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On stable exponential solutions in Einstein-Gauss-Bonnet cosmology with zero variation of \(G\). (English) Zbl 1380.83052

Gravit. Cosmol. 22, No. 4, 329-332 (2016); erratum ibid. 23, No. 4, 401 (2017).
Summary: A \(D\)-dimensional gravitational model with a Gauss-Bonnet term and the cosmological constant \(\Lambda\) is considered. Assuming diagonal cosmological metrics, we find, for certain \(\Lambda > 0\), new examples of solutions with an exponential time dependence of two scale factors, governed by two Hubble-like parameters \(H > 0\) and \(h < 0\), corresponding to submanifolds of dimensions m and l, respectively, with \((m, l) = (4, 2), (5, 2), (5, 3), (6, 7), (7, 5), (7, 6)\) and \(D = 1 + m + l\). Any of these solutions describes an exponential expansion of our 3-dimensional factor space with the Hubble parameter H and zero variation of the effective gravitational constant \(G\). We also prove the stability of these solutions in the class of cosmological solutions with diagonal metrics.

MSC:

83C15 Exact solutions to problems in general relativity and gravitational theory
83F05 Relativistic cosmology
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
53Z05 Applications of differential geometry to physics
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
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