Exact (1 + 3 + 6)-Dimensional Cosmological-Type Solutions in Gravitational Model with Yang–Mills Field, Gauss–Bonnet Term and Λ Term

Abstract

We consider a 10-dimensional gravitational model with an SO(6)Yang–Mills field, Gauss–Bonnet term, and Λ term. We study so-called cosmological-type solutions defined on the product manifold M=R×R3×K, where K is 6d a Calabi–Yau manifold. By setting the gauge field 1-form to coincide with the 1-form spin connection on K, we obtain exact cosmological solutions with exponential dependence of scale factors (upon t-variable) governed by two non-coinciding Hubble-like parameters: H>0 and h obeying H+2h≠0. We also present static analogs of these cosmological solutions (for H≠0, h≠H, and H+2h≠0). The islands of stability for both classes of solutions are outlined.