We discuss the field theory expectations for very light scalar states which may give rise to a late stage of spontaneous symmetry breaking, paying particular regard to the spontaneous breaking of the discrete symmetries which commonly occur in compactified string or Grand Unified theories. We consider the possibility that the large scale structure of the universe is generated due to domain walls associated with this late phase transition. Efficient dissipation of the wall energy in a dark matter component may occur leading to large local density fluctuations which generate a component of the large scale structure today. Provided the walls decay at an early time the magnitude of fluctuations needed to explain the present day structure is consistent with induced fluctuations in the cosmic microwave background radiation of order 10(-5). The model also predicts early quasar formation (at redshifts approximately 10).