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

A D-dimensional gravitational model with a Gauss–Bonnet term and the cosmological term Λ is studied. We assume the metrics to be diagonal cosmological ones. For certain fine-tuned Λ , 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 Λ = Λ (x, l, α) depends upon the ratio h/ H= x, l and the ratio α= α2/ α1 of two constants (α2 and α1) of the model. For fixed Λ , α and l> 2 the equation Λ (x, l, α) = Λ 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. © 2018, The Author(s)

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

A D-dimensional gravitational model with a Gauss–Bonnet term and the cosmological term Λ is studied. We assume the metrics to be diagonal cosmological ones. For certain fine-tuned Λ , 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 Λ = Λ (x, l, α) depends upon the ratio h/ H= x, l and the ratio α= α2/ α1 of two constants (α2 and α1) of the model. For fixed Λ , α and l> 2 the equation Λ (x, l, α) = Λ 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. © 2018, The Author(s)

Stable exponential cosmological solutions with two factor spaces in the Einstein–Gauss–Bonnet model with a Λ -term

We study D-dimensional Einstein–Gauss–Bonnet gravitational model including the Gauss–Bonnet term and the cosmological term Λ. 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 m> 2 and l> 2 , respectively. These solutions contain a fine-tuned Λ = Λ (x, m, l, α) , which depends upon the ratio h/ H= x, dimensions of factor spaces m and l, and the ratio α= α2/ α1 of two constants (α2 and α1) of the model. The master equation Λ (x, m, l, α) = Λ is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals. The explicit solution for m= l is presented in “Appendix”. Imposing certain restrictions on x, we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. We also consider a subclass of solutions with small enough variation of the effective gravitational constant G and show the stability of all solutions from this subclass. © 2018, Springer Science+Business Media, LLC, part of Springer Nature

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)

Unfortunately, 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)

On exponential cosmological type solutions in the model with Gauss–Bonnet term and variation of gravitational constant

A $$D$$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 $$G$$G. Among them there are two exact solutions in dimensions $$D = 22, 28$$D=22,28 with constant $$G$$G and also an infinite series of solutions in dimensions $$D \ge 2690$$D≥2690 with the variation of $$G$$G obeying the observational data. © 2015, The Author(s)