On-shell Homogeneous Curvature Modes in Quadratic F(R,𝒢) Cosmology

Abstract

5We study homogeneous cosmological perturbations in the quadratic model F(R,𝒢)=R+αR²+β𝒢². Linearization of the modified Friedmann equation together with dust conservation yields a second-order equation for the homogeneous Hubble perturbation, or equivalently a third-order equation for the matter contrast. We then restrict the asymptotic analysis to backgrounds that satisfy the zeroth-order equations of the same quadratic theory. Besides the low-curvature dust branch, which approaches H=2/(3t), the model admits a nontrivial vacuum de Sitter solution with βH_dS⁶=1/96. Its homogeneous curvature modes are stable only when α<−1/(6H_dS²). At high curvature the background equation also admits a vacuum big-rip asymptotic branch beginning with H=7/(t_s−t); the first corrections are fixed by the quadratic couplings. The corresponding 𝒢²-dominated perturbation has one divergent homogeneous mode. The simultaneous Einstein limit is taken only as a consistency check and recovers the standard dust behavior.

Dynamical systems in quadratic teleparallel cosmology
Manuel Hohmann
arXiv8 Sep 2026PreprintarXiv licenceFull textGravitation & general relativityarXiv
Fission Modes and Fragment Shell Structures in ²⁵⁸Md^* from Six-Dimensional Langevin Calculations
K Okada, K Nishio, T Wada +1
HAL22 Sep 2026PreprintarXiv licenceFull textNuclear physicsHALarXiv
Plasmon modes in three-dimensional multifold semimetals. I. Triple-point semimetal, its quadratic cousin, and Hopf semimetal
Ipsita Mandal
arXiv20 Oct 2026PreprintarXiv licenceFull textCondensed matter High-energy & particle physicsarXiv
Bose-Einstein condensate in a shell: nonlinear modes and symmetry breaking
Alexander Wolf, Vladimir V. Konotop, Maxim A. Efremov
arXiv23 Oct 2026PreprintCC BY 4.0Full textAtomic, molecular & optical physics Condensed matterarXiv
Comparing critical regions in Polyakov-quark-meson models: Effects of flavor (two versus 2+1) under on-shell renormalization, and on-shell versus curvature-mass parameter fixing for the two-flavor case
Pooja Kumari, Suraj Kumar Rai, Vivek Kumar Tiwari
arXiv23 Sep 2026PreprintCC BY 4.0Full textHigh-energy & particle physicsarXiv

Cite

BibTeX RIS

BibTeX

@misc{telloortiz2026onshell,
  title = {{On-shell Homogeneous Curvature Modes in Quadratic $F(R,\mathcal G)$ Cosmology}},
  author = {Francisco Tello-Ortiz and B. Mishra and Y. Gómez-Leyton and Jean Báez Cuevas},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03752},
  eprint = {2610.03752},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03752},
}

RIS

TY  - UNPB
TI  - On-shell Homogeneous Curvature Modes in Quadratic F(R,𝒢) Cosmology
AU  - Francisco Tello-Ortiz
AU  - B. Mishra
AU  - Y. Gómez-Leyton
AU  - Jean Báez Cuevas
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.03752
UR  - https://arxiv.org/abs/2610.03752
AB  - 5We study homogeneous cosmological perturbations in the quadratic model F(R,𝒢)=R+αR^2+β𝒢^2. Linearization of the modified Friedmann equation together with dust conservation yields a second-order equation for the homogeneous Hubble perturbation, or equivalently a third-order equation for the matter contrast. We then restrict the asymptotic analysis to backgrounds that satisfy the zeroth-order equations of the same quadratic theory. Besides the low-curvature dust branch, which approaches H=2/(3t), the model admits a nontrivial vacuum de Sitter solution with βH_dS^6=1/96. Its homogeneous curvature modes are stable only when α<−1/(6H_dS^2). At high curvature the background equation also admits a vacuum big-rip asymptotic branch beginning with H=7/(t_s−t); the first corrections are fixed by the quadratic couplings. The corresponding 𝒢^2-dominated perturbation has one divergent homogeneous mode. The simultaneous Einstein limit is taken only as a consistency check and recovers the standard dust behavior.
ER  -

Abstract

Related

Cite