DOI: 10.1140/epjc/s10052-026-16171-4 ISSN: 1434-6052
Integrability of $$R^2$$ gravity cosmological models with radiation
Vsevolod R. Ivanov, Sergey Yu. Vernov Abstract
We consider
$$R^2$$
R
2
gravity cosmological models with radiation. We find the general solution to the trace equation
$$\Box R=0$$
□
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
$$R^2$$
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.