#912 New Work on the BGV Theorem

Dr. craig’s response

The articles your friend refers to are:

These articles are so recent that it will take some time for the physics community to digest and assess them. Nonetheless, on the basis of personal conversations with some prominent physicists, I think that your atheist friend has misunderstood the significance of these articles.

By way of background, the Borde Guth Vilenkin Theorem is now widely accepted within the physics community. As of today, it has gone largely unchallenged. In order to avoid its implications, cosmologists attempt to craft models of the universe based upon possible exceptions to the theorem’s one condition that the universe has, on average, been in a state of cosmic expansion throughout its history. Since in these proposed models the universe does not satisfy that one condition, the BGV Theorem does not apply to them. So the fact that there are exception classes of models to the theorem is nothing new.

In our article “The Kalām Cosmological Argument” in the Blackwell Companion to Natural Theology, James Sinclair lists four such exception classes of models:

The articles quoted by your friend aim at refining the exception classes of models to the BGV Theorem. By redefining the way in which the average expansion rate H_av is defined or calculated, the authors argue that one can have past-eternal asymptotically emergent models according to which H_av > 0 by having the universe’s expansion rate approach 0 at -∞. (It will be interesting to see what Borde, Guth, or Vilenkin think of the proposed re-definition). Granting for the sake of argument the legitimacy of this redefinition, Carballo-Rubio et al. arrive at a three-fold classification of models which are exceptions to the BGV theorem (Raúl Carballo-Rubio, Stefano Liberati, and Vania Vellucci, “Geodesically complete universes,” arXiv:2404.13112v2 [gr-qc] 29 August 2024). They lump all models featuring a contracting phase, including Sinclair’s (iv), into the same category, so that all viable, singularity-free, classical geometries must feature either (i) a bouncing universe, (ii) an emergent universe, or (iii) an asymptotically emergent universe.

The significance of these studies is that they show that in order to avoid the implications of the BGV Theorem for the finitude of the past, you have only these three options to choose from. Thus, if you want to defend the possibility of a past eternal universe, your options are extremely restricted.

Now these three model classes are based on a purely mathematical analysis. Nothing has been said of the models’ physical tenability or evidential credibility. Carballo-Rubio et al. therefore rightly advise that these mathematical findings pave the way for now refining cosmological models based on observational data and theoretical considerations. They state, “Efforts to reconcile these theoretical studies with empirical observations and astrophysical data would be instrumental in refining and validating cosmological models” (“Geodesically complete universes,” p. 28).

These models face an array of problems which render them unlikely to be physically realistic, including violating not only the so-called strong energy condition, but also the weak energy condition, the null energy condition, and, in many cases, the averaged null energy condition, which serves to prevent time-like loops and time machines, along with the Generalized Second Law of Thermodynamics. Sinclair shows that these speculative models are all either in contradiction to observational cosmology or else wind up implying the very beginning of the universe they sought to avert.[1] Thus the papers cited by your friend do not even aspire to show that models belonging to these classes are physically tenable or credible but serve merely to narrowly limit the exception classes to the BGV Theorem to but three options. So what is the atheist to do?