The Real Physics of Cosmic Inflation (Patreon)

Every astronomy textbook tells us that soon after the Big Bang, there was a 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? What what we’re covering today – the real physics of cosmic inflation.

INTRO

Most cosmologists buy some variation of the inflation hypothesis. It seems to 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. We explored these problems in an earlier video – worth a look if you really want to get inflation. Another problem fixed by inflation is the absence of magnetic monopoles – 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 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 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 it back together – resists the expansion with a positive gravitational effect. But there’s one type of energy that can have an antigravitational 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 an insight into the actual math. The upshot is that if the vacuum of space itself has constant energy density then Einstein’s equations end up having a term 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 add up over an enormous amount of space.

On the other hand, in order to solve the smoothness, flatness, and monopole problems, inflation needed to expand the universe by a factor of 10^25 in less than 10^-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 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 particular, 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, another review:

The universe is filled with quantum fields. A field is just some property that takes 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 field has energy in the form of particles AND if space is expanding – as in the case of our universe – then that energy gets 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. [inverted parabola] If the field finds itself in a high-energy, high field strength state it’ll sort of roll down to the minimum and stay there. By the way, the lowest energy state of a field is called its vacuum state.

But sometimes the energy contained by a field had a more complex relationship with the field strength. I’m going 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 could 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 positive vacuum energy density, and I’ll come back to those. But for now let’s just assume 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 inflaton 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 gets stuck in this local energy minimum. 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 so. 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 to a low temperature. In fact it supercools –remaining in a vacuum state that does‘t match its temperature. In the same way that water can become a supercooled liquid, much colder than ice, if you cool it but prevent ice crystals from forming.

This supercooling and inflation would go on forever if the inflaton field stayed stuck. But quantum fields have a tendency randomly fluctuate to different values, thanks to the Heisenberg uncertainty principle. Somewhere in the inflating universe the inflaton field fluctuates to the other side of the local minimum barrier – it quantum tunnels. There it sees a deeper, truer minimum – perhaps the true vacuum state – and the suddenly starts to lose energy again, racing towards it. Inflation would stop at that point.

Regions of space adjacent to that point would also 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. That’s a phase transition. The inflaton field also undergoes a phase transition towards a new vacuum state. And just like with a growing ice crystal, this effect would propagate outwards from the starting point – which we call a nucleation point by analogy. This bubble would grow into surrounding inflating regions at the speed of light, and inside the bubble inflation would end. Inside the bubble space would still be expanding at 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 was shifted down. At every point in space, what was once “pure inflaton field” is converted to a stack of inflaton particles. But 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 that the universe was rethermalized or reheated  by this process – in fact it would reheat to the extreme energies that we expect existed right after the Big Bang. At that 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 the 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. They’re expanding spherical firewalls that are otherwise empty – which isn’t exactly what our universe looks like. The only way to get the sort of evenly distributed temperatures 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 – ruling 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 inspired other physicists to find better solutions – mostly by changing the nature of the inflaton field so that it allow a smooth exit from inflation across the universe, rather than in a series of bubbles.  These new inflationary 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, then 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 followup episode, when we step into the multiverse of an infinitely inflating space time.