There is a beginning universe.

The BVG has been used effectively by William Craig to show the universe (if not ours) must have a beginning. He defended it effectively against Lawrence Krauss, Sean Carroll and others.

I saw the Carroll debate in New Orleans where in order to defend against the BVG Carroll showed a picture of Allen Guth holding his laptop with the words "there is no beginning". debate Of course as a contributor to the BVG Guth was joking around. Nevertheless it's telling that a celebrated physicist (Carroll) could not defeat the BVG as given by a philosopher.

This is a clip where Guth confirms a beginning. Guth. 

The BVG proof in pdf form is described here BVD proof

It concludes:

"we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating -- or just expanding sufficiently fast -- must be incomplete in null and timelike past directions.

Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime."

In short if the universe is expanding (and they have to for life) then there is a past beginning from which they came.

What's interesting about the BVG is it's based on a thought experiment (Gedankenexperiment) much like Einstein used.

The layperson Gedankenexperiment is laid out by Alexander Vilenkin in his book,"Many Worlds in One".

In it he concludes," It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape: they have to face the problem of a cosmic beginning."

To save you the cost of a book included the Gedankenexperiment below.

Ref

"Borde, Guth, and I studied what an expanding universe looks like from the point of view of different observers. We considered imaginary observers moving through the universe under the action of gravity and inertia and recording what they see. If the universe had no beginning, then the histories of all such observers should extend into the infinite past. We showed that this assumption leads to a contradiction. To have a specific picture in mind, suppose there is an observer in every galaxy of our local region. Since the universe is expanding, each of these observers will see the others moving away. Galaxies may not exist in some regions of space and time, but we can still imagine the entire universe “sprinkled” with observers in such a way that all of them are moving away from one another.bj To give these observers some name, we shall call them “spectators.” Let us now introduce another observer who is moving relative to the spectators. We shall call him the space traveler he is moving by inertia, with the engines of his spaceship turned off, and has been doing so for all eternity. As he passes the spectators, they register his velocity. Since the spectators are flying apart, the space traveler’s velocity relative to each successive spectator will be smaller than his velocity relative to the preceding one. Suppose, for example, the 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 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, 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. The key insight of my paper with Borde and Guth is that as we go into the past and approach past infinity by the clocks of the spectators, the time elapsed by the clock of the space traveler is still finite. The reason is that according to Einstein’s theory of relativity, a moving clock ticks slower, and the closer you get to the speed of light, the more slowly it ticks. As we go backward in time, the speed of the space traveler approaches the speed of light and his clock essentially comes to a halt. This is from the spectator’s point of view. But the space traveler himself does not notice anything unusual. For him, what spectators perceive as a frozen moment, stretched into eternity, is a moment like any other, which has to be preceded by earlier moments. Like the histories of the spectators, the space traveler’s history should extend into the infinite past. The fact that the time elapsed by the space traveler’s clock is finite indicates that we do not have his full history. This means that some part of the past history of the universe is missing; it is not included in the model. Thus, the assumption that the entire spacetime can be covered by an expanding “dust” of observers has led to a contradiction, and therefore it cannot be true.6 A remarkable thing about this theorem is its sweeping generality. We made no assumptions about the material content of the universe. We did not even assume that gravity is described by Einstein’s equations. So, if Einstein’s gravity requires some modification, our conclusion will still hold. The only assumption that we made was that the expansion rate of the universe never gets below some nonzero value, no matter how small.7 This assumption should certainly be satisfied in the inflating false vacuum. The conclusion is that past-eternal inflation without a beginning is impossible. What about a cyclic universe? It has alternating periods of expansion and contraction. Can this help the universe to escape from the clutches of the theorem? The answer turns out to be no. An essential feature of the cyclic scenario, which allows it to avoid the heat-death problem, is that the volume of the universe increases in every cycle, so on average the universe is expanding. In my paper with Borde and Guth, we show that as a result of this expansion, the space traveler’s velocity increases on average as we go back in time and still approaches the speed of light in the limit. Hence, the same conclusions apply.8 It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape: they have to face the problem of a cosmic beginning."