  We investigated the cosmology in a higher-curvature gravity where the
dimensionality of spacetime gives rise to only quantitative difference,
contrary to Einstein gravity. We found exponential type solutions for flat
isotropic and homogeneous vacuum universe for the case in which the
higher-curvature term in the Lagrangian density is quadratic in the scalar
curvature, $\xi R^2$. The solutions are classified according to the sign of the
cosmological constant, $\Lambda$, and the magnitude of $\Lambda\xi$. For these
solutions 3-dimensional space has a specific feature in that the solutions are
independent of the higher curvature term. For the universe filled with perfect
fluid, numerical solutions are investigated for various values of the parameter
$\xi$. Evolutions of the universes in different dimensionality of spacetime are
compared.
