How Many Universes Are There? (Script) (Patreon)

The universe is big, but it’s peanuts compared to the eternally inflating multiverse. But just how many universes are there? What are they like? And most importantly, what can they tell us about … aliens?

Imagine it: the observable part of our universe is 93 billion light years across, and that’s just a small fraction of the stuff created in our Big Bang. But in the eternal inflation picture, ours is just one among uncountable bubble universes. Bubbles that are continuously appearing and growing within a vastly larger spacetime that itself expands at an exponentially accelerating rate. A greater inflationary spacetime whose expansion never ends. We looked at the bizarre idea of eternal inflation in recent episodes – but we stopped short of exploring the full implications of this proposition. Those implications are, frankly, completely nuts. Some may also be true.

Here’s the scenario: the default state of the greater universe – or multiverse - is to expand exponentially due to the vacuum of space itself having a large and constant energy density. Energy locked into something called the inflaton field. Within that inflating space, tiny patches stop inflating – the inflaton field in that patch loses its energy and so accelerating expansion stops there. Within each bubble we get a new Big Bang that kicks off a more slowly expanding universe. But that bubble has an edge, and the edge spreads into the surrounding inflating spacetime at the speed of light, causing inflation to stop within the growing bubble.

If lots of these bubbles form, they could collide with each other to produce a connected network of non-inflating universe. But the little patches where inflation persists are expanding so fast that they quickly dominate the non-inflating network of bubbles, and so the cycle of inflation continues.

Some questions spring to mind: - I mean, besides “what the bleep”. For example, how many bubble universes can be made this way? How often do they collide? Are those universes similar to each other, or wildly different? And if eternal inflation never ends, did it have a beginning? I’ll give you an idea of our best thinking for all of these.  Let’s start with the first two, because these are basically our challenge question. To fully answer these we’d need to know the true physics of the inflaton field. But we can figure some stuff out just based on the exponential nature of the expansion. For example, in the challenge question I asked you to calculate the RELATIVE number of new bubble universes that formed in one second compared to the previous second.

We assumed that there’s a fixed but unknown probability that a bubble universe will form in any given volume of inflating space. That means the number of bubbles forming at each point in time should be proportional to the volume of the inflating universe at that time. So the rate at which that volume is increasing is the same as the rate at which bubble universes multiply. We assumed the minimum inflation rate that we think was needed to kick off our own universe. The scale factor – or radius of the universe – increased by a factor of at least 10^26 in less than 10^-32 seconds. So how much did the volume increase over 1 full second at this rate?

Well, a scale factor or radius increase of 10^26 means a volume increase of that cubed – so 10^78. Every 10^-32 seconds one cubic meter of volume becomes 10^78 cubic meters, which is approximately the volume of our entire universe. And then in the next 10^-32 seconds each of those 10^78 new 1-meter cubes spawns just as many new entire universe-sized volumes. So we have 10^78-squared, then 10^78-cubed, etc. By the time we get to one full second we’ve multiplied by 10^78 10^32 times, so our volume is 10^78 to the power of 10^32, or around 10^10^34. And our number of new bubble universes should multiply by the same insane factor each second.

This gives us a ridiculously large number of universes even if the probability of making one per unit of volume is insanely low. The exponential nature of the expansion guarantees that. As soon as the inflating spacetime is big enough to make one universe, in the next second it should make 10^10^34 universes, and so on. If you got this right then congrats. We’ll list the winners as well as answer the extra credit question at the end of this video.

As crazy as eternal inflation sounds, it’s still fun to think about the consequences if all of this is true. Here’s another one: do all of these bubble universes the same laws of physics, or could they be wildly different from each other? Based on standard ideas, they probably have the same number of dimensions as ours – 3 space, 1 time – but their contents and physics could be very different.

For example the cosmological constant – the strength of dark energy – could be different. Remember that it was the high energy density of the inflaton field that drove inflation, and the loss of that energy density that ended it. But what if the inflaton field retained just a tiny bit of energy after its decay? That residual field might be what we observe as dark energy. 

It’s an open and contentious question why the current energy density of the vacuum should be so low without being exactly zero given that it started out so large. Seems awfully lucky – if dark energy were much stronger then our universe would have restarted its accelerating expansion too quickly for galaxies and stars and life to ever form.

Here’s a possible explanation: what different bubble universes can end up with different vacuum energies? Very low vacuum energies like ours might be extremely rare, but there are so many bubble universes that at least some will have a low enough cosmological constant for life to form. Naturally, we would be in such a universe. This is an example of using the Anthropic Principle - we must exist in a universe capable of producing us, so if there are many universes it is natural that we find ourselves in one finely tuned for life.

People have also invoked the anthropic principle plus eternal inflation to explain a conundrum in string theory. As we’ve talked about before, modern string theory is difficult to pin down because there are countless possible minimum-energy configurations of its 6 curled up dimensions. More than 10^500 possible vacuum states – probably a lot more. The vast space of possible configurations of these compact dimensions is referred to as the string landscape. Each different configuration results in a different family of particles and also a different cosmological constant. We don’t know why our universe has the particular string vacuum state that it does. But it’s lucky it does – because the resulting particles allow for things like complex chemistry. Enter the anthropic principle once again: eternal inflation gives us enough universes to easily populate the entire string landscape. All different vacuum states exist, and our universe necessarily has one  that leads to life-friendly particles. As well as a decent cosmological constant.

Some people aren’t comfortable with the anthropic principle. Those people will  be even less comfortable with the next idea. This one is from Alan Guth, the guy who invented inflation in the first place. Here it is: eternal inflation may solve the Fermi Paradox. It may explain why we don’t see aliens.

The argument goes like this: if the number of new universes increases by a factor of some impossibly large number every second, then the vast, vast majority universes in existence were born recently. There are vastly more universes born one second after ours than were born at the same time as ours. Now, imagine that there’s a set amount of time for the first intelligent life to form in any one of these universes. Let’s say 10 billion years. Pretend that it’s the same in all universes down to the second. The real timescale is going to be much more fuzzy than this, but it also doesn’t really matter for this argument.

So, the first intelligence appears in our universe after exactly 10 billion years – we’ll call that moment “second one”. The same happens in the exact same second for universes that formed at the same time as ours. 

One second later – “second two” – you might get some more intelligent lifeforms forming in those same universes. Maybe just as many as in second one. But consider the wave of universes that formed one second after our own. These are only now reaching the 10 billion year mark and producing their first intelligent lifeforms. 

And of course there are vastly more of those slightly younger universes – more than all the atoms in all the universes that are one second older. So first civilizations in those younger universes will always outnumber all the civilizations in all older universes.

The result is that at any one moment, almost all of the intelligent beings in the eternally inflating multiverse are in the youngest universes that have had time to form intelligent life. So if we imagine that we are a typical intelligent lifeform, then we’re most likely the most common type across the multiverse, which means we’re the first to appear in our universe.  Ergo we shouldn’t be surprised that we don’t see aliens.

Guth calls this argument the Youngness Paradox. Let’s be clear – he doesn’t necessarily believe it to be right. He admits that, while it seems logically sound, it does seem weird enough to force us to question the premises. He proposes that there may be something off in the logic of weighing up probabilities over bubble universes. He also doesn’t rule it out.

OK, the last thing I want to talk about is colliding universes. How often does it happen? Let’s start by answering the extra credit question: how close to bubbles need to be in order to collide? I won’t go through the detailed calculation because it takes a wee bit of calculus. Instead I’ll provide a link to the answer in the description. But the too-long-didn’t-calculate is this: remember that bubble edges expand at the speed of light. If they form too far apart then the intervening inflating spacetime will throw them apart at faster than light speed before they can merge. Assuming the crazy rate of inflation in the question, you get that two bubble edges need to be closer than 6x10^-50 m in order to reach each other.

This is something like 15 orders of magnitude smaller than the Planck length. The implication is that universes don’t collide very often unless their rate of production is extremely high. And it might be very high – especially if the inflaton field is highly correlated from one point to the next, as in slow-roll inflation. But it still should NOT be surprising that we don’t see evidence of bubble collisions in our observable universe. If such collisions happened, they’re probably too far away for us to see.

OK, so we’re come up with a lot of ridiculously large AND small numbers, and convincingly shown that none of this is easily testable. Where does that leave eternal inflation? Well we probably shouldn’t just accept it – but at the same time, current lack of proof doesn’t mean something is wrong. Just that the universe – or multiverse is playing hard to get. But here’s something that’s not hard to get – Space Time swag. If your name is listed below, you’re a winner of the challenge question and you get your pick of a swag item from our merch store. Email us your choice, any relevant size info, and your mailing address and we’ll get it out to you. Of course you can reward yourself for just listening to the answer by buying your own swag. Link in the description. It’s the best humorous science apparel in all of spacetime.