Saturday, January 28, 2017

The Significance of the BGV Theorem

Let's continue to explore the question of whether or not our universe had an actual beginning.  In two previous posts I have said that (1) if our universe had a beginning, then the cause of the universe must be transcendent, a characteristic of the Christian God, and (2) we may never have any observational or theoretical evidence about what happened in the first 10-35 seconds of the universe.

However, there have still been a lot of ideas from theoretical physicists about what may have happened to bring the universe into being and what we can surmise from the equations and laws that we know describe our universe.  One of the most often discussed papers dealing with our past was published by Arvind Borde, Alan H. Guth, and Alexander Vilenkin in 20031 and called the BGV theorem after the three authors.  In this paper, the authors show that any universe which is on average expanding has a timeline that cannot be infinite into the past, it must have had a beginning when it started to expand.  Since our universe is known to be expanding this theorem seems to require that it had a beginning.  (There are some technicalities to this conclusion like, for instance, the difference between "expanding" and "on average expanding" but, in general, what is known about our universe corresponds with the requirements of the BGV theorem.)

The BGV theorem has been used extensively by theists such as William Lane Craig to argue that the universe had a beginning which then points to a transcendent cause like God.  Opponents of that view provide an alternative scenario by citing some technical aspects of the BGV theorem, or other theoretical ideas which either contradict the BGV theorem or provide special circumstances where it may not be applicable.  For instance, although the BGV theorem has very few assumptions, it is formulated in a classical space-time which may not give valid conclusions during the first 10-35 seconds of the universe when quantum gravity would have been in effect as described in the previous post already mentioned.  I will discuss some of the challenges to the BGV theorem and alternative ideas like those proposed by Anthony Aguirre and Steven Gratton2 in later posts as we explore this topic even further.  But a good synopsis of how the BGV theorem has been received is given by Vilenkin himself when he says "The validity of the BGV theorem is not in question, but its interpretation has generated some controversy."3

As an experimental physicist I tend to draw conclusions based on what is known observationally and experimentally rather than on conjecture or speculation.  So what are the facts about the origin of our universe? The equations of general relativity suggest that the universe had an actual beginning of space, time, matter, and energy and the BGV theorem along with the expansion of the universe would require that this universe had an actual beginning of the expansion.   Other ideas about the origin of the universe like those proposed by Lawrence Krauss4 or Sean Carroll5 do not have real scientific evidence to back them up.  They are conjecture.  (Still I'll talk about them in more detail in future posts.)

I have had the "privilege" to sit on a few juries during my life.  Any jury is supposed to determine a verdict based on the evidence beyond a reasonable doubt.  As with scientific conclusions, a jury knows there is no certainty or proof, but there is evidence.  The conjecture or speculations made by many theoretical physicists in order to avoid a beginning to this universe would not be admitted as evidence since they are not based on observable or demonstrable phenomena.  Considering only the factual evidence for an origin of the universe, I'm confident a jury would come to the conclusion that our universe had a beginning.  Alexander Vilenkin, with co-author Audrey Mithani, come to a similar conclusion in a paper titled, "Did the universe have a beginning?"  Their answer is, "At this point, it seems the answer to this question is probably yes."6  Any other conclusion draws not on what we know, but on what we don't know.

1Borde, Guth, Vilenkin, "Inflationary spacetimes are not past-complete," Phys. Rev. Lett. 90 (2003) 151301.
2Aguirre, Gratton, "Inflation without a beginning, a null boundary proposal," Phys. Rev. D 67 (2003) 083515.
3Vilenkin, "Arrows of time and the beginning of the universe," Phys. Rev. D 88 (2013) 043516.
4Krauss, Lawrence, "A Universe From Nothing," Simon and Schuster, New York, 2012.
5Carroll, "What if Time Really Exists," arXiv:0811.3722 [gr-qc] (2008).
6Mithani, Vilenkin, "Did the universe have a beginning," arXiv:1204.4658 [hep-th] (2012).


  1. Dr. Strauss, thank you for posting this. I look forward to your analyses of Sean Carroll's and Lawrence Krauss' proposed models.

  2. Excellent work! Love reading about your work!

  3. Yes thank you! You make incredibly complex ideas very accessible to people like me who don't share your genius. Thank you very much.