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Exponential Cosmological Solutions with Three Different Hubble-Like Parameters in (1 + 3 + k1 + k2)-Dimensional EGB Model with a Λ-Term

1
Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198 Moscow, Russia
2
Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya Street, 119361 Moscow, Russia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(2), 250; https://doi.org/10.3390/sym12020250
Received: 15 January 2020 / Revised: 31 January 2020 / Accepted: 2 February 2020 / Published: 6 February 2020
(This article belongs to the Special Issue Cosmology)
A D-dimensional Einstein–Gauss–Bonnet model with a cosmological term Λ , governed by two non-zero constants: α 1 and α 2 , is considered. By restricting the metrics to diagonal ones, we study a class of solutions with the exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters: H > 0 , h 1 , and h 2 , obeying 3 H + k 1 h 1 + k 2 h 2 0 and corresponding to factor spaces of dimensions: 3, k 1 > 1 , and k 2 > 1 , respectively, with D = 4 + k 1 + k 2 . The internal flat factor spaces of dimensions k 1 and k 2 have non-trivial symmetry groups, which depend on the number of compactified dimensions. Two cases: (i) 3 < k 1 < k 2 and (ii) 1 < k 1 = k 2 = k , k 3 , are analyzed. It is shown that in both cases, the solutions exist if α = α 2 / α 1 > 0 and α Λ > 0 obey certain restrictions, e.g., upper and lower bounds. In Case (ii), explicit relations for exact solutions are found. In both cases, the subclasses of stable and non-stable solutions are singled out. Case (i) contains a subclass of solutions describing an exponential expansion of 3 d subspace with Hubble parameter H > 0 and zero variation of the effective gravitational constant G. View Full-Text
Keywords: Gauss–Bonnet; variation of G; accelerated expansion of the universe Gauss–Bonnet; variation of G; accelerated expansion of the universe
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Ernazarov, K.K.; Ivashchuk, V.D. Exponential Cosmological Solutions with Three Different Hubble-Like Parameters in (1 + 3 + k1 + k2)-Dimensional EGB Model with a Λ-Term. Symmetry 2020, 12, 250.

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