Every astronomy textbook tells us that soon after the Big Bang there was this period of exponentially accelerating expansion called Cosmic Inflation. In a tiny fraction of a second, inflationary expansion multiplied the size of the universe by a larger factor than in the following 13 and a half billion years of regular expansion. This story seems like a bit of a… …stretch. Is there really any mechanism that could cause something like this to happen? Well, that’s what we’re covering today: the real physics of cosmic inflation. Most cosmologists buy some variation of the inflation hypothesis. It seems to have very neatly solve some of the biggest questions in cosmology, those being: why is matter and energy so smoothly spread out across the entire observable universe? – and why is the geometry of the universe so flat? Neither should be expected unless the universe expanded much more rapidly early on. Another problem fixed by inflation is the absence of magnetic monopoles. And these are strange particles predicted to have been produced in the early universe. We’ll come back to those another time. The inflation hypothesis solves these problems with a single simple idea. In addition, inflation gives us an explanation for why the universe is expanding in the first place. It puts the ‘bang’ in Big Bang. After the exponential expansion ended the universe would have continued to coast outwards just like a thrown ball continues to rise after it leaves your hand. This is the Hubble expansion that we observe today. Inflation trades four mysteries for one: the problems of smoothness, flatness, missing monopoles, and expansion are all solved if we assume a single phenomenon. But physicists are a skeptical bunch and most of the time they don’t just make up stories and start believing them without good reason. Especially something as extravagant as inflation. For a hypothesis like this to be taken seriously, the physics also has to make sense. In the case of inflation part of the appeal is that it fits extremely nicely into our modern understanding of gravity and quantum mechanics. Let’s dig into each of these one at a time. First up, the equations of Einstein’s general theory of relativity. Our modern theory of gravity can be used to predict the behavior of the universe as a whole. They describe how its expansion or contraction depend on the matter and energy it contains. Mostly, the stuff in the universe pulls the universe back together; resists the expansion with a positive gravitational effect. But there’s one type of energy that can have an anti gravitational effect. Anything that causes the fabric of space itself to have energy – anything that has a constant energy density pushes rather than pulls. Now, we know that something like this exists because we’ve observed it in the accelerating expansion produced by dark energy. We’ve covered how this works for dark energy in a lot of detail. Check out the playlist if you want to get an insight into the actual math. But the upshot is that if the vacuum of space has a constant energy density, then Einstein’s equations end up having a term that we call the cosmological constant – A positive value for the cosmological constant means a constant doubling rate for the size of the universe. That means exponential expansion. The speed of that exponential expansion depends on the strength of the vacuum energy density. For dark energy, that number is incredibly small and so dark energy only works because it adds up over an enormous amount of space. On the other hand, in order to solve the smoothness, flatness, and monopole problems inflation needs to expand the universe by a factor of 10 to the power of 25 in less than 10 to the power of negative 30 seconds. To do this, the energy density of the vacuum during inflation would need to be vastly stronger than dark energy. Also, for inflation to make sense presumably the universe also needed to stop inflating at some point giving way to the regular Hubble expansion that we see today. So, the vacuum energy would need to drop from a very high value to basically zero. To see how this could happen we need to move beyond Einstein’s general relativity. We need some quantum physics. In fact, we need some quantum field theory. QFT can explain how a vacuum can have energy, which – surprise surprise – we also covered in a playlist. There’s some more homework for you. For now, a review: the universe is filled with quantum fields. Now, a field is just some property that takes on a numerical value at every point in space. We call that the “field strength”. The field strength determines how much force a quantum field exerts on other fields and particles. A familiar example is the magnetic field. The stronger the field, the more it pulls or pushes. By the way, an elementary particle is just an oscillation in this field strength – a little packet of energy held by the field. If a quantum field has energy in the form of particles and if space is expanding – as is the case for our universe – then that energy gets more and more spread out over time. Particles get dispersed and so the energy density goes down. A quantum field can contain an intrinsic energy even without particles. In that case, it will always try to drop to the lowest energy state and typically that means losing all energy besides whatever is bound up in particles. For example, a magnetic field will quickly fade away if we take away the electric currents that created it. Now, a field doesn’t just jump to the lowest energy state, it makes its way there by changing the field strength one step at a time. If we graph a quantum field potential energy versus field strength, it might look something like this: If the field finds itself at a high energy – high field strength state, it’ll sort of roll down to the minimum and stay there. And by the way, the lowest energy state of a field is called its vacuum state. But sometimes, the energy contained by a field has a more complex relationship with the field strength. I’m gonna have to save the how and why of these potential energy curves for another video. For now, let’s just go with it. One possibility is that the field could have what we call a local energy minimum. If such a quantum field found itself near that local minimum then it would roll to the bottom and get stuck there. It would have a lot of energy but no particles. We would call this a false vacuum and it gives us exactly the constant vacuum energy density needed for inflation. There are other ways for a field to end up with a positive vacuum energy density and I’ll come back to these. But for now, let’s just assume that such a field exists and give it a name: “the inflaton field”. The original idea for inflation proposed by Alan Guth in 1979 goes something like this: In the early universe this mysterious in flattened field has a high field strength due to the extreme temperatures of that time. As the universe cools the field loses strength and energy. But then, it gets stuck in this local energy minima. The universe keeps cooling, but the inflaton field can’t lose more strength. It would have to get over this potential energy barrier to do that. Stuck at a constant very high energy density, inflation takes hold; the exponential nature of inflation quickly blows up the volume of the universe, rendering it, basically, empty and cools it to a low temperature. In fact, it super cools the inflaton field. The field remains in a vacuum state that doesn’t matches temperature – in the same way that water can become a supercooled liquid, much colder than ice. If you cool it prevent ice crystals from forming. Inflation and the corresponding super cooling would go on forever if the inflaton field stays stuck. But quantum fields have a tendency to randomly fluctuate to different values, thanks to the Heisenberg uncertainty principle. Somewhere in the inflating universe, the inflaton field is going to fluctuate to the other side of this local minimum barrier. It’s going to quantum tunnel and on that other side, it sees a deeper truer minimum – perhaps the true vacuum state – and suddenly starts to lose energy again racing towards that minimum. Inflation would stop at that point. Regions of space adjacent to that point would also be dragged out of the local minimum towards the true vacuum and so the entire inflaton field would cascade down in energy. The analogy with supercooled water still works. Introduce an ice crystal or even a speck of dust to the water and it will quickly turn to ice. Now, that’s a phase transition. The inflaton field also undergoes a phase transition towards the new vacuum state. And just like a growing ice crystal, this effect will propagate outwards from the starting point, which we call a nucleation point, by analogy. This bubble would grow into the surrounding inflating regions at the speed of light. And inside the bubble, inflation would end. Inside the bubble, space would still be expanding out whatever speed it had at the end of inflation, but that expansion would no longer be exponentially accelerating. The energy that existed in the inflaton field doesn’t just go away, it remains in that field very briefly, but now in the form of inflaton particles. It’s like the entire floor of the field is shifted down at every point in space; what was once pure inflaton field is converted to a stack of inflaton particles. Those particles are unstable and they very quickly disperse their energy into the other quantum fields. The inflatons decay into the familiar particles of the standard model – quarks, electrons, etc. So, the vacuum of inflation is converted into an extremely hot ocean of particles. We say the universe was ‘rethermalized’ or reheated by this process. In fact, this process would reheat the universe to the extreme energies that we expect existed right after the Big Bang. At this point, the universe should evolve as the rest of the Big Bang story predicts: An extremely hot dense ocean of matter and radiation that slowly cools and disperses and forms structure as the universe expands. This is the rough sequence laid out in Alan Guth’s original paper. But, right from the start Guth admits a number of problems with his story. The big one is about how inflation stops. See, when these non inflating bubbles form, all of the energy gets released at their boundaries; their expanding spherical fire walls – that are otherwise empty – which isn’t exactly what our universe looks like. The only way to get the sort of evenly distributed temperature we see in the Cosmic Microwave Background, is if lots of these bubbles collide and then have time to mix. But in order for inflation to last long enough to do its job, the probability for the appearance of a bubble can’t be too high and that rules out sufficient collisions. The upshot is that the lumpiness of the CMB is not consistent with lots of colliding bubbles. Guth’s idea is now called old inflation. It solved several problems in cosmology and it also inspired other physicists to find even better solutions, mostly by changing the nature of the in flattened field so that allows a smooth exit from inflation across the universe rather than in a series of bubbles. bThese new inflation models are much more successful and we’ll get into them in an upcoming episode. But, by delving deeper into the physics of inflation, physicists discovered some pretty crazy predictions. If inflation happened at all, that it’s hard to avoid two conclusions: Once started, inflation should continue… eternally – Only stopping in patches where a bubble universe forms. And once started, inflation should produce infinite such universes. But these will have to wait for a follow-up episode when we step into the multiverse of an infinitely inflating… Space Time.