Big Bang: Limitations of the Theory

The Big Bang theory is the accepted theory about the evolution of the Universe over billions of years. However, the theory is often misunderstood as dealing with an initial explosion. Judging by the title of Steven Weinberg's popular exposition, The First Three Minutes, it seems as if the Universe has a beginning and as if we can describe processes right from the very first instant.

The Big Bang theory is a combination of two theoretical systems describing the processes happening to the contents of the Universe: general relativity for spacetime and quantum theory for matter. This implies three limits to the Big Bang theory:

On the left the Big Bang model is depicted as a cone, with each horizontal slice representing the three-dimensional universe at a given moment of time. On the right the major uncertainties are stressed.

1. Current theories about matter are valid only up to a finite temperature, and hence valid only after the first fraction of a second following the Singularity, the initial moment entailed by general relativity. This implies a, perhaps temporary, epistemological boundary to the domain where the Big Bang theory can be trusted. Further speculations have to deal with temperatures and densities for which particle physics is not yet well established.

2. Closer to the Singularity there comes a moment, presumably the ‘Planck Time’—a number constructed from the fundamental constants of quantum theory and gravity, about 10^-43 seconds after the initial Singularity—when general relativity must be replaced by a quantum theory of gravity. Theories of space and time applicable before the Planck Time are not known; even the meaningfulness of 'space' and 'time' is uncertain. (Which is troublesome; once time is no longer meaningful, it becomes unclear what can be meant by 'before'.)

3. The initial Singularity itself is a third limit, at least if there is such an initial Singularity. The Big Bang theory results in unrealistic numbers, like infinite density and so on. For some time it was assumed that the unrealistic breakdown of the solutions was a feature of idealizations made in the calculations, for instance the assumption of perfect homogeneity. However, it has since been shown that such peculiarities are unavoidable in general relativity, once certain very general assumptions are made, like causality and a positive energy density. On the other hand, general relativity itself is probably invalid in the moments before the Planck Time. Whether there is such a singular moment in a theory of quantum gravity which is to supersede general relativity cannot be decided a priori, before such a theory of quantum gravity has been proposed.

The first and second limits are clearly limits to our present knowledge, the third, the Singularity, seems to be an edge of reality, but is hidden behind the other two.

- 'Beyond the Big Bang: Quantum Cosmologies and God', Willem B. Drees, Chapter 2: Quantum Cosmologies and the Beginning.