Stable exponential cosmological solutions with three different Hubble-like parameters in EGB model with a $$\Lambda $$ Λ -term

Abstract

Abstract We consider a D-dimensional Einstein-Gauss-Bonnet model with a cosmological term $$\Lambda $$ Λ and two non-zero constants: $$\alpha _1$$ α1 and $$\alpha _2$$ α2 . We restrict the metrics to be diagonal ones and study a class of solutions with exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters: $$H \ne 0$$ H≠0 , $$h_1$$ h1 and $$h_2$$ h2 , obeying $$m H + k_1 h_1 + k_2 h_2 \ne 0$$ mH+k1h1+k2h2≠0 and corresponding to factor spaces of dimensions $$m > 1$$ m>1 , $$k_1 > 1$$ k1>1 and $$k_2 > 1$$ k2>1 , respectively ($$D = 1 + m + k_1 + k_2$$ D=1+m+k1+k2 ). We analyse two cases: i) $$m 0$$ α=α2/α1>0 and $$\alpha \Lambda > 0$$ αΛ>0 satisfies 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. For $$m > 3$$ m>3 the case i) contains a subclass of solutions describing an exponential expansion of 3-dimensional subspace with Hubble parameter $$H > 0$$ H>0 and zero variation of the effective gravitational constant G. The case $$H = 0$$ H=0 is also considered.