Spontaneous symmetry breaking as a result of extra dimensions compactification

We consider dynamics of a scalar field in compactification scenario of Einstein-Gauss-Bonnet cosmology. It is shown that if the field is non-minimally coupled to curvature, its asymptotic value under certain conditions may be shifted from the minimum of its potential. This means that due to influence of extra dimensions a scalar field with $\lambda {\phi }^4$ potential can stabilise away from $\phi =0$ stable point which means an effective symmetry breaking occurs in such a system.