Elementary-Symmetric Ricci Gravity: Metric Formulation
Abstract
We investigate a four-dimensional metric theory of gravity whose Lagrangian is a linear combination of the elementary symmetric polynomials of the Ricci tensor. We derive the field equations and characterize Einstein vacua and a real, diagonalizable class of parallel-Ricci vacua. The latter includes direct products of two constant-curvature surfaces and can exhibit a hierarchy of curvature radii. The Einstein vacua possess multiple branches associated with the distinct roots of a polynomial, whose multiple roots define boundaries in parameter space. We derive the linearized equations on maximally symmetric backgrounds, distinguish the scalar and spin-2 degrees of freedom, and then analyze their classical linear stability. We also obtain the generalized Friedmann constraint and the associated homogeneous evolution equations. An illustrative spatially flat solution evolves from the neighborhood of an unstable de Sitter solution toward a stable de Sitter solution. This behavior may motivate further investigation into early- and late-time accelerated expansion and provide a gravity-driven mechanism for automatic end of inflation.
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BibTeX
@misc{suo2026elementarysymmetric,
title = {{Elementary-Symmetric Ricci Gravity: Metric Formulation}},
author = {Xingpao Suo and Dianxu Ma and Yuqiong Shan and Xingyan Suo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26980},
eprint = {2610.26980},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26980},
}
RIS
TY - UNPB
TI - Elementary-Symmetric Ricci Gravity: Metric Formulation
AU - Xingpao Suo
AU - Dianxu Ma
AU - Yuqiong Shan
AU - Xingyan Suo
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26980
UR - https://arxiv.org/abs/2610.26980
AB - We investigate a four-dimensional metric theory of gravity whose Lagrangian is a linear combination of the elementary symmetric polynomials of the Ricci tensor. We derive the field equations and characterize Einstein vacua and a real, diagonalizable class of parallel-Ricci vacua. The latter includes direct products of two constant-curvature surfaces and can exhibit a hierarchy of curvature radii. The Einstein vacua possess multiple branches associated with the distinct roots of a polynomial, whose multiple roots define boundaries in parameter space. We derive the linearized equations on maximally symmetric backgrounds, distinguish the scalar and spin-2 degrees of freedom, and then analyze their classical linear stability. We also obtain the generalized Friedmann constraint and the associated homogeneous evolution equations. An illustrative spatially flat solution evolves from the neighborhood of an unstable de Sitter solution toward a stable de Sitter solution. This behavior may motivate further investigation into early- and late-time accelerated expansion and provide a gravity-driven mechanism for automatic end of inflation.
ER -