Abstract
Ever since the Hawking-Penrose singularity theorems of the 1960s, it has become clear that our universe possesses an unavoidable singularity in the past. The only ways to avoid the singularity using purely classical physics is either to postulate special kinds of matter or move to higher order Lagrangian theories. Alternatively one can appeal to quantum gravity, thermodynamic arguments or the discretisation of space-time to avoid the singularity predicament. None of these approaches provide totally satisfactory answers to the singularity problem.
If one stays within classical general relativity and accepts singularities as part of physics then it is necessary to define a boundary structure to space-time in a mathematically consistent and rigorous manner. Such boundary structures are briefly described here and the behaviour of cosmological models near the boundary is discussed. Particular reference is made to the blue-shift problem and the Weyl curvature hypothesis.