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On a model of quantum quadratic gravity in 7 + 1-dimensional spacetime

  • Vsevolod Chistiakov
  • Artur Mingaleev
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Abstract

We consider a quadratic gravity model supplemented by the terms ∇μR∇μR and (∇2R)2. For specific relations among the coupling constants, the action takes a perfect-square form. In the spatially flat FLRW model, we perform a reduction to a dynamical variable invariant under time reparameterizations. We construct a nonlinear change of variable that transforms the reduced action into the Gaussian action associated with the Wiener measure. An analysis of the transformation Jacobian within a time discretization singles out the case of 7+1-dimensional spacetime, in which the Jacobian of the discrete transformation under consideration is independent of the dynamical variable. On this basis, we propose a formal representation of expectation values of observables in the reduced model as integrals with respect to the Wiener measure.

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Cite

BibTeXRIS
BibTeX
@misc{chistiakov2026model,
  title = {{On a model of quantum quadratic gravity in 7 + 1-dimensional spacetime}},
  author = {Vsevolod Chistiakov and Artur Mingaleev},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37780},
  eprint = {2610.37780},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37780},
}
RIS
TY  - UNPB
TI  - On a model of quantum quadratic gravity in 7 + 1-dimensional spacetime
AU  - Vsevolod Chistiakov
AU  - Artur Mingaleev
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37780
UR  - https://arxiv.org/abs/2610.37780
AB  - We consider a quadratic gravity model supplemented by the terms ∇_μR∇^μR and (∇^2R)^2. For specific relations among the coupling constants, the action takes a perfect-square form. In the spatially flat FLRW model, we perform a reduction to a dynamical variable invariant under time reparameterizations. We construct a nonlinear change of variable that transforms the reduced action into the Gaussian action associated with the Wiener measure. An analysis of the transformation Jacobian within a time discretization singles out the case of 7+1-dimensional spacetime, in which the Jacobian of the discrete transformation under consideration is independent of the dynamical variable. On this basis, we propose a formal representation of expectation values of observables in the reduced model as integrals with respect to the Wiener measure.
ER  -