1,721,075 research outputs found
On stability of exponential cosmological solutions with non-static volume factor in the Einstein–Gauss–Bonnet model
No full textA (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, ai∼ exp (vit) , 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)=∑k=1nvk≠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 v1= v2= v3= H> 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed. © 2016, The Author(s)
On stability of exponential cosmological solutions with non-static volume factor in the Einstein–Gauss–Bonnet model
No full textA (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, ai∼ exp (vit) , 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)=∑k=1nvk≠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 v1= v2= v3= H> 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed. © 2016, The Author(s)
Quantum billiards with branes on product of Einstein spaces
No full textWe consider a gravitational model in dimension D with several forms, l scalar fields and a Λ -term. We study cosmological-type block-diagonal metrics defined on a product of an 1-dimensional interval and n oriented Einstein spaces. As an electromagnetic composite brane ansatz is adopted and certain restrictions on the branes are imposed the conformally covariant Wheeler–DeWitt (WDW) equation for the model is studied. Under certain restrictions, asymptotic solutions to the WDW equation are found in the limit of the formation of the billiard walls. These solutions reduce the problem to the so-called quantum billiard in (n+ l- 1) -dimensional hyperbolic space. Several examples of quantum billiards in the model with electric and magnetic branes, e.g. corresponding to hyperbolic Kac–Moody algebras, are considered. In the case n= 2 we find a set of basis asymptotic solutions to the WDW equation and derive asymptotic solutions for the metric in the classical case. © 2016, The Author(s)
Quantum billiards with branes on product of Einstein spaces
No full textWe consider a gravitational model in dimension D with several forms, l scalar fields and a Λ -term. We study cosmological-type block-diagonal metrics defined on a product of an 1-dimensional interval and n oriented Einstein spaces. As an electromagnetic composite brane ansatz is adopted and certain restrictions on the branes are imposed the conformally covariant Wheeler–DeWitt (WDW) equation for the model is studied. Under certain restrictions, asymptotic solutions to the WDW equation are found in the limit of the formation of the billiard walls. These solutions reduce the problem to the so-called quantum billiard in (n+ l- 1) -dimensional hyperbolic space. Several examples of quantum billiards in the model with electric and magnetic branes, e.g. corresponding to hyperbolic Kac–Moody algebras, are considered. In the case n= 2 we find a set of basis asymptotic solutions to the WDW equation and derive asymptotic solutions for the metric in the classical case. © 2016, The Author(s)
On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra
No full textA generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra G is considered. The solution contains a metric, n Abelian 2-forms and n scalar fields, where n is the rank of G. It is governed by a set of n moduli functions Hs(z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials—the so-called fluxbrane polynomials. These polynomials depend upon integration constants qs, s= 1 , ⋯ , n. In the case when the conjecture on the polynomial structure for the Lie algebra G is satisfied, it is proved that 2-form flux integrals Φ s over a proper 2d submanifold are finite and obey the relations qsΦ s= 4 πnshs, where the hs> 0 are certain constants (related to dilatonic coupling vectors) and the ns are powers of the polynomials, which are components of a twice dual Weyl vector in the basis of simple (co-)roots, s= 1 , ⋯ , n. The main relations of the paper are valid for a solution corresponding to a finite-dimensional semi-simple Lie algebra G. Examples of polynomials and fluxes for the Lie algebras A1, A2, A3, C2, G2 and A1+ A1 are presented. © 2017, The Author(s)
On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra
No full textA generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra G is considered. The solution contains a metric, n Abelian 2-forms and n scalar fields, where n is the rank of G. It is governed by a set of n moduli functions Hs(z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials—the so-called fluxbrane polynomials. These polynomials depend upon integration constants qs, s= 1 , ⋯ , n. In the case when the conjecture on the polynomial structure for the Lie algebra G is satisfied, it is proved that 2-form flux integrals Φ s over a proper 2d submanifold are finite and obey the relations qsΦ s= 4 πnshs, where the hs> 0 are certain constants (related to dilatonic coupling vectors) and the ns are powers of the polynomials, which are components of a twice dual Weyl vector in the basis of simple (co-)roots, s= 1 , ⋯ , n. The main relations of the paper are valid for a solution corresponding to a finite-dimensional semi-simple Lie algebra G. Examples of polynomials and fluxes for the Lie algebras A1, A2, A3, C2, G2 and A1+ A1 are presented. © 2017, The Author(s)
On exponential cosmological type solutions in the model with Gauss–Bonnet term and variation of gravitational constant
No full textA D-dimensional gravitational model with Gauss–Bonnet term is considered. When an ansatz with diagonal cosmological type metrics is adopted, we find solutions with an exponential dependence of the scale factors (with respect to a “synchronous-like” variable) which describe an exponential expansion of “our” 3-dimensional factor space and obey the observational constraints on the temporal variation of effective gravitational constant G. Among them there are two exact solutions in dimensions D=22,28 with constant G and also an infinite series of solutions in dimensions D≥2690 with the variation of G obeying the observational data. © 2015, The Author(s)
On exponential cosmological type solutions in the model with Gauss–Bonnet term and variation of gravitational constant
No full textA D-dimensional gravitational model with Gauss–Bonnet term is considered. When an ansatz with diagonal cosmological type metrics is adopted, we find solutions with an exponential dependence of the scale factors (with respect to a “synchronous-like” variable) which describe an exponential expansion of “our” 3-dimensional factor space and obey the observational constraints on the temporal variation of effective gravitational constant G. Among them there are two exact solutions in dimensions D=22,28 with constant G and also an infinite series of solutions in dimensions D≥2690 with the variation of G obeying the observational data. © 2015, The Author(s)
Stable exponential cosmological solutions with zero variation of G and three different Hubble-like parameters in the Einstein–Gauss–Bonnet model with a Λ -term
No full textWe consider a D-dimensional gravitational model with a Gauss–Bonnet term and the cosmological term Λ. We restrict the metrics to diagonal cosmological ones and find for certain Λ a class of solutions with exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters H> 0 , h1 and h2, corresponding to factor spaces of dimensions m> 2 , k1> 1 and k2> 1 , respectively, with k1≠ k2 and D= 1 + m+ k1+ k2. Any of these solutions describes an exponential expansion of 3d subspace with Hubble parameter H and zero variation of the effective gravitational constant G. We prove the stability of these solutions in a class of cosmological solutions with diagonal metrics. © 2017, The Author(s)
Erratum to: On exponential cosmological type solutions in the model with Gauss–Bonnet term and variation of gravitational constant (Eur. Phys. J. C, (2015), 75, (177), 10.1140/epjc/s10052-015-3394-9)
No full textUnfortunately, the equation (3.13) of the original version of this paper contained a typo. The correct relation reads as follows (Formula presented.) Here the correct value of the power 1/2 eliminates the typo (−1/2) in the earlier published version of the paper. It was a typo—not a mistake: i.e. all other relations were correct. Unfortunately the following Acknowledgments are missing in the original article: Acknowledgements The research was funded by the Ministry of Education and Science of the Russian Federation in the Program to increase the competitiveness of Peoples’ Friendship University (RUDN University) among the world’s leading research and education centers in the 2016–2020 and by the Russian Foundation for Basic Research, Grant Nr. 16-02-00602. © 2016, The Author(s)
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