On exponential solutions in the Einstein–Gauss–Bonnet cosmology, stability and variation of G

Ernazarov, K. K.; Ivashchuk, V. D.; Kobtsev, A. A.

doi:10.1134/s0202289316030051

Cited by 32 publications

(54 citation statements)

References 26 publications

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“…Here we outline main relations from [25,26], devoted to stability analysis of exponential solutions (2.3) with non-static volume factor [proportional to exp(…”

Section: Stability Analysismentioning

confidence: 99%

Stable exponential cosmological solutions with 3- and l-dimensional factor spaces in the Einstein–Gauss–Bonnet model with a $$\Lambda $$ Λ -term

Ivashchuk

Kobtsev

2018

Eur. Phys. J. C

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A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term is studied. We assume the metrics to be diagonal cosmological ones. For certain fine-tuned , we find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters H > 0 and h, corresponding to factor spaces of dimensions 3 and l > 2, respectively and D = 1 + 3 + l. The fine-tuned = (x, l, α) depends upon the ratio h/H = x, l and the ratio α = α 2 /α 1 of two constants (α 2 and α 1 ) of the model. For fixed , α and l > 2 the equation (x, l, α) = is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals (the example l = 3 is presented). For certain restrictions on x we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. A subclass of solutions with small enough variation of the effective gravitational constant G is considered. It is shown that all solutions from this subclass are stable.

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“…Here we outline main relations from [25,26], devoted to stability analysis of exponential solutions (2.3) with non-static volume factor [proportional to exp(…”

Section: Stability Analysismentioning

confidence: 99%

Stable exponential cosmological solutions with 3- and l-dimensional factor spaces in the Einstein–Gauss–Bonnet model with a $$\Lambda $$ Λ -term

Ivashchuk

Kobtsev

2018

Eur. Phys. J. C

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“…Here, as in [28,29], we deal with exponential solutions (2.3) with non-static volume factor, which is proportional to exp(…”

Section: Conditions For Stabilitymentioning

confidence: 99%

“…We study the stability of these solutions in a class of cosmological solutions with diagonal metrics by using results of refs. [28,29], see also approach of ref. [26].…”

Section: Introductionmentioning

confidence: 99%

On stable exponential cosmological solutions in the EGB model with a cosmological constant in dimensions D = 5, 6, 7, 8

Chirkov

Toporensky

2017

Gravit. Cosmol.

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A D-dimensional Einstein-Gauss-Bonnet (EGB) flat cosmological model with a cosmological term Λ is considered. We focus on solutions with exponential dependence of scale factor on time. Using previously developed general analysis of stability of such solutions done by V.D.Ivashchuk (2016) we apply the criterion from that paper to all known exponential solutions upto dimensionality 7+1. We show that this criterion which guarantees stability of solution under consideration is fulfilled for all combination of coupling constant of the theory except for some discrete set.

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“…[23] by using rather tedious calculations based on Eqs. (3.3) and (3.6) without using the identity (3.13).…”

Section: Remarkmentioning

confidence: 99%

“…The appearance of the Gauss-Bonnet term was motivated by string theory [1][2][3]. At present, the so-called Einstein-Gauss-Bonnet (EGB) gravitational model which is governed by the action (1.1) a e-mail: ivashchuk@mail.ru and its modifications are intensively used in cosmology; see [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and references therein, e.g. for explanation of accelerating expansion of the Universe following from supernovae (type Ia) observational data [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

On stability of exponential cosmological solutions with non-static volume factor in the Einstein–Gauss–Bonnet model

Ivashchuk

2016

Eur. Phys. J. C

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A (n + 1)-dimensional gravitational model with Gauss-Bonnet term and a cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with an exponential dependence of the scale factors, a i ∼ exp (v i t), i = 1, . . . , n, are analyzed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. if K (v) = n k=1 v k = 0. We prove that under a certain restriction R imposed solutions with K (v) > 0 are stable, while solutions with K (v) < 0 are unstable. Certain examples of stable solutions are presented. We show that the solutions with v 1 = v 2 = v 3 = H > 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed.

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On exponential solutions in the Einstein–Gauss–Bonnet cosmology, stability and variation of G

Cited by 32 publications

References 26 publications

Stable exponential cosmological solutions with 3- and l-dimensional factor spaces in the Einstein–Gauss–Bonnet model with a $$\Lambda $$ Λ -term

Stable exponential cosmological solutions with 3- and l-dimensional factor spaces in the Einstein–Gauss–Bonnet model with a $$\Lambda $$ Λ -term

On stable exponential cosmological solutions in the EGB model with a cosmological constant in dimensions D = 5, 6, 7, 8

On stability of exponential cosmological solutions with non-static volume factor in the Einstein–Gauss–Bonnet model

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