Did the Big Bang happen?

[Jehanne]

In his undergraduate textbook, Modern Physics (4th edition), Professor Kenneth S. Krane discusses cosmology in his last chapter.  In it, he states that the Universe is either finite or infinite in spatial extent.  Do you agree?  He also states that General Relativity can handle both scenarios, a finite Universe or an infinite one.  In either scenario, our Universe is expanding.  Of course, if our Universe is infinite, then, it is certainly conceivable that there are events that occurred in our infinite past or will occur in our infinite future, given that the speed of light, the rate of information transfer, is finite.

Now, if our Universe is finite, it is expanding, not only into its future, but in all three spatial directions, hence, its overall volume is increasing over time.  What, exactly, do you think, in this scenario, the Universe is expanding "into"?

When cosmologists speak of the universe being finite or infinite, they usually mean in spatial extent using a comoving frame.

In the classical version of general relativity, there were three options: either space is positively curved (like a sphere) and time is finite in both directions, space is flat (like a plane) and time is infinite into the future but not the past, or space is negatively curved (like a saddle) and time is infinite into the future and not into the past.

Which of the three possibilities actually occurs depends on the density of matter and energy: a higher density leads to more gravity and an eventual collapse associated with the positive curvature. Less density leads to negative curvature and expansion forever. A critical density leads to flatness (and, yes, expansion forever).

This whole description became more complicated with the discovery of dark energy (also known as the cosmological constant). Einstein had originally introduced this notion as a way of having a static universe but it was discarded (except for graduate student exercises) after the expansion of the universe was discovered.

I won't go into specifics, but the nice trichotomy above is shifted and it is possible to have expansion forever even if the universe is positively curved.

Anyway, in anything based on general relativity and NO quantum mechanics, the universe is finite into the past.

The question of what the universe is expanding into is a subtle one and requires a bit different perspective.

In modern cosmology, we discuss the geometry of spacetime, not just of space itself or time itself. The two together form the basic geometry of the universe. So when a cosmologists models the universe, they model it throughout both space and time as a single object. All dynamics occur within this object at different time slices.

So, as an analogy, I'm going to describe a 'universe' that is one dimensional in space and one dimensional in time and that is also curved in spacetime.

Imagine a globe. Imagine the latitude of a point describes the time and the longitude describes the spatial location. The two together will characterize the point. We imagine points further south are previous to those further north.

Space is then the collection of points at a particular time: this corresponds to a latitude line.

Now, starting at the 'beginning' of the south pole (more about this later), the latitude lines get larger as we approach the equator: in other words, space is expanding as we move forward in time. At the equator, we have maximum expansion, and then space begins to contract until we get to the end (the north pole).

So, looking at this analogy: what does space expand into?

The answer, literally and geometrically, is *the future*. And that is the answer to what space expands into.

Finally, notice that it is impossible to go south of the south pole: there is no 'before the south pole'. This is analogous to there being no 'before the Big Bang'. This is a geometrical aspect of this particular universe of spacetime.

I have other analogies along this line, but his one handles many questions many people have. I hope it helps.

Professor Sir Roger Penrose, a Nobel lauerate, has a model of an eternal Universe based upon General Relativity:

Wikipedia -- Conformal cyclic cosmology