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Another eternal cosmology model shot down by the BGV Theorem

I saw this article on Evolution News, and thought it might a good time for me to review the BGV Theorem that Dr. William Lane Craig brings up in all his recent debates.

First, let’s review the BGV Theorem.

The Borde-Guth-Vilenkin (BGV) theorem shows that every universe that is on balance expanding must have a space-time boundary in the past (a beginning). Even cyclical models of the universe count as expanding “on balance” if their later expansions go further than the previous ones.

Here’s the article from Evolution News:

A key argument in Stephen Meyer’s Return of the God Hypothesis centers on the universe having a beginning. He argues that the beginning points to the cosmos resulting from the mind of a creator. Meyer’s case for the God Hypothesis includes discrediting the claim that cyclical cosmological models could avoid a beginning by his appealing to the Borde-Guth-Vilenkin (BGV) theorem. His reasoning was recently reaffirmed by University of Buffalo physicists Will Kinney and Nina Stein in their analysis of Ijjas and Steinhardt’s (IS) cosmological model. They published their results in the Journal of Cosmology and Astroparticle Physics.

By the way, the Kindle edition of the Meyer book is on sale for $2.99 right now. Get it while it’s cheap!


Correspondent Charlotte Hsu summarizes the research at

“People proposed bouncing universes to make the universe infinite into the past, but what we show is that one of the newest types of these models doesn’t work,” says Kinney, Ph.D., professor of physics in the UB College of Arts and Sciences. “In this new type of model, which addresses problems with entropy, even if the universe has cycles, it still has to have a beginning.”

Kinney and Stein applied the BGV theorem to the IS model, which I have previously critiqued. Anna Ijjas and Paul Steinhardt propose that the universe expanded, then contracted, and then bounced back into an expansion stage in a never-ending cycle. Each iteration grows vastly larger than the previous one, so the universe is on average always expanding. Kinney and Stein rigorously demonstrate that the BGV theorem mandates the IS model being “geodesically pastincomplete,” meaning that spacetime had an absolute beginning:

In this paper, we use the BGV theorem to demonstrate that growth in the scale factor inevitably means that the spacetime is geodesically pastincomplete. … This result is completely general: any bouncing spacetime which obeys the condition for entropy dissipation and the Null Energy Condition outside the bounce must be geodesically incomplete. This is consistent with the BGV theorem, which shows that any spacetime for which the average Hubble parameter is positive must be similarly geodesically incomplete. The IS cosmology satisfies this condition and therefore cannot be past eternal, independent of the details of the dynamics.

In other words, this new cyclical / oscillating model of the universe does not avoid the need for a beginning… and a cause of the creation event.

So, when you hear Dr. Craig talking about the BGV Theorem in debates, now you’ll know what it’s for. It’s real, and it works.

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