# B What is the Borde-Guth-Vilenkin theorem?

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1. Dec 20, 2017

### relatively-uncertain

My question is, what is the BGV theorem? and what exactly does it say?
I was watching A debate on cosmology where William Lane Craig uses the Borde, Guth and Vilenkin theorem to say the universe had a beginning.

I was wondering if someone could possibly explain the case of the BGV theorem and what it says?

Does this theorem make other cosmologies such as the Hawking-Hartle less likely than one that had a beginning?

Thanks so much if you are able to help out :) !

Mentor note: edited to remove debate video reference.

Last edited by a moderator: Dec 20, 2017
2. Dec 20, 2017

### Orodruin

Staff Emeritus
The BGV theorem states that even in an inflationary universe, timelike and null geodesics are not past-complete, i.e., you cannot extend those geodesics to negative infinity within the spacetime itself. In essence and layman terms, this means that at some point you have to impose initial conditions on your spacetime or have your assumptions break down, e.g., by having the inflationary universe created through some sort of nucleation event in a larger spacetime.

The original reference is https://arxiv.org/abs/gr-qc/0110012

3. Dec 20, 2017

### kimbyd

A super-basic explanation of how it operates is that during inflation, any irregularities get smoothed out. Any matter that exists gets diluted so much that it effectively disappears.

If you take this fact and run the clock backward, it means that unless the inflating universe is perfectly empty, then the other matter exists during inflation will, looking into the past, get more dense. Eventually it will get dense enough that inflation is no longer possible. This indicates that inflation cannot be extended infinitely into the past. It had to have a beginning at some point.

There is some debate as to whether or not this theorem actually applies to our universe.

4. Dec 20, 2017

### Chronos

To restate what has already been said, an inflating universe cannot be regressed indefinitely into the past, or, In other words, an inflating universe has a beginning at some finite time in the past. It is pleasing in the sense it affirms the universe is of a finite age, which is logically consistent with all we know of it, but, unpleasantly disturbing in that it insists it at least passed through a singularity phase - which scientists have been desperately trying rid from the model. It is otherwise known as the Kinematic Incompleteness Theorem. For the original paper, and further discussion, see; https://arxiv.org/abs/gr-qc/0110012, Inflationary spacetimes are not past-complete. It does not confilict with the Hawking-Hartle model because HH attempts to address what preceded inflation. Adding a preinflationary phase to the history of the universe sidesteps this pitfall.

Last edited: Dec 20, 2017