Integrable modified gravity cosmological models with an additional scalar field

Abstract

We consider modified gravity cosmological models that can be transformed into two-field chiral cosmological models by the conformal metric transformation. For the $R^2$ gravity model with an additional scalar field and the corresponding two-field model with the cosmological constant and nonstandard kinetic part of the action, the general solutions have been obtained in the spatially flat FLRW metric. We analyze the correspondence of the cosmic time solutions obtained and different possible evolutions of the Hubble parameters in the Einstein and Jordan frames.

11 pages, 3 figures, v2: minor corrections, references are added, to appear in EPJC

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• Multiscalar-torsion Cosmology: Exact and Analytic Solutions from Noether Symmetries
• Hyperbolic inflation in the Jordan frame
• New method of exponential potentials reconstruction based on given scale factor in phantonical two-field models
• Multiscalar field cosmological model and possible solutions using Noether symmetry approach
• Variational symmetries and superintegrability in multifield cosmology
• Anisotropic solutions for $R^2$ gravity model with a scalar field
• Primordial black holes formation in inflationary $F(R)$ models with scalar fields
• Painlevé analysis for the cosmological field equations in Weyl Integrable Spacetime
• New Integrable Chiral Cosmological Models with Two Scalar Fields
• Integrable Cosmological Models with an Arbitrary Number of Scalar Fields
• Scheme of integration of vacuum $F(R)$ gravity in a travelling wave variable
• Anisotropic Spacetimes in Chiral Scalar Field Cosmology