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 Pozdeeva and Alessandro Tronconi and Giovanni Venturi and Sergey Vernov},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2016}
}
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. 
View PDF on arXiv
10 Citations
Highly Influential Citations
1
Background Citations
1

10 Citations

Integrable cosmological models in the Einstein and in the Jordan frames and Bianchi-I cosmology

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…

Induced Gravity Models with Exact Bounce Solutions

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…

Superpotential Method for $$F(R)$$ Cosmological Models

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…

Asymptotically safe non-minimal inflation

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…

Integrable Cosmological Models with Liouville Field: Energy Density Self-Adjointness and Semiclassical Wave Packets

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…

Integrable minisuperspace models with Liouville field: energy density self-adjointness and semiclassical wave packets

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…

Scalar-tensor cosmologies in a minisuperspace formulation: a case study

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…

$$f(\mathcal {G})$$ Noether cosmology

<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…

. 08 31 3 v 2 [ gr-q c ] 1 6 Ju l 2 02 0 f ( G ) Noether cosmology

  • 2020

5 . 08 31 3 v 1 [ gr-q c ] 1 7 M ay 2 02 0 f ( G ) Noether cosmology

  • 2020

References

SHOWING 1-10 OF 53 REFERENCES

Interdependence between integrable cosmological models with minimal and non-minimal coupling

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…

Integrable cosmological models with non-minimally coupled scalar fields

We obtain general solutions for some flat Friedmann universes filled with a scalar field in induced gravity models and models including the Hilbert–Einstein curvature term plus a scalar field…

Simplest Cosmological Model with the Scalar Field

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…

Stable Exact Cosmological Solutions in Induced Gravity Models

We study dynamics of induced gravity cosmological models with the sixth degree polynomial potentials, that have found using the superpotential method. The important property of these models are…

Global integrability of cosmological scalar fields

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…

Reconstruction of Scalar Potentials in Modified Gravity Models

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 as an inflaton

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)…

The Standard Model Higgs boson as the inflaton

COSMOLOGY WITH NON-MINIMAL SCALAR FIELD : GRACEFUL ENTRANCE INTO INFLATION

Scalar field cosmologies with inverted potentials

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…
...