Dynamics of the cosmological models with perfect fluid in Einstein-Gauss-Bonnet gravity: low-dimensional case

In this paper we performed investigation of the spatially-flat cosmological models whose spatial section is product of three- ("our Universe") and extra-dimensional parts. The matter source chosen to be the perfect fluid which exists in the entire space. We described all physically sensible cases for the entire range of possible initial conditions and parameters as well as brought the connections with vacuum and $\Lambda$-term regimes described earlier. In the present paper we limit ourselves with $D=1, 2$ (number of extra dimensions). The results suggest that in $D=1$ there are no realistic compactification regimes while in $D=2$ there is if $\alpha > 0$ (the Gauss-Bonnet coupling) and the equation of state $\omega < 1/3$, the measure of the initial conditions leading to this regime is increasing with growth of $\omega$ and reaches its maximum at $\omega \to 1/3 - 0$. We also describe some pecularities of the model, distinct to the vacuum and $\Lambda$-term cases -- existence of the isotropic power-law regime, different role of the constant-volume solution and the presence of the maximal density for $D = 2$, $\alpha < 0$ subcase and associated features.