Exact and Approximate Solutions in the Friedmann Cosmology

Фомин, И. В.; Chervon, S. V.

doi:10.1007/s11182-017-1091-x

Cited by 25 publications

(30 citation statements)

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“…Let us prove, for any h BB given by (32), that we can construct the CCM with exact solutions obtained either in analytic form or in quadratures. We choose…”

Section: The Superpotential Methods For the Ccmmentioning

confidence: 99%

“…Under condition h 12 (χ, ψ) = 0 one has the same solutions for the trivial case of a constant diagonal tensor h AB . Similarly, one can generalize any exact solutions in single-field models (see, for example, [33,87]) on this special class of chiral cosmological models with two components.…”

Section: Reducing Two-field Dynamic Equations To the Single-fieldmentioning

confidence: 99%

“…In the case of single scalar cosmology with a generic potential, the integration procedure is reduced to solving the Ivanov-Salopek-Bond equation [7,30]. There are many methods of obtaining physically relevant solutions, including that with the Higgs potential [30][31][32][33]. The reduction of a CCM to a single scalar field model was proposed in [34].…”

Section: Introductionmentioning

confidence: 99%

“…It is difficult to consider such solutions as exact ones without involving the dynamic equations of the chiral fields 2. Other methods allowing to find exact solutions in inflationary models were presented in[26,31,32,34,[51][52][53][54][55][56][57][58] (for recent review, see[33]). …”

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confidence: 99%

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Superpotential method for chiral cosmological models connected with modified gravity

et al. 2019

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We consider the Chiral Cosmological Models (CCMs) and modified gravity theories associated with them. Generalization of the superpotential method for a general CCM with several scalar fields is performed, and the method of construction CCMs admitting exact solutions is developed. New classes of exact solutions in the two-component CCM connected with an f (R) gravity model with an additional scalar field have been constructed. We construct new cosmological solutions for a diagonal metric of the target space, including modified power-law solutions. In particular, we propose the reconstruction procedure based on the superpotential method and present examples of kinetic part reconstruction for periodic and hyperbolic Hubble parameters. We also focus on a cyclic type of Universe dubbed the Quasi-Steady State (QSS) model, with the aim of constructing single-and double-field potentials for one and the same behaviour of the Hubble parameter using the developed superpotential method for the CCM. The realization of this task includes a new set of solutions for a CCM with a scale factor characterized by the QSS theory. We also propose a method for reducing the two-field CCM to the single scalar field model.

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“…Let us prove, for any h BB given by (32), that we can construct the CCM with exact solutions obtained either in analytic form or in quadratures. We choose…”

Section: The Superpotential Methods For the Ccmmentioning

confidence: 99%

Section: Reducing Two-field Dynamic Equations To the Single-fieldmentioning

confidence: 99%