Scalar Laplace-Beltrami harmonics and curvature-induced radial mode mixing in Friedmann-like cosmologies
Abstract
We develop a harmonic framework for spherically symmetric Friedmann-like geometries with constant scalar curvature but non-zero trace-free Ricci curvature. This preserves Friedmann-type isotropic expansion while introducing a radially varying tidal field and supporting anisotropic stress. We formulate the scalar Laplace-Beltrami operator as a Sturm-Liouville problem and establish its self-adjoint domains and regularity at minimal spheres. Robertson-Walker harmonics are recovered in the maximally symmetric limit. Trace-free curvature terms are expressed as spectral projection kernels. Rotational symmetry preserves angular labels and parity, while the tidal profile couples different radial eigenmodes. A finite-shell calculation displays this off-diagonal structure, verifies consistency between radial representations, and confirms the expected weak-field scaling. A minimally coupled scalar field remains diagonal in the exact basis, indicating operator-dependent mixing rather than mixing solely due to inhomogeneity. We formulate transverse-traceless kernels, whose dynamical application requires a specified model for the supporting anisotropic matter. This converts curvature-induced mode mixing into a spectral problem for perturbations beyond maximally symmetric cosmologies.
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BibTeX
@misc{bittencourt2026scalar,
title = {{Scalar Laplace-Beltrami harmonics and curvature-induced radial mode mixing in Friedmann-like cosmologies}},
author = {Eduardo Bittencourt and Peter K. S. Dunsby and Bob Osano and Muzikayise E. Sikhonde},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20199},
eprint = {2610.20199},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20199},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Scalar Laplace-Beltrami harmonics and curvature-induced radial mode mixing in Friedmann-like cosmologies
AU - Eduardo Bittencourt
AU - Peter K. S. Dunsby
AU - Bob Osano
AU - Muzikayise E. Sikhonde
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20199
UR - https://arxiv.org/abs/2610.20199
AB - We develop a harmonic framework for spherically symmetric Friedmann-like geometries with constant scalar curvature but non-zero trace-free Ricci curvature. This preserves Friedmann-type isotropic expansion while introducing a radially varying tidal field and supporting anisotropic stress. We formulate the scalar Laplace-Beltrami operator as a Sturm-Liouville problem and establish its self-adjoint domains and regularity at minimal spheres. Robertson-Walker harmonics are recovered in the maximally symmetric limit. Trace-free curvature terms are expressed as spectral projection kernels. Rotational symmetry preserves angular labels and parity, while the tidal profile couples different radial eigenmodes. A finite-shell calculation displays this off-diagonal structure, verifies consistency between radial representations, and confirms the expected weak-field scaling. A minimally coupled scalar field remains diagonal in the exact basis, indicating operator-dependent mixing rather than mixing solely due to inhomogeneity. We formulate transverse-traceless kernels, whose dynamical application requires a specified model for the supporting anisotropic matter. This converts curvature-induced mode mixing into a spectral problem for perturbations beyond maximally symmetric cosmologies.
ER -