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).