Did the universe begin with a singularity? A point in space and/or a moment in time where everything in the universe was crushed together, infinitely hot and infinitely densely packed?
Doesn’t the Big Bang Theory say so?
Well, let me ask you a question. Did you begin with a singularity?
Let’s see. Some decades ago, you were smaller. And then before that, you were even smaller. At some point you could fit inside your mother’s body, and if we follow time backwards, you were even much smaller than that.
If we follow your growth curve back, it would be very natural — if we didn’t know anything about biology, cells, and human reproduction — to assume that initially you were infinitesimally small… that you were created from a single point!
But that would be wrong. The mistake is obvious — it doesn’t make sense to assume that the period of rapid growth that you went through as a tiny embryo was the simple continuation of a process that extends on and on into the past, back until you were infinitely small. Instead, there was a point where something changed… the growth began not from a point but from a single object of definite size: a fertilized egg.
The notion that the Universe started with a Big Bang, and that this Big Bang started from a singularity — a point in space and/or a moment in time where the universe was infinitely hot and dense — is not that different, really, from assuming humans begin their lives as infinitely small eggs. It’s about over-extrapolating into the past.
The connection with some kind of singularity dates back to the original Big Bang idea, the one which precedes the notion of cosmic inflation that’s been in the news over the past few days. [Here's an FAQ for non-experts about the news; the news itself; and what the news might mean if it holds up.] The part of the universe that we can see with our eyes and telescopes is the “observable patch” of the universe; it is probably far smaller than the whole universe (or, if it’s sufficiently complicated, “the multiverse”). What we know from interpreting various observations of the cosmos is that
today the observable patch is cold and diffuse and expanding
once upon a time, billions of years ago, the observable patch was hot and dense
To the extent that we trust Einstein’s equations for gravity, we can use those equations to understand how the Universe might have had this present and that past. People studying those equations (Friedmann, LeMaître, Robertson and Walker) learned that a universe can go through a process of expanding, cooling and diffusing — and thus could proceed from a hot, dense, rapidly expanding past to a cool, diffuse and slowly expanding present. This process is what we think our observable patch (and probably a larger region in which it is contained) has been doing for almost all of its 13.7 billion year history.
But suppose, seeing this behavior, we use these equations try to follow time backwards — just as we tried to infer the past of an embryo. We find our equations suggest a universe in which the further you go back, the hotter it was, the more dense, and the more rapidly it was expanding. If you keep going back and back, then (in the Old Big Bang model, before we knew about inflation) you find that at a sufficiently early time, 13.7 billion years ago, the density, temperature and expansion rate start off as infinite. That’s a singularity!
But would you have a reason to believe in that singularity?
I’ve talked over the years with many experts in “quantum gravity” [the poorly understood but required blend of Einstein's gravity and quantum physics, a blend that will be needed to explain extreme gravitational phenomena] and I’ve never spoken to one who believed that the universe began with a real singularity. Why? Because
the singularity arises from using Einstein’s equations for gravity
but we know Einstein’s equations aren’t sufficient — they aren’t able to describe certain extreme gravitational phenomena.
Specifically, when the density and heat become extremely large, quantum physics of gravity becomes important. But Einstein’s equations ignore all these quantum effects. So we already know that in certain extreme conditions, Einstein’s equations simply don’t apply. How could we then use those very same equations to conclude there’s a singularity at the beginning of the universe?
We can’t.
And if we don’t know how to alter Einstein’s gravity equations to make them into quantum gravity equations, then — well, we don’t know what happens instead of a singularity.
Now that was where things stood before inflation was known. Inflation changes the details of the history of the universe quite a lot. But it doesn’t change the basic conclusion about singularities: we don’t and can’t yet know what happened at the earliest moments of the universe, because we have neither data nor sufficiently clear equations to help us answer basic questions about it. Related to this, we don’t know precisely how inflation started (or even could have started) in the first place.
I’m not making this up out of my head. Just yesterday I was involved in a long conversation with professors and post-doctoral researchers at Harvard, in which we discussed various exotic mathematical methods for exploring the inflationary epoch and the era before it. The possibility that there really is a singularity at the beginning of the universe never came up once.
Or you can look at papers by the world’s experts — say, one by Alan Guth, a 17-page review of “eternal” inflation (i.e. inflation that continues, at least somewhere in our very large universe, into the infinite future) — and although he devotes some pages to the issue of what might have preceded inflation, the word “singularity” does not appear anywhere in his text.
Or look at the figure below, taken from page 6 of a lecture by Andrei Linde in 2007, giving a schematic depiction of the history of the part of the universe that contains our observable patch. You see that he shows it as beginning not in a singularity but in “space-time foam”. [Compare his picture with the one in my History of the Universe article.] What’s space-time foam? It’s space-time that is undergoing quantum fluctuations — quantum jitter — in which space itself is changing its shape from moment to moment! Well, when someone writes “space-time foam” on a graph, to physicists it means almost the same as writing “somehow quantum gravity takes care of everything”, without specifics. (I am confident that Linde will agree that the extreme left of his figure is quite speculative.)
From a lecture by Andrei Linde (link is in the text): a schematic plot of the size, over time, of the part of the universe that contains our observable patch. The extreme left is speculative, while the right-hand part of the inflationary epoch is the one probed by the recent BICEP2 measurement that was in the press this week.
Yet all over the media and all over the web, we can find articles, including ones published just after this week’s cosmic announcement of new evidence in favor of inflation, that state with great confidence that in the Big Bang Theory the universe started from a singularity. So I’m honestly very confused. Who is still telling the media and the public that the universe really started with a singularity, or that the modern Big Bang Theory says that it does? I’ve never heard an expert physicist say that. And with good reason: when singularities and other infinities have turned up in our equations in the past, those singularities disappeared when our equations, or our understanding of how to use our equations, improved.
Moreover, there’s a point of logic here. How could we possibly know what happened at the very beginning of the universe? No experiment can yet probe such an early time, and none of the available equations are powerful enough or usable enough to allow us to come to clear and unique conclusions.
The modern Big Bang Theory really starts after this period of ignorance, with a burst of inflation that creates a large expanding universe, and the end of inflation which allows for the creation of the heat of the Hot Big Bang. The equations for the theory, as it currently stands, can be used to make predictions even though we don’t know the precise nature of our universe’s birth. Yes, a singularity often turns up in our equations when we extend them as far as they can go in the past; but a singularity of this sort is far from likely to be an aspect of nature, and instead should be interpreted as a sign of what we don’t yet understand.
Filed under: Astronomy, Quantum Gravity, Science and Modern Society Tagged: astronomy, cosmology, Einstein, inflation, press, PublicPerception, QuantumGravity, relativity 
