Constraint closure and gravitational-wave content of shear-free cosmologies in metric f(R) gravity
Abstract
We derive the consistency conditions governing the propagating content of linear shear-free perturbations of Friedmann-Lema\^ıtre-Robertson-Walker cosmologies in metric f(R) gravity. The divergence of the shear-free constraint is shown to be the total momentum-conservation equation and therefore does not imply geodesic flow. Its projected time derivative instead supplies a nontrivial integrability condition. Scalar, vector, and tensor sectors must then be tested separately. Shear-freeness removes the independent transverse-traceless electric-magnetic Weyl pair, so no ordinary + or × tensor gravitational wave survives. The scalaron is not removed algebraically, but its four-variable harmonic system must remain in the time-dependent consistent subspace generated by the shear-free constraint and all of its time derivatives. For a geodesic shear-free congruence in the spatially flat expanding de Sitter patch, this excludes every nonzero fixed comoving scalar harmonic, including the healthy R+αR2−2Λ model with α,Λ>0. Vector modes obey a curvature-dependent global eigenvalue condition whose right-hand side is negative for positive-density matter with f'>0 and 1+w>0; hence no nonzero vector harmonic survives on that branch. The familiar coasting R3 example evades this sign obstruction only because it lies on an f'<0 branch. Thus tensor radiation is absent in the imposed shear-free sector, whereas scalar radiation is not excluded kinematically but remains a model- and background-dependent constraint-closure question.
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BibTeX
@misc{ajmi2026constraint,
title = {{Constraint closure and gravitational-wave content of shear-free cosmologies in metric f(R) gravity}},
author = {Mudhahir Al Ajmi and Amare Abebe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03260},
eprint = {2609.03260},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03260},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constraint closure and gravitational-wave content of shear-free cosmologies in metric f(R) gravity
AU - Mudhahir Al Ajmi
AU - Amare Abebe
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03260
UR - https://arxiv.org/abs/2609.03260
AB - We derive the consistency conditions governing the propagating content of linear shear-free perturbations of Friedmann-Lema\^ıtre-Robertson-Walker cosmologies in metric f(R) gravity. The divergence of the shear-free constraint is shown to be the total momentum-conservation equation and therefore does not imply geodesic flow. Its projected time derivative instead supplies a nontrivial integrability condition. Scalar, vector, and tensor sectors must then be tested separately. Shear-freeness removes the independent transverse-traceless electric-magnetic Weyl pair, so no ordinary + or × tensor gravitational wave survives. The scalaron is not removed algebraically, but its four-variable harmonic system must remain in the time-dependent consistent subspace generated by the shear-free constraint and all of its time derivatives. For a geodesic shear-free congruence in the spatially flat expanding de Sitter patch, this excludes every nonzero fixed comoving scalar harmonic, including the healthy R+αR^2−2Λ model with α,Λ>0. Vector modes obey a curvature-dependent global eigenvalue condition whose right-hand side is negative for positive-density matter with f'>0 and 1+w>0; hence no nonzero vector harmonic survives on that branch. The familiar coasting R^3 example evades this sign obstruction only because it lies on an f'<0 branch. Thus tensor radiation is absent in the imposed shear-free sector, whereas scalar radiation is not excluded kinematically but remains a model- and background-dependent constraint-closure question.
ER -