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arXiv · 2606.05075

Integrability of $R^2$ gravity cosmological models with radiation

Vsevolod R. Ivanov·Sergey Yu. Vernov
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Abstract

We consider cosmological $R^2$ gravity models with radiation. We find the general solution to the trace equation $\Box R=0$ in the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric. We analyze possible evolution of the Hubble parameter depending on the sign of the radiation energy density and find conditions for the existence of a bounce solution. A scalar field Lagrangian with the induced gravity term and the fourth-order monomial potential can play a role of radiation. In this case, we also obtain the general solution to the field equation. Therefore, the resulting $R^2$ gravity model with a scalar field is integrable in the spatially flat FLRW metric. Using a conformal metric transformation, we obtain a two-field chiral cosmological model that is also integrable in the spatially flat FLRW metric.

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Vsevolod R. Ivanov, Sergey Yu. Vernov. 2026-06-03. Integrability of $R^2$ gravity cosmological models with radiation. https://doi.org/10.1140/epjc%2Fs10052-026-16171-4

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