The mass of universe at the point of the Big Bang

The density of universe at the time of the Big-Bang was infinitely high. Does that mean that the mass was also infinitely high? ( the universe was extremely small at that time)

• How do you know what the density of the universe was and how do you define the mass of the universe? – CuriousOne Dec 16 '14 at 10:52
• According to the energy conservation law I don't think so, except you see black holes as energy-consuming (not sure about that). If the energy/mass would be indefinitely high during big bang, it would mean that even if the universe expands (lowering the energy density) it still would be indefinite (And I think that that is not true... – arc_lupus Dec 16 '14 at 10:52
• I mean was mass extremely high? ( how could such a small thing could have mass?) I mean, when density increases mass also increases,isn't it? What is the estimated mass of universe at the time of big-bang? – user67822 Dec 16 '14 at 11:31
• What does "extremely high" mean? And compared to what? Nobody can make a scale that can measure the universe against the hunk of alloy that rests in an outskirt of Paris and that we use as a standard definition of a kg. It is by no means clear that "the mass of the universe" has any meaning, at all. – CuriousOne Dec 16 '14 at 12:31
• possible duplicate of Why does a black hole have a finite mass? – Kyle Kanos Dec 16 '14 at 13:41

Firstly, it is important to note that the old Big Bang cosmology is no longer the most widely accepted theory. We include inflation into the mix in current theories. That said, there is an ambiguity in the definition of the Big Bang (you can find information on that in my question here).

If we take the definition of the Big Bang as coming before inflation, then we are probably referring to a curvature singularity. During this time, our best theories vary by a great deal in what we would expect to find. Many of them theorize the existence of one or more massive inflaton fields that eventually drive inflation. While we say they have mass, it is not the same as how a brick of iron has mass. The inflaton has a mass in much the same way that radiation or dark energy has a mass; there is a gravitational/inertial mass but not necessarily a rest mass. The mass density of inflatons is not usually volumetric, which means it does not scale with the size of the container. Furthermore, the mass in this case is used more as a coupling constant for the field. However, this is all besides the point, at a curvature singularity, the energy scales would be well above the range of most of our theories. Standard general relativity is not expected to accurately describe the universe at a point like that; we need a GUT and quantum gravity to accurately describe the physics of an initial curvature singularity. Short answer: No, the mass is not infinitely high. It is finite with a non-zero probability of being zero.

If we use the second definition of the Big Bang, where it occurs after inflation, then there is no curvature singularity. Under this interpretation, it is also common to treat the Big Bang as an era rather than a single moment, however we can look at the start of this era to answer the question. After inflation, the universe enters into its more regular routine. There is matter and radiation and it is very hot; everything one expects when they imagine the beginning of the universe (it's only $10^{-30}s$ old after all). The matter and radiation present comes from a few sources, mostly from the decay of the inflatons and quantum fluctuations during inflation. Since the universe is not confined to a curvature singularity and since the amount of matter and radiation is finite and generated by mostly decaying inflatons, the total mass of the universe is certainly finite. Furthermore, at the initial moment of the Big Bang era, not all inflatons would have decayed; the full compliment of matter in the universe is not yet present.

Now, there is one important thing left to consider. What do I mean when I say "the universe"? The possibility of the universe being infinite in extent means that the total mass of the entire universe is possibly infinite. So to clarify, when I refer to "the universe" I mean the observable universe. More specifically, because I'm a cosmologist and we like this value, I am referring to the region bounded within the comoving Hubble radius at the time of interest. This means we can further answer your question. Even though the mass is finite, I cannot deny that the universe was significantly smaller and denser than it is now. However, not only was the universe unexpanded (a small scale factor), the Hubble radius was much smaller back then. The energy density of matter is volumetric; it is inversely proportional to the size of the container. This means that, if no matter is created or destroyed, the mass of the universe now would have to be greater than or equal to the mass of the universe at the beginning of the Big Bang era (the comoving Hubble radius is larger now, which means the present universe can encompass more matter that was not inside it in the past).

This brings us to the end, for which I have saved the simplest (if not the most accurate) answer to your question. Your premise that the density is infinitely high is based on the following logic:

1) The universe has a mass $M$ now and a large volume, therefore a low density

2) At the time of the Big Bang, the universe was a singularity with zero volume

3) Therefore, the density is $\rho=M/V$, $V=0$, so $\rho=M/0\to\infty$

4) If the density is infinite, mustn't the mass be infinite as well?

Do you see the problem with point (4)? You used $M$ and $V$ to solve for the density, then you are using that to solve again for $M$. Logically, you can only retrieve the value you initially used. In other words, it's the same as the mass of the universe now (according to your reasoning): $\rho=M/V=M_{now}/0\to\infty$ but $M=\rho V=(\infty)(0)=M_{now}$

• What evidence do we have for inflation? – CuriousOne Dec 16 '14 at 14:13
• @CuriousOne That depends what counts as evidence. It solves numerous problems with the old Big Bang model as well as explains the scarcity of magnetic monopoles. People thought BICEP2 results were a promising source of direct evidence, but that's become more skeptical as of late. Does better fitting the theories to the data than previous models count as evidence? I wouldn't say inflation is proven. But it is more accepted than the old Big Bang model, which has many problems – Jim Dec 16 '14 at 14:18
• I don't think there is an actual problem with "the old" big bang. The problem is with general relativity at that scale. Why there should be a problem with magnetic monopole density is a mystery to me, since we haven't seen even one. It's not very intuitive to assume that something unseen exists just so we can make ourselves a problem that needs to be discussed away with an additional assumption. BICEP2 I would discount completely. Does model fitting count? Only if we are near 100% sure that the model is correct. Quite to the contrary we are almost certain that it isn't... – CuriousOne Dec 16 '14 at 15:07
• @CuriousOne the old big bang has the horizon and flatness problems to start with. And the magnetic monopole density (if they exist) is large according to the old big bang model. Large enough that we should see them. Whereas with inflation, that density drops to only a handful in the observable universe. General relativity was not the problem, the old big bang model clearly fails to explain things like the horizon problem – Jim Dec 16 '14 at 16:04
• Both the horizon and the flatness problem are the result of extrapolating general relativity beyond its limits. General relativity has ZERO to say about magnetic monopoles... or any other type of elementary particle, while particle physics has next to nothing of relevance to say about what happens beyond the TeV scale. It certainly can't help you with monopoles... we simply haven't found any. The only reason for any of these issues are breakdowns in our theories, not relevant experimental facts. What inflation is trying to cure is incurable without massive progress in HEP and QG. – CuriousOne Dec 16 '14 at 16:31