 15 Oct 2026) in Section 9, subsection “Analysis of the damping tail,” final paragraph before Section 10