Cosmological dynamics in higher-dimensional Einstein–Gauss–Bonnet gravity

Canfora, Fabrizio; Giacomini, Alex; Pavluchenko, Sergey A.

doi:10.1007/s10714-014-1805-0

Cited by 31 publications

(87 citation statements)

References 64 publications

(85 reference statements)

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“…For example, the scheme of dynamical compactification in higher curvature gravity introduced in [20] has been applied to EinsteinGauss-Bonnet gravity in higher dimensions to obtain exact solutions in various cosmological models [21][22][23][24][25]. The dynamical compactification scheme has also been applied in numerical investigations of cosmological scenarios in [26,27]. In particular it has been observed in [28] that one can have standard Friedmann dynamics even though the gravity theory is that of Einstein-Gauss-Bonnet.…”

Section: Introductionmentioning

confidence: 99%

1/r potential in higher dimensions

Chakraborty

Dadhich

2018

Eur. Phys. J. C

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In Einstein gravity, gravitational potential goes as 1/r d−3 in d non-compactified spacetime dimensions, which assumes the familiar 1/r form in four dimensions. On the other hand, it goes as 1/r α , with α = (d −2m −1)/m, in pure Lovelock gravity involving only one mth order term of the Lovelock polynomial in the gravitational action. The latter offers a novel possibility of having 1/r potential for the noncompactified dimension spectrum given by d = 3m+1. Thus it turns out that in the two prototype gravitational settings of isolated objects, like black holes and the universe as a whole -cosmological models, the Einstein gravity in four and mth order pure Lovelock gravity in 3m + 1 dimensions behave in a similar fashion as far as gravitational interactions are considered. However propagation of gravitational waves (or the number of degrees of freedom) does indeed serve as a discriminator because it has two polarizations only in four dimensions.

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Section: Introductionmentioning

confidence: 99%

1/r potential in higher dimensions

Chakraborty

Dadhich

2018

Eur. Phys. J. C

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“…This kind of singularity is "weak" by Tipler's classification [69], and "type II" in the classification by Kitaura and Wheeler [70,71]. Recent studies of the singularities of this kind in the cosmological context in Lovelock and Einstein-Gauss-Bonnet gravity demonstrate [27,49,50,52,54] that their presence is not suppressed and they are abundant for a wide range of initial conditions and parameters and sometimes [50] they are the only option for future behavior.…”

Section: Discussionmentioning

confidence: 99%

“…In [22], the dynamical compactification solutions were studied with the use of Hamiltonian formalism. More recently, searches for spontaneous compactifications were made in [23], where the dynamical compactification of the (5+1)-dimensional Einstein-Gauss-Bonnet model was considered; in [24,25] with different metric Ansätze for scale factors corresponding to (3+1)-and extra-dimensional parts; and in [26][27][28], where general (e.g., without any Ansatz) scale factors and curved manifolds were considered. Also, apart from cosmology, the recent analysis has focused on properties of black holes in Gauss-Bonnet [29][30][31][32][33][34][35][36][37] and Lovelock [38][39][40][41][42] gravities, features of gravitational collapse in these theories [43][44][45], general features of spherical-symmetric solutions [46], and many others.…”

Section: Introductionmentioning

confidence: 99%

“…In this case both the three-dimensional Hubble parameter and the extra-dimensional scale factor asymptotically tend to the constant values. In [27] we performed a detailed analysis of the cosmological dynamics in this model with generic couplings. Recently we studied this model in [28] and demonstrated that, with an additional constraint on the couplings, Friedmann-type late-time behavior could be restored.…”

Section: Introductionmentioning

confidence: 99%

“…Thus in this paper we continue the investigation of the -term case for D = 3 and general D ≥ 4 cases. Let us also note that in [26][27][28] we considered a similar model but with both manifolds a constant (generally non-zero) curvature; the realistic regime in that model has exponential expansion of the three-dimensional subspace and constant-size extra dimensions.…”

Section: Introductionmentioning

confidence: 99%

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Cosmological dynamics of spatially flat Einstein–Gauss–Bonnet models in various dimensions: high-dimensional $$\Lambda $$ Λ -term case

Pavluchenko

2017

Eur. Phys. J. C

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In this paper we perform a systematic study of spatially flat [(3 + D) + 1]-dimensional Einstein-GaussBonnet cosmological models with -term. We consider models that topologically are the product of two flat isotropic subspaces with different scale factors. One of these subspaces is three-dimensional and represents our space and the other is D-dimensional and represents extra dimensions. We consider no ansatz of the scale factors, which makes our results quite general. With both Einstein-Hilbert and Gauss-Bonnet contributions in play, D = 3 and the general D ≥ 4 cases have slightly different dynamics due to the different structure of the equations of motion. We analytically study the equations of motion in both cases and describe all possible regimes with special interest on the realistic regimes. Our analysis suggests that the only realistic regime is the transition from high-energy (Gauss-Bonnet) Kasner regime, which is the standard cosmological singularity in that case, to the anisotropic exponential regime with expanding three and contracting extra dimensions. Availability of this regime allows us to put a constraint on the value of Gauss-Bonnet coupling α and the -term -this regime appears in two regions on the (α, ) plane: α < 0, > 0, α ≤ −3/2 and α > 0, α ≤ (3D 2 − 7D + 6)/(4D(D − 1)), including the entire < 0 region. The obtained bounds are confronted with the restrictions on α and from other considerations, like causality, entropy-to-viscosity ratio in AdS/CFT and others. Joint analysis constrains (α, ) even further: α > 0, D ≥ 2 with (3D 2 − 7D + 6)/(4D(D − 1)) ≥ α ≥ −(D + 2)(D + 3)(D 2 + 5D + 12)/(8(D 2 + 3D + 6) 2 ).

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Non-constant volume exponential solutions in higher-dimensional Lovelock cosmologies

2015

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In this paper we propose a scheme which allows one to find all possible exponential solutions of special class-non-constant volume solutions-in Lovelock gravity in arbitrary number of dimensions and with arbitrate combinations of Lovelock terms. We apply this scheme to (6 + 1)-and (7 + 1)-dimensional flat anisotropic cosmologies in Einstein-Gauss-Bonnet and third-order Lovelock gravity to demonstrate how our scheme does work. In course of this demonstration we derive all possible solutions in (6 + 1) and (7 + 1) dimensions and compare solutions and their abundance between cases with different Lovelock terms present. As a special but more "physical" case we consider spaces which allow three-dimensional isotropic subspace for they could be viewed as examples of compactification schemes. Our results suggest that the same solution with three-dimensional isotropic subspace is more "probable" to occur in the model with most possible Lovelock terms taken into account, which could be used as kind of anthropic argument for consideration of Lovelock and other higher-order gravity models in multidimensional cosmologies.

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Cosmological dynamics in higher-dimensional Einstein–Gauss–Bonnet gravity

Cited by 31 publications

References 64 publications

1/r potential in higher dimensions

1/r potential in higher dimensions

Cosmological dynamics of spatially flat Einstein–Gauss–Bonnet models in various dimensions: high-dimensional $$\Lambda $$ Λ -term case

Non-constant volume exponential solutions in higher-dimensional Lovelock cosmologies

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