# Stable exponential cosmological type solutions with three factor spaces in EGB model with a $\\Lambda$-term

Source: [Stable exponential cosmological type solutions with three factor spaces in EGB model with a $\\Lambda$-term](<https://www.sota2.com/research/paper/68fa41fe1e209131ce8fee9d>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T03:34:12.889Z

Authors: K. K. Ernazarov, V. D. Ivashchuk

Published: 2022-01-10T00:05:34.000Z

## Abstract

We study a $D$-dimensional Einstein-Gauss-Bonnet model which includes the Gauss-Bonnet term, the cosmological term $\\Lambda$ and two non-zero constants: $\\alpha\_1$ and $\\alpha\_2$. Under imposing the metric to be diagonal one, we find cosmological type solutions with exponential dependence of three scale factors in a variable $u$, governed by three non-coinciding Hubble-like parameters: $H \\neq 0$, $h\_1$ and $h\_2$, obeying $m H + k\_1 h\_1 + k\_2 h\_2 \\neq 0$, corresponding to factor spaces of dimensions $m \> 1$, $k\_1 \> 1$ and $k\_2 \> 1$, respectively, and depending upon sign parameter $\\varepsilon = \\pm 1$, where $\\varepsilon = 1$ corresponds to cosmological case and $\\varepsilon = - 1$ - to static one). We deal with two cases: i) $m \< k\_1 \< k\_2$ and ii) $1\< k\_1 = k\_2 = k$, $k \\neq m$. We show that in both cases the solutions exist if $\\varepsilon \\alpha = \\varepsilon \\alpha\_2 / \\alpha\_1 \> 0$ and $\\alpha \\Lambda \> 0$ satisfies certain (upper and lower) bounds. The solutions are defined up to solutions of certain polynomial master equation of order four (or less) which may be solved in radicals. In case ii) explicit solutions are presented. In both cases we single out stable and non-stable solutions as $u \\to \\pm \\infty$. The case $H = 0$ is also considered.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2201.03118>)

[PDF](<https://arxiv.org/pdf/2201.03118.pdf>)