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### CHIRAL COSMOLOGICAL MODEL OF \(f(R, \square R)\) GRAVITY

#### Chervon S.V., Fomin I.V., Chaadaeva T.I.

We study the modified gravity \(f(R, \square R)\), which can be reduced to a chiral cosmological model of a particular type with scalar field observers \(\chi, \varphi, \phi\). The method of studying the chiral cosmological model was used for the \(f(R, (\nabla R)^2)\) models, but was first used by Naruko for the more general \(f(R)\) Gracing model. In this paper, equations for chiral fields and the Einstein-Friedmann equations in the Friedmann-Robertson-Walker metric are presented. Note that the solutions for this chosen model are based on a special choice of one of the chiral fields: \(\chi = -\sqrt{\frac{3}{2}}\ln 2\). Solutions are considered in the case of reducing the model to a one-field model: two chiral fields of the model depend linearly on the third one. The obtained solutions are of interest, since quantum corrections must also be taken into account in the analysis.

** Keywords:** chiral cosmological model, scalar-tensor and \(f(R)\) gravity theory, Friedman universe, cosmological parameters, spectral parameters.

** UDC:** 53.1

** PACS:** 04.20.Kd, 04.50.Kd

** DOI:** 10.17238/issn2226-8812.2023.1.117–120

*Please cite this article in English as:*

Chervon S.V., Fomin I.V., Chaadaeva T.I. Chiral cosmological model of \(f(R, \square R)\) gravity. Space, Time and Fundamental Interactions, 2023, no. 1, pp. 117–120.