# General solutions of integrable cosmological models with non-minimal coupling

@article{Kamenshchik2016GeneralSO,
title={General solutions of integrable cosmological models with non-minimal coupling},
author={Alexander Yu. Kamenshchik and Ekaterina O. Pozdeeva and Alessandro Tronconi and Giovanni Venturi and Sergey Yu. Vernov},
journal={Physics of Particles and Nuclei Letters},
year={2016},
volume={14},
pages={382 - 385}
}
• Published 7 April 2016
• Physics, Mathematics
• Physics of Particles and Nuclei Letters
We study the integrable model with minimally and non-minimally coupled scalar fields and the correspondence of their general solutions. Using the model with a minimally coupled scalar field and a the constant potential as an example we demonstrate the difference between the general solutions of the corresponding models in the Jordan and the Einstein frames.
12 Citations
• Physics, Mathematics
Physics of Particles and Nuclei
• 2018
We study integrable models in the Bianchi I metric case with scalar fields minimally and non-minimally coupled with gravity and the correspondence between their general solutions. Using the model
• Physics
• 2020
—We construct the gravity models with exact particular solutions using the conformal transformation and the superpotential method for the corresponding models in the Einstein frame. The functions are
• Mathematics, Physics
Physics of Particles and Nuclei
• 2018
We study dynamics of induced gravity cosmological models with the sixth-degree polynomial potentials, that have been constructed using the superpotential method. We find conditions on the potential
• Physics
• 2019
We construct the $F(R)$ gravity models with exact particular solutions using the conformal transformation and the superpotential method for the corresponding models in the Einstein frame. The
We study the constraints imposed by the requirement of Asymptotic Safety on a class of inflationary models with an inflaton field non-minimally coupled to the Ricci scalar. The critical surface in
• Physics
• 2018
The homogeneous cosmological models with a Liouville scalar field are investigated in classical and quantum context of geometrodynamics. An integral of motion is used to eliminate the lapse function
• Physics
The European Physical Journal C
• 2018
The homogeneous cosmological models with a Liouville scalar field are investigated in classical and quantum contexts of Wheeler–DeWitt geometrodynamics. In the quantum case of quintessence field with
• Physics
• 2021
We revisit a general minisuperspace (MSS) formalism for scalar tensor (ST) FLRW type cosmological models in arbitrary frame with perfect fluid source. We discuss how to impose Cauchy data on the
• Physics, Mathematics
• 2020
We develop the n -dimensional cosmology for f ( G ) gravity, where G is the Gauss–Bonnet topological invariant. Speciﬁcally, by the so-called Noether Symmetry Approach, we select f ( G ) (cid:2) G k
• Physics
The European Physical Journal C
• 2020
<jats:p>We develop the <jats:italic>n</jats:italic>-dimensional cosmology for <jats:inline-formula><jats:alternatives><jats:tex-math>$$f(\mathcal {G})$$</jats:tex-math><mml:math

## References

SHOWING 1-10 OF 40 REFERENCES

• Mathematics, Physics
• 2015
We consider the relation between exact solutions of cosmological models having minimally and non-minimally coupled scalar fields. This is done for a particular class of solvable models which, in the
• Physics
• 1997
We investigate the simplest cosmological model with the massive real scalar non-interacting inflaton field minimally coupled to gravity. The classification of trajectories in closed minisuperspace
• Mathematics, Physics
• 2008
We investigate the Liouvillian integrability of Hamiltonian systems describing a universe filled with a scalar field (possibly complex). The tool used is the differential Galois group approach, as
• Physics, Mathematics
• 2013
We employ the superpotential technique for the reconstruction of cosmological models with a non-minimally coupled scalar field evolving on a spatially flat Friedmann-Robertson-Walker background. The
The Higgs field of the pure Standard Model can lead to the inflationary expansion of the early Universe if it is non-minimally coupled to gravity. The model predicts Cosmic Microwave Background (CMB)
• Physics
• 2015
Regular bouncing solutions in the framework of a scalar-tensor gravity model were found in a recent work. We reconsider the problem in the Einstein frame (EF) in the present work. Singularities
• Physics
• 2016
We study the relation between the Jordan-Einstein frame transition and the possible description of the crossing of singularities in flat Friedmann universes, using the fact that the regular evolution