The most formidable weapon against errors of every kind is reason. I have never used any other, and I trust I never shall. -Thomas Paine
I’ve been telling you the history of the Universe over the past few months in serial. Parts 1 through 8 are currently up, and have taken us from Inflation up through the formation of neutral atoms, covering the first 380,000 years of the Universe. During this whole time, like a giant balloon, space has been expanding.
One thing I haven’t paid much mind to is just how the Universe has been expanding during this time. The concept is relatively straightforward: the Universe expands faster based on the amount of energy density in it. More matter and energy packed inside a smaller volume means faster expansion.
What does this means for our Universe, which spends most of its time expanding and cooling?
If we want to know how the Universe expands, we need to know its energy density at any given time. Well, there are three general types of things that make up the Universe, and they’re important at different times. What are they?
1.) Matter. Normal matter is stuff like you and me… stuff with mass. As the Universe expands, the matter density dilutes. You may remember that density is just mass over volume, and so as the volume increases, the energy decreases.
2.) Radiation. Radiation is stuff with either no mass or very little mass, like photons or (sometimes) neutrinos, which move either at or extremely close to the speed of light. But unlike matter, radiation loses extra energy as the Universe expands!
How? The energy intrinsic to radiation is determined by its wavelength. Long wavelength photons (like radio waves) have less energy than short wavelength ones (like X-rays). But as the Universe expands, in addition to volume increasing (as it does for matter), the wavelengths also get stretched. This means that a Universe full of radiation loses energy faster than a comparable Universe filled with matter.
3.) A constant energy source. It’s also possible for space to be filled with a constant source of energy that doesn’t dilute as the Universe expand. This not only happens in our Universe, it looks like it has all happened before (during inflation), and like it’s all happening again (with dark energy)! In this case, the expansion rate remains constant, and the energy density also remains constant as long as the Universe is full of this type of energy.
So, what does this mean for our Universe’s beginning? We know it’s expanding and cooling, we know it has matter and radiation in it now, and we know that before that, towards the beginning (see parts 1 and 2 of my series), it had a constant source of energy in it. What I’d like to do is to work backwards from now, and ask whether the Universe started from a singularity or not?
Well, diagrams on the internet aren’t going to hold the answer. For billions of years, until the recent takeover of dark energy, the Universe was dominated by matter. Prior to that, though, when the Universe was only a few thousand years old (and earlier), the radiation was more energetic! It lost its energy more quickly due to that extra “stretching” of its wavelength, but for the first few thousand years, the Universe was dominated by radiation. And then if we go back even farther — towards the instant the big bang was created at the end of inflation — we come to the epoch of inflation, where the Universe is dominated by a constant energy source, and expands exponentially. Let’s compare, graphically, what these three cases look like. (The next three graphs — unlike most of the ones on this blog — were generated by me.)
Well, quite clearly, a Universe with exponential expansion expands the fastest over time, and one with matter expands faster than one with radiation. No big deal. But I want to go backwards, and take a look at what happens when we extrapolate back to a time where the size of the Universe should shrink to zero! After all, that’s what a singularity is defined to be, where all of the matter and energy in the Universe is concentrated in a single point. Let’s calculate it and see what we get.
What’s this?! A Universe with matter or radiation totally has a singularity at time t=0, but — and this is very, very important — an inflating Universe does not! In fact, we can take the inflating, exponentially expanding Universe back arbitrarily far, and what do we find?
It never reaches a size of zero! If you want an inflating Universe to have a singularity, you need to go back an infinite amount of time! Physically, of course, we can’t do that. The only information we have about inflation is from whatever comes at the very end of it. Everything else is wiped away from our field of view by the exponential expansion!
So what does this all mean? It means the idea that our Universe started from a singularity was a very good one back when we thought that the only important things in our Universe were matter and radiation, but now that we know about inflation, there is no reason to believe that our Universe ever had a singularity in the past.
And this is different from what you’ll read almost everywhere — on the internet, in textbooks, even at many colleges and Universities — but it’s right. Now that we know about inflation, it’s time to admit that we can’t with any sort of certainty speak about what came before it. That means there is no reason to believe that our Universe came from a singularity, and this outdated idea should have died as soon as inflation was accepted.
And isn’t that a surprise for most of us! So my answer — to the best of our current knowledge about the Universe — is no, it didn’t. What do you think about that?