The present-day universe appears to be homogeneous on very-large scales. Yet when the casual structure of the early universe is considered, it becomes apparent that the early universe must have been highly inhomogeneous. The current paradigm attempts to answer this problem by postulating the inflation mechanism. However, inflation in order to start requires a homogeneous patch of at least the horizon size. This paper examines if dynamical processes of the early universe could lead to homogenization. In the past similar studies seem to imply that the set of initial conditions that leads to homogenization is of measure zero. This essay proves the contrary: a set of initial conditions for spontaneous homogenization of cosmological models can form a set of nonzero measure.
A fully nonlinear, degenerate parabolic equation arising in the theory of damage mechanics is shown to be well-posed. Its solutions blow up in finite time and, under suitable conditions on the initial configuration, the blow-up set, corresponding to the portion of the material which breaks at the blow-up time, is an interval of nonzero measure. In a special but physically relevant case the problem reduces to the study of the blow-up set of solutions of the quasilinear equation
Impossibility of masking a set of quantum states of nonzero measure