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arXiv · 2607.24347

Multi-gravity cosmology beyond pairwise interactions

J. Flinckman
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Abstract

We develop the cosmological framework for Hassan--Schmidt-May multi-gravity, a ghost-free extension of bimetric theory with genuinely non-pairwise interactions of multiple spin-2 fields. For metrics that are simultaneously homogeneous and isotropic, the background dynamics reduce to a modified Friedmann equation supplemented by a system of coupled quartic polynomial equations for the scale-factor ratios. The spin-2 interaction contributes to the Friedmann equation as an additional effective fluid. We identify a regular high-density branch that approaches the standard radiation- or matter-dominated Universe, while regular low-density branches approach proportional vacuum solutions, where the interaction acts as a cosmological constant and the leading correction to the effective spin-2 energy density provides an additional matter contribution. We also determine the relative null-cone structure: on the regular high-density branch, the additional null cones approach wider opening angles than the matter-coupled null cone, while all null cones coincide in the vacuum limit. At linear order, we solve the algebraic equations determining the non-metric vielbein perturbations, derive the first-order consistency equations and their scalar and vector projections, and obtain the complete system of coupled tensor perturbation equations. These results establish a framework for studying cosmological solutions and perturbations in ghost-free multi-gravity beyond bimetric theory and its pairwise-interacting extensions.

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J. Flinckman. 2026-07-27. Multi-gravity cosmology beyond pairwise interactions. https://arxiv.org/abs/2607.24347

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