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PreprintCC BY 4.0arXiv

FLRW-Compatible Tensors and Perfect-Fluid Universality in Modified Gravity

  • Cem Dalkırmaz
  • Yaghoub Heydarzade
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Abstract

We study FLRW-compatible tensor fields on Friedmann--Lemaître--Robertson--Walker spacetimes in (D+1) dimensions equipped with Levi-Civita connection. We prove that any covariant rank-N tensor field invariant under the spatial homogeneity and isotropy group, with D>N, admits a finite decomposition into monomials constructed from the metric tensor gμν and the unit timelike vector uμ, with scalar coefficients depending only on cosmic time. As a direct consequence, any rank-two correction term appearing in an Einstein-like rearrangement of the FLRW background field equations has the effective perfect-fluid form for D>2. Thus, the result provides an arbitrary-rank tensorial classification underlying the perfect-fluid structure of modified gravity equations on FLRW backgrounds, complementing existing rank-two universality results. Applications to generalized Friedmann equations and to the geodesic deviation equation in modified gravity are also discussed.

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Cite

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BibTeX
@misc{dalkırmaz2026flrwcompatible,
  title = {{FLRW-Compatible Tensors and Perfect-Fluid Universality in Modified Gravity}},
  author = {Cem Dalkırmaz and Yaghoub Heydarzade},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11626},
  eprint = {2610.11626},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11626},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - FLRW-Compatible Tensors and Perfect-Fluid Universality in Modified Gravity
AU  - Cem Dalkırmaz
AU  - Yaghoub Heydarzade
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11626
UR  - https://arxiv.org/abs/2610.11626
AB  - We study FLRW-compatible tensor fields on Friedmann--Lemaître--Robertson--Walker spacetimes in (D+1) dimensions equipped with Levi-Civita connection. We prove that any covariant rank-N tensor field invariant under the spatial homogeneity and isotropy group, with D>N, admits a finite decomposition into monomials constructed from the metric tensor g_μν and the unit timelike vector u_μ, with scalar coefficients depending only on cosmic time. As a direct consequence, any rank-two correction term appearing in an Einstein-like rearrangement of the FLRW background field equations has the effective perfect-fluid form for D>2. Thus, the result provides an arbitrary-rank tensorial classification underlying the perfect-fluid structure of modified gravity equations on FLRW backgrounds, complementing existing rank-two universality results. Applications to generalized Friedmann equations and to the geodesic deviation equation in modified gravity are also discussed.
ER  -