**VI. Evidence of a beginning of all expanding pre-Big Bang models from space-time geometry**

There are three pieces of evidence from space-time geometry that require a beginning of the universe (or multiverse) under certain assumptions.

It will be helpful to start with a description of the spacetime field. Recall that space-time is like a field with known properties, conditions, and constants. It is dimensional and orientable; its geometry is compressed and reconfigured through the density of mass-energy in it; it can warp and vibrate; and it can affect the mass energy in it. These characteristics enable physicists to demonstrate the necessity of a beginning under certain assumptions.

All postulated models of a pre-big-bang era fall under these assumptions, and so the following three mutually corroborating pieces of evidence ground the high probability of a beginning of our universe (or multiverse in which it might be situated).

The 1993 Borde-Vilenkin Proof:

Arvin Borde and Alexander Vilenkin gave a proof in 1993 that every inflationary universe meeting five assumptions would have to have a singularity (a beginning of the universe/multiverse in a finite proper time). In 1997 they discovered a possible exception to one of their assumptions (concerning weak energy conditions) which was very, very unlikely within our universe. Physicists (including Alan Guth) did not consider this exception to be very important, meaning that the proof still shows the likelihood of a beginning of time in our universe (or a multiverse in which it might be situated).

Alan Guth’s 1999 analysis of expanding pre-big-bang models:

Guth concluded his study as follows: “In my own opinion, it looks like eternally inflating models necessarily have a beginning. I believe this for two reasons. The first is the fact that, as hard as physicists have worked to try to construct an alternative, so far all the models that we construct have a beginning; they are eternal into the future, but not into the past.

The second reason is that the technical assumption questioned in the 1997 Borde-Vilenkin paper does not seem important enough to me to change the conclusion.”

The 2003 Borde-Vilenkin-Guth Theorem (the BVG Theorem):

Borde, Vilenkin, and Guth joined together to formulate an elegant and applicable demonstration of a beginning of expanding universes in a famous article in Physical Review Letters. Alexander Vilenkin explained it as follows:

Suppose, for example, that [a] space traveler has just zoomed by the earth at the speed of 100,000 kilometers per second and is now headed toward a distant galaxy, about a billion light years away. That galaxy is moving away from us at a speed of 20,000 kilometers per second, so when the space traveler catches up with it, the observers there will see him moving at 80,000 kilometers per second.

If the velocity of the space traveler relative to the spectators gets smaller and smaller into the future, then it follows that his velocity should get larger and larger as we follow his history into the past. In the limit, his velocity should get arbitrarily close to the speed of light.

This point constitutes a boundary to past time in any expanding universe or multiverse. This boundary to past time could indicate an absolute beginning of the universe or a pre-Big Bang era with a completely different physics. If the latter, then the pre-Big Bang period would also have to have had a boundary to its past time (because it would be expanding). Eventually, one will reach an absolute beginning when there are no more pre-pre- Big Bang eras. What does this mean? It means that there must be an absolute beginning of any expanding universe or multiverse (even if it has multiple pre-Big Bang eras).

This demonstration is applicable to just about any model universe or multiverse that could be connected with our universe. It applies also to oscillating universe conjectures where the average Hubble expansion is greater than zero. Exceptions to this theorem are very difficult to formulate and are quite tenuous because they require either a universe with an average Hubble expansion less than or equal to zero (which is difficult to connect to our expanding universe) or a deconstruction of time (which is physically unrealistic). For this reason all attempts to get around the BVG Theorem to date have been unsuccessful. Even if physicists in the future are able to formulate a hypothetical model which could get around the BVG Theorem, it would not mean that this hypothetical model is true for our universe. It is likely to be only a testimony to human ingenuity. Therefore, it is quite likely that our universe (or any multiverse in which it might be situated) had an absolute beginning. This implies a creation of the universe by a Power transcending our universe.

The above three mutually corroborating pieces of evidence (the 1993 Borde-Vilenkin singularity proof; Guth’s analysis showing that every constructed expanding cosmology has a beginning; and the 2003 BVG theorem showing that every expanding cosmology has a boundary to past time) show the high probability of a beginning of our universe (or any hypothetical multiverse in which it might be situated) from the vantage point of space-time geometry.

(to be continued..)

GOD AND MODERN PHYSICS privious notes:

Intro: Astrophysics – Can science show God created the universe?

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I. The standard The Big Bang model

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II. The Big Bang model: A well-corroborated theory

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III. What is the significance of a beginning?

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IV. Three pre-Big Bang models

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V. Evidence for a beginning from the law of entropy

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