Abstract
A D-dimensional gravitational model with Gauss-Bonnet term is considered. When ansatz with diagonal cosmological type metrics is adopted, we find solutions with exponential dependence of scale factors (with respect to "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. Among them there are two exact solutions in dimensions D = 22, 28 with constant G and also an infinite series of solutions in dimensions D \ge 2690 with the variation of G obeying the observational data.
Highlights
We deal with D-dimensional gravitational model with the Gauss–Bonnet term
Where g = gM N dz M ⊗ dz N is the metric defined on the manifold M, dim M = D, |g| = | det(gM N )|, and
The Einstein–Gauss–Bonnet (EGB) gravitational model and its modifications are intensively used in cosmology; see [6,7] [8,9,10,11,12,13,14,15,17], and references therein, e.g. for the explanation of the accelerating expansion of the Universe following from supernovae observational data [18,19,20]
Summary
We deal with D-dimensional gravitational model with the Gauss–Bonnet term. The (so-called) Einstein–Gauss–Bonnet (EGB) gravitational model and its modifications are intensively used in cosmology; see [6,7] (for D = 4) [8,9,10,11,12,13,14,15,17], and references therein, e.g. for the explanation of the accelerating expansion of the Universe following from supernovae (type Ia) observational data [18,19,20]. Allowed at 95 % confidence (2-σ ) level and the present value of the Hubble parameter [27] (which characterizes the rate of expansion of the observable Universe), H0 = (67.80 ± 1.54) km/s Mpc−1 = (6.929 ± 0.157) × 10−11 year−1,. 3 some cosmological solutions with an exponential behavior of the scale factors satisfying the restriction (1.8) are obtained for two isotropic factor spaces and a positive value of α = α2/α1
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