# Exact $(1 + 3 + 6)$-dimensional cosmological-type solutions in gravitational model with Yang-Mills field, Gauss-Bonnet term and $\Lambda$-term

## TL;DR

This paper derives exact 10-dimensional cosmological solutions in a gravitational model with Yang-Mills, Gauss-Bonnet, and cosmological constant terms, analyzing their stability and static counterparts.

## Contribution

It presents new exact exponential solutions in a 10D gravitational-Yang-Mills-Gauss-Bonnet model with specific product manifolds, including stability analysis.

## Key findings

- Exact exponential cosmological solutions with two Hubble-like parameters.
- Static solutions with similar properties.
- Identification of stability regions for these solutions.

## Abstract

We consider $10$-dimensional gravitational model with $SO(6)$ Yang-Mills field, Gauss-Bonnet term and $\Lambda$-term. We study so-called cosmological type solutions defined on product manifold $M = R \times R^3 \times K$, where $K$ is $6d$ Calabi-Yau manifold. By putting the gauge field 1-form to be coinciding with 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: $H >0$, $h$, obeying $ H + 2 h \neq 0$. We also present static analogs of these cosmological solutions (for $H \neq 0$, $h \neq H$ and $ H + 2 h \neq 0$). The islands of stability for both classes of solutions are outlined.