Chiral cosmological models (CCM) can be used to describe not only inflation, but also the formation of primordial black holes (PBH) in the early Universe, because these models can produce large amplitude peaks at small scales. CCMs are related to modified gravity models through a conformal transformation of the metric. Two-field CCMs are actively studied. One of the most well-known modified gravity models that leads to such a CCM is the Higgs-$R^2$ inflationary model, which reproduces the Planck/BICEP observational data, but deviates from more recent data of the Atacama Cosmological Telescope (ACT).
In two-field CCMs with PBH formation, inflation includes two stages. In the first stage, one scalar field evolves, while the second one remains almost constant. This stage satisfies the slow-roll conditions, which allows us to calculate the inflationary parameters using the slow-roll approximation. The second stage of inflation corresponds to the evolution of the second scalar field. The slow-roll regime is violated during a few e-folds after the end of the first stage of inflation. After that, the slow-roll approximation is restored. This breaking of the slow-roll approximation is a necessary condition for PBH formation. The duration of the second inflationary stage affects the mass of these PBHs.
We have constructed new two-field CCMs that are connected with induced and F(R) gravity models. At certain values of the model parameters, these models are in good agreement with ACT observation data and are suitable to describe the formation of primordial black holes with masses similar to those of dark matter candidates. This talk is based on the papers by E.O. Pozdeeva and S.Yu. Vernov (Phys. Part. Nucl. 56 (2025) 542 [arXiv:2407.00999] and arXiv:2509.21220) as well as recent investigations.