Higher-multipole modulation of the matter density field

Investigate the detailed observational and theoretical consequences of modulating the matter density field by multipoles with L>1, extending the dipolar L=1 analysis.

Background

The paper develops a full-sky spin-weighted TripoSH formalism for dipolar, L=1, position-dependent primordial power modulation and applies it to two-point correlations of galaxy density, peculiar velocity, and intrinsic ellipticity. The concluding section notes that analogous modulations with higher multipoles are physically natural possibilities but are not analyzed in the present work.

The authors explicitly state that higher-multipole extensions are expected to differ from the dipolar case in both their observational signatures and theoretical angular-momentum structure. A detailed treatment is therefore deferred to future work.

References

Although we have focused on the dipolar modulation with L=1, which is directly motivated by the observed hemispherical power asymmetry in the CMB, it would be natural to expect that the matter density field can also be modulated by higher multipoles with L>1. Such extensions are expected to differ from the dipolar case, both observationally and theoretically. We therefore leave a detailed analysis to a forthcoming paper.

— Dipolar power asymmetry in wide-angle correlations of galaxy density, velocity and ellipticity  (2608.19039 - Mikura et al., 19 Aug 2026) in Section Conclusions