Cosmology in sixth-order higher-derivative theories of gravity
Abstract
We analyze the cosmological implications of theories of gravity with quadratic curvature invariants R2 and CμνρσCμνρσ, and six-derivative operators RBox R and CμνρσBox Cμνρσ. We first analyze homogeneous and isotropic cosmological solutions, showing that the theory admits expanding, recollapsing and non-singular bouncing solutions. We clarify in the Einstein-frame formulation the mechanism that circumvents the Hawking--Penrose singularity theorems, and identify the role played by the additional higher-derivative degrees of freedom in that mechanism. We show that the complete set of linear equations governing tensor perturbations on standard backgrounds admit analytically stable solutions. The analysis reveals that the stability properties are determined by the pole structure of the propagator and by specific relations among the higher-derivative couplings, while the singularity-free backgrounds are found to be unstable against tensor perturbations. For scalar cosmological perturbations, the higher-derivative theories presents super-horizon scalar instabilities in de Sitter spacetimes for both quadratic and sixth-order gravity. To extract inflationary observables, we adopt an EFT approach to the sixth-order theory, treating these terms as perturbative corrections around the Starobinsky background. Within this framework, we compute the modification of the primordial scalar and tensor power spectra, obtaining predictions for the scalar spectral index and tensor-to-scalar ratio. We find that sixth-order operators produce controlled deviations from the Starobinsky model while preserving the EFT expansion, thereby providing a consistent phenomenological framework to probe ultraviolet gravitational corrections through cosmological observables.
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BibTeX
@misc{aguilar2026cosmology,
title = {{Cosmology in sixth-order higher-derivative theories of gravity}},
author = {Carlos Aguilar and Manuel Asorey and Diego Muñoz and Miguel Pardina},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25387},
eprint = {2609.25387},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25387},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cosmology in sixth-order higher-derivative theories of gravity
AU - Carlos Aguilar
AU - Manuel Asorey
AU - Diego Muñoz
AU - Miguel Pardina
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25387
UR - https://arxiv.org/abs/2609.25387
AB - We analyze the cosmological implications of theories of gravity with quadratic curvature invariants R^2 and C^μνρσC_μνρσ, and six-derivative operators RBox R and C^μνρσBox C_μνρσ. We first analyze homogeneous and isotropic cosmological solutions, showing that the theory admits expanding, recollapsing and non-singular bouncing solutions. We clarify in the Einstein-frame formulation the mechanism that circumvents the Hawking--Penrose singularity theorems, and identify the role played by the additional higher-derivative degrees of freedom in that mechanism. We show that the complete set of linear equations governing tensor perturbations on standard backgrounds admit analytically stable solutions. The analysis reveals that the stability properties are determined by the pole structure of the propagator and by specific relations among the higher-derivative couplings, while the singularity-free backgrounds are found to be unstable against tensor perturbations. For scalar cosmological perturbations, the higher-derivative theories presents super-horizon scalar instabilities in de Sitter spacetimes for both quadratic and sixth-order gravity. To extract inflationary observables, we adopt an EFT approach to the sixth-order theory, treating these terms as perturbative corrections around the Starobinsky background. Within this framework, we compute the modification of the primordial scalar and tensor power spectra, obtaining predictions for the scalar spectral index and tensor-to-scalar ratio. We find that sixth-order operators produce controlled deviations from the Starobinsky model while preserving the EFT expansion, thereby providing a consistent phenomenological framework to probe ultraviolet gravitational corrections through cosmological observables.
ER -