New classes of exact solutions in inflationary cosmology

Zhuravlev, V. M.; Chervon, S. V.; Shchigolev, V. K.

doi:10.1134/1.558649

Cited by 40 publications

(51 citation statements)

References 7 publications

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“…Exact inflationary solutions have been studied before [1,2,3,4,5,6,8,9,10,11,12] and we would like to point out the difference between previous work and the present work. It is well known that inflationary potentials of the form V (φ) ∝ e ±φ can be solved exactly and these types of models were studied in [5,8,11,12].…”

Section: Introductionmentioning

confidence: 75%

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Another exact inflationary solution

Kruger

Norbury

2000

Phys. Rev. D

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Section: Introductionmentioning

confidence: 75%

“…Exact inflationary solutions [1,2,3,4,5,6] are of interest because they allow one to study physical effects in a simple manner than would otherwise be allowed from numerical studies. In addition, they allow one to write down exact forms for decaying cosmological constant models [7] as we shall see below.…”

Section: Introductionmentioning

confidence: 99%

Another exact inflationary solution

Kruger

Norbury

2000

Phys. Rev. D

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“…Finally, we made connection of one special anzats with evolutionary scale factor and presented the system of equations in the form which allowed us to generate exact solutions (at least in quadratures) of wide class for given scale factor. Thus the analog of fine tuning of the potential method [29][30][31] we proposed for EGB cosmology with scalar field and non-minimal interaction with GB term.…”

Section: Resultsmentioning

confidence: 99%

“…To this end we can express t as the function on φ using the relation (31). Then we will substitute it into (29).…”

Section: ξ = C 1 Tmentioning

confidence: 99%

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Exact inflation in Einstein–Gauss–Bonnet gravity

Фомин

Chervon

2017

Gravit. Cosmol.

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We study cosmological inflation in the Einstein gravity model, where additionally the Gauss-Bonnet term non-minimally coupled to a scalar field is included. We prove that inflationary solutions of exponential and power-law types are allowable and we found few examples of them. We also proposed the method of the exact inflationary solutions construction for a single scalar field with given scale factor and Gauss-Bonnet coupling term in the spatially flat Friedmann-Robertson-Walker Universe on the basis of connection with standard inflation and using special anzatses. With one special anzats we presented the system of equations in the form which allowed generation of exact solutions (at least in quadratures) of wide class by setting the scale factor.

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The cosmological constant as an eigenvalue of a Sturm-Liouville problem

Astashenok

Elizalde

Yurov

2013

Astrophys Space Sci

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It is observed that one of Einstein-Friedmann's equations has formally the aspect of a Sturm-Liouville problem, and that the cosmological constant, Λ, plays thereby the role of spectral parameter (what hints to its connection with the Casimir effect). The subsequent formulation of appropriate boundary conditions leads to a set of admissible values for Λ, considered as eigenvalues of the corresponding linear operator. Simplest boundary conditions are assumed, namely that the eigenfunctions belong to L 2 space, with the result that, when all energy conditions are satisfied, they yield a discrete spectrum for Λ > 0 and a continuous one for Λ < 0. A very interesting situation is seen to occur when the discrete spectrum contains only one point: then, there is the possibility to obtain appropriate cosmological conditions without invoking the anthropic principle. This possibility is shown to be realized in cyclic cosmological models, provided the potential of the matter field is similar to the potential of the scalar field. The dynamics of the universe in this case contains a sudden future singularity.Recently Barrow and Shaw [5] suggested a non-anthropic solution to the problem: by making Λ into a field and restricting the variations of the action with respect to it by causality, they managed to obtain an additional Einstein constraint equation. One can say that this approach is based on a different interpretation of the cosmological constant, notably to consider the cosmological constant to be a field variable.In the present work we use a somehow similar procedure to calculate the value of Λ, namely to interpret it as an eigenvalue of a Sturm-Liouville problem, rather than as an integration constant. Our approach is in fact more conservative than the method in [5] since we use the standard Einstein-Friedmann equations without any additional constraint equation. Instead, we consider one of Friedmann's equations as a spectral problem and look for a class of boundary conditions which may allow us to actually calculate the corresponding eigenvalues (in this way, our procedure is closely related to standard investigations of the Casimir effect [6, 1, 2] by spectral methods). A most simple condition is to impose that eigenfunctions be elements of L 2 . As we will show, this choice results in the following interesting consequence: if the universe is filled up with a matter field, φ (except for Λ), such that all the strong energy conditions are satisfied, then one gets a point spectrum for positive values of the cosmological constant, and a continuous spectrum for negative ones.The next step will be to consider models which actually result in a positive discrete spectrum with just one single point. This idea is inspired in the conceptual approach developed in the paper by Linde and Vanchurin [7]: one can fix all the parameters in the landscape, including the value of the cosmological constant, without using any anthropic considerations, what "will give us a chance to return to Einstein's dream of a final theory, which may all...

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New classes of exact solutions in inflationary cosmology

Cited by 40 publications

References 7 publications

Another exact inflationary solution

Another exact inflationary solution

Exact inflation in Einstein–Gauss–Bonnet gravity

The cosmological constant as an eigenvalue of a Sturm-Liouville problem

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