  We study cosmology of the Einstein-Yang-Mills theory in ten dimensions with a
quartic term in the Yang-Mills field strength. We obtain analytically a class
of cosmological solutions in which the extra dimensions are static and the
scale factor of the four-dimensional Friedmann-Lemaitre-Robertson-Walker metric
is an exponential function of time. This means that the model can explain
inflation. Then we look for solutions that describe dynamical compactification
of the extra dimensions. The effective cosmological constant $\lambda_1$ in the
four-dimensional universe is determined from the gravitational coupling,
ten-dimensional cosmological constant, gauge coupling and higher derivative
coupling. By numerical integration, the solution with $\lambda_1=0$ is found to
behave as a matter-dominated universe which asymptotically approaches flat
space-time, while the solution with a non-vanishing $\lambda_1$ approaches de
Sitter space-time in the asymptotic future.
