We consider modified f(R) gravity with a kinetic curvature scalar, which can be reduced to a chiral cosmological model of special kind. A detailed derivation is presented for the action of a chiral cosmological model as an equivalent to a gravitational model with higher derivatives with respect to the Ricci scalar using Lagrange multipliers and a transition from the Jordan frame to the Einstein one. The equations of the model are written in the spatially flat Friedmann-Robertson-Walker metric on the basis of the constructed chiral cosmological model. Examples of solutions are found, corresponding to a special choice of the field χ = χ_* = const, and its fixed value \(\chi_0=-\sqrt{3/2}\;\text{ln}2\). For this value of χ₀, in the case of the canonical inclusion of the kinetic component of the Ricci scalar, we have obtained a nonlinear second-order differential equation with respect to H, which is not amenable to analytic solution. Therefore we implement a transition to a noncanonical form of the kinetic term. Using a fixed value of χ₀, an exact solution is obtained for power-law inflation. We have considered a transition from the de Sitter and power-law solutions specified in the Jordan frame to the Einstein frame for comparison with the results obtained in f(R) gravity with higher derivatives. It is proved that there is a Weyl conformal transformation which transforms the de Sitter and power-law solutions in one frame to similar solutions in the other.

中文翻译：

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具有动态曲率标量的f（R）引力手性宇宙模型。

我们考虑使用动曲率标量修改的f（R）引力，可以将其简化为一种特殊的手性宇宙学模型。对于手性宇宙学模型的作用，给出了详细的推导，等效于使用拉格朗日乘子对Ricci标量具有较高导数的引力模型，并且从约旦框架过渡到爱因斯坦框架。在构造的手性宇宙学模型的基础上，以空间平坦的Friedmann-Robertson-Walker度量编写模型的方程。找到解决方案的示例，对应于字段χ = χ _* = const的特殊选择及其固定值\（\ chi_0 =-\ sqrt {3/2} \; \ text {ln} 2 \）。对于χ0的_值，在规范包含Ricci标量的动力学分量的情况下，我们获得了相对于H的非线性二阶微分方程，该方程不适合解析解。因此，我们实现了动力学术语向非规范形式的过渡。使用的固定值χ ₀，对于幂律充气获得的精确解。我们考虑了从Jordan框架中指定的de Sitter和幂定律解到Einstein框架的过渡，以便与在f（R）具有较高导数的重力。证明了存在Weyl保形变换，它将一帧中的de Sitter和幂律解转换为另一帧中的相似解。