Princeton cosmologists J.Richard Gott III and Li-Xin Li suggested in 1997 that the universe could be self-creating. They suggested that if one traces the history of the universe back, one might eventually reach not the beginning, but a loop containing 'closed timelike curves' (CTCs). (Massive systems follow timelike curves in space-time, hence the presence of closed timelike curves in a region of space-time entails the presence of loops in time.) Such a universe is neither past-infinite, nor does it have a beginning. Each 3-dimensional spatial slice of the universe in the region with CTCs lies both to the past and the future of itself; it is both the cause and the effect of itself. Such a universe is its own parent. Gott explains his proposal as follows:
"We believe today that the Universe started after a state of very rapid expansion called inflation, back at the Big Bang. The Universe inflated very rapidly during this phase. This has been confirmed by recent observations of the cosmic microwave background, as the theory of inflation is made definite predictions of what we should have seen and they have been confirmed quite nicely. Professor Linde at Stanford has shown that if you have an inflating Universe like this that the quantum fluctuations cause it to create baby universes, like branches growing out of a tree. Each branch grows up to be as big as the trunk and it sprouts branches of its own. Thus, you have an infinite...tree of branching universes in this theory of inflation. You still might ask yourself the question, though, where did the trunk come from. Li-Xin Li and I proposed that simply one of the branches circles back around and grows up to become the trunk. This is a model where the Universe is its own mother. It is a model with a little time loop at the very beginning."
Gott and Li consider the 'universe creation in a laboratory' scenarios, and suggest that one of the baby universes created by an intelligent civilization could be the 'original' universe, from which the universe containing that same civilization ultimately sprang. They consider the possibility that the evolution of intelligent species is therefore a necessary self-consistency requirement of a self-creating universe. If, however, it is possible to create a universe by artificial means, it is likely that baby universes could also be created by natural processes.
Moreover, the notion of a self-creating universe does not explain the existence of the universe. One can ask 'Why does a 4-dimensional space-time containing an initial time loop exist, rather than no 4-dimensional space-time at all?' and one can ask 'Why does a 4-dimensional space-time containing an initial time loop exist, rather than one of the infinite variety of other 4-dimensional space-times?'
A self-creating universe provides no explanatory loss or gain over a past-infinite 4-dimensional space-time. For the latter, one can similarly ask 'Why does a past-infinite 4-dimensional space-time exist, rather than no space-time at all?' and one can ask 'Why does a past-infinite 4-dimensional space-time exist, rather than one of the infinite variety of other 4-dimensional space-times?'
In addition, there is no explanatory problem with the 'Big-Bang' (Friedmann-Robertson-Walker (FRW)) cosmological models, which is solved by the postulate of an initial time loop. Contrary to popular belief, the FRW models do not have an uncaused beginning. The time axis of a FRW model is an open interval (0,t) of the real number line, which is bounded by, but does not contain time zero. (0,t) is topologically identical to (-∞,t). Hence, each moment of time in a FRW model has prior moments of time; each 3-dimensional spatial slice in a FRW model is caused by preceding 3-dimensional spatial slices. There is no initial instant in a FRW model. A FRW model is past-finite in the sense that all past-directed timelike curves are of finite length, but this is because of the limiting behaviour of the spatial geometry as the time tends to zero, not because those past-directed curves have a starting point.