What is the Borde-Guth-Vilenkin theorem?

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In summary, the BGV theorem states that an inflating universe cannot be extended infinitely into the past and must have had a beginning at some finite time in the past. This supports the idea that the universe is of a finite age, but also suggests that it may have passed through a singularity phase. The original paper can be found at https://arxiv.org/abs/gr-qc/0110012, and it does not conflict with the Hawking-Hartle model as it attempts to address what preceded inflation.
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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?

If this subject has already been answered, could someone refer me to a link?
Thanks so much if you are able to help out :) !

Mentor note: edited to remove debate video reference.
 
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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
 
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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.
 
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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.
 
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1. What is the Borde-Guth-Vilenkin theorem?

The Borde-Guth-Vilenkin theorem is a cosmological theorem that states that under certain conditions, a universe that has been expanding on average throughout its history cannot be infinite in the past but must have a beginning.

2. Who are the scientists behind the Borde-Guth-Vilenkin theorem?

The Borde-Guth-Vilenkin theorem was developed by Alan Guth, Alexander Vilenkin, and Arvind Borde in the 2000s as a refinement of the earlier BGV theorem proposed by Vilenkin in the 1980s.

3. What conditions must be met for the Borde-Guth-Vilenkin theorem to apply?

The Borde-Guth-Vilenkin theorem applies to universes that are expanding on average, have a finite amount of energy, and do not undergo any sudden changes in the rate of expansion.

4. How does the Borde-Guth-Vilenkin theorem support the Big Bang theory?

The Borde-Guth-Vilenkin theorem supports the Big Bang theory by providing evidence for the idea that the universe had a beginning and has been expanding since then. This aligns with the Big Bang model, which suggests that the universe originated from a singularity and has been expanding ever since.

5. Are there any criticisms of the Borde-Guth-Vilenkin theorem?

Yes, there are some criticisms of the Borde-Guth-Vilenkin theorem. Some scientists argue that the theorem relies on certain assumptions, such as the absence of a multiverse, which may not be accurate. Additionally, the concept of a beginning of the universe is still a subject of debate in the scientific community, and the theorem does not provide a definitive answer to this question.

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