Since it is not obvious that one can rid oneself of all constraints in realistic models, let us examine the argument that time travel is implausible, and we should think it unlikely to exist in our world, in so far as it implies such constraints. The argument goes something like the following. In order to satisfy such constraints one needs some pre-established divine harmony between the global (time travel) structure of space-time and the distribution of particles and fields on space-like surfaces in it. But it is not plausible that the actual world, or any world even remotely like ours, is constructed with divine harmony as part of the plan. In fact, one might argue, we have empirical evidence that conditions in any spatial region can vary quite arbitrarily. So we have evidence that such constraints, whatever they are, do not in fact exist in our world. So we have evidence that there are no closed time-like lines in our world or one remotely like it.
What’s striking about this objection is the admission that the possibility or impossibility of time-travel isn’t theologically value-free. All other things being equal, time-travel might be possible in a theistic universe, but impossible in an atheistic universe.
Of course, that, of itself, doesn’t resolve other issues concerning the logical, physical, or metaphysical possibility of time-travel. But it does illustrate the fact that bringing God into the picture or leaving God out of the picture is a game-changer. What is unrealistic in an atheistic universe may be realistic in a theistic universe.