[music playing] Cosmic inflation describes a period of insane exponential expansion right after the instant of the Big Bang.

It calls into question our very understanding of what the beginning of the universe even means.

[music playing] The Big Bang theory describes the earliest epochs of our universe amazingly well.

It has made predictions that have been verified beyond reasonable doubt.

But two significant problems with the simple model tell us that something strange must have happened in early times, an insane growth spurt that we call inflation.

Today, I want to explain what inflation is, why we need it, and why essentially all cosmologists believe that it really happened.

The observable universe is impossibly huge.

And I'm not exaggerating the situation here.

It's so huge, 93 billion light years from one edge to the other, that those most distant points should never have had time to communicate with each other.

And yet, at some point in the distant past, they must have been in contact.

The cosmic microwave background tells us that they were once close enough together to become perfectly, smoothly mixed.

This smoothness of the CMB is called the horizon problem.

And we talk about it in the last video.

The horizon problem isn't the only troubling feature of the CMB.

We can use the apparent size of the very subtle fluctuations in the CMB to measure the flatness of the fabric of the universe, of spacetime.

And the answer we get is very strange.

Let me explain.

A flat sheet of paper is flat.

Duh.

Draw any triangle on one and add up the angles.

It's always 180 degrees.

Draw the same triangle on the surface of a sphere, which has what we call positive curvature, and the angles add up to more than 180.

On a negative curvature hyperbolic plane-- a saddle-like structure-- they add up to less.

Triangles in 3D space obey exactly the same rules as on 2D surfaces, and their geometry measures the curvature of space.

So now, think of those blobs in the CMB as the ends of very, very long triangles.

We know the size of the brightest of those blobs.

They're defined by how fast sound waves could have traveled by the time the CMB was created.

And we know how far away they are.

They're really, really far.

Using basic trigonometry, those distances tell us what the little angle at this end should be.

It should be 1 degree, assuming the universe is flat.

It should be larger if the universe is positively curved, smaller if negatively curved.

And yes, it's pretty much exactly one degree.

Based on the precision of our measurements so far, we know that the curvature is within 0.4 of 1% of perfect flatness.

OK.

So what?

The universe is flat.

No, actually, it's extremely weird.

An expanding universe doesn't tend to stay flat, even if it starts that way.

Analogy-- one way to bowl a strike is to keep the ball near the center of the alley all the way to the pins.

If the ball isn't moving fast enough, then any initial deviation from dead center will send it towards the gutter.

Same with the universe.

If the center of the alley represents a flat universe, then the gutters represent extreme curvature in the positive or negative directions.

If the universe starts out even a little bit not flat, then that not-flatness will amplify quickly.

So if our universe is flat to within 0.4 of a percent now, then in the first instant, the universe had to be flat to one part in 10 to the power of 62.

That's like rolling your ball really, really slowly and having it stay within 0.4 of a percent of the center of the alley, and the alley is a light year long.

Nice bowling, universe.

This flatness problem is just as much of an issue as the horizon problem.

Both seem strange if we assume that regular gravity was always the only force affecting the rate of expansion after the initial kick of the Big Bang.

We need to throw out that assumption because it is giving us the wrong answer.

That's a science thing, questioning your assumptions.

Try it.

It's fun.

So it turns out that we can fix both of these problems with a single, elegant idea called inflation.

It goes like this-- start with a universe so crunched down that the entire currently observable part of it was all causally connected.

Then, for a very short period of time, blow it up much faster than the speed of light so that most of it appears causally disconnected, at which point inflation stops and regular expansion takes over.

This works because even a very blotchy, curvy universe is going to be much smoother and flatter on its smallest scales.

Inflation takes a very tiny, smooth, flat speck of that blotchy, curvy greater universe and blows it up to a macroscopic volume really, really fast.

That inflated speck subsequently grows into the universe that we know, but retains its once subatomic smoothness and flatness.

That's right.

According to inflation, the universe that we see is a tiny part of a vastly larger universe that itself may well be curved.

The neatness with which this inflation solves both the horizon and flatness problems really has most cosmologists thinking that something like this must have happened.

For this to work, that inflationary expansion had to throw neighboring regions of space apart at many times faster than the speed of light.

It needed to increase the size of the universe by a factor of at least 10 to the power of 26 in less than 10 to the minus 32 seconds, ending when the universe was just macroscopic, something you could hold in your hand.

In the subsequent 13.7 billion years since, the universe has expanded by about the same amount that it did during inflation.

So what sort of mad physics could do something like that?

Actually, Einstein came up with the exact mathematical description that we need-- an antigravity term called the cosmological constant.

In the field equations of his general theory of relativity, he added this as a way to allow his theory to describe a static space time, a universe that's neither expanding nor contracting.

When it was later discovered that the universe is indeed expanding, Einstein retracted his constant.

But this bit of math gives us exactly the type of expansion that we need for inflation.

Incidentally, it also describes the effect of dark energy, and that may not be a coincidence.

The cosmological constant represents something that can happen to our spacetime.

Einstein is right, even when he's wrong.

The cosmological constant adds some energetic stuff to empty space.

It doesn't tell us what this stuff is, just that it's a property of space itself and that it acts to drive expansion.

The more space, the more of this stuff.

And so the more space, the more expansion.

We'll delve pretty deep into how this works in terms of general relativity on a future episode on dark energy.

And we'll explore exactly what could cause such a weird sort of energetic vacuum real soon-- inflatons, scalar fields, forced vacuums, all of that.

For now, let's just go with the fact that empty space can propel its own expansion and will do so if the vacuum contains a ubiquitous constant energy density.

Another really important thing about the driving mechanism of inflation is that it stopped.

The universe slowed down from exponential to the regular old expansion that we see today, what we call Hubble expansion.

And while we know the minimum amount of inflation needed before that stopping point, we don't really know when it began or even if it had a beginning.

It may have, and there are some ideas about what got it started.

But it's also possible that inflationary expansion is the default state of the greater universe-- I should say multiverse at this point.

This is the idea of eternal inflation.

I'll get to all of these wild ideas very soon.

With inflation, the Big Bang theory takes on new meaning.

When first conceived, the inflationary period was thought to have started at a particular point after the instant of the Big Bang.

But once you accept inflation, there isn't necessarily a good reason to think that there was a normal expansion period before, if there was even was a "before inflation."

In fact, the instant that inflation ended can perhaps be thought of as the moment that our universe as we know it came into being.

In that sense, inflation is the initial kick of the Big Bang.

We don't need to talk about an exploding singularity at all.

Time may not have begun with the Big Bang.

And so we'll rewind to before the beginning of the universe very soon on "Space Time."

In a recent episode, we told you why space things are the shape they are.

And you guys brought it with the big questions.

Frank Schneider asks, "Why does dark matter in a galaxy seem to form a sphere?"

Well, this is because dark matter doesn't really interact with itself except gravitationally.

The Milky Way and our solar system were originally made of gas, giant clouds of the stuff.

And gas does interact with itself.

It drags on itself.

So even though the gas originally had motion in many directions, over time, it sweeps into a single bog flow.

Dark matter doesn't sweep itself.

It just passes by with a tiny gravitational tug.

So the orbits of any bit of dark matter can be in any orientation or direction.

And random orientation orbits give you a spheroid.

This is also true of the stars in a eliptical galaxies.

Stars a small enough, compared to the distances between them, that they can be in these random orbits.

The reason spiral galaxies are discy is that those discs formed before the stars actually formed, back when the material was mostly gas.

DBlanding and a few others questioned my use of the concept of a centrifugal force.

And DBlanding, I definitely chose yours because of your particular phrasing.

It's true that this force is, in a sense, fictitious.

It emerges in a rotating reference frame as a force-like term that resists inward motion.

It doesn't exist in the inertial reference frames for which Newton's laws are valid.

For example, in a reference frame of an unmoving center of mass, you have a center-pointing or centripetal force-- in this case, that's gravity-- acting on the orbiting object.

And the force is resisted by nothing.

The orbiting object is subject to the full acceleration caused by gravity, which is what causes it to move in an orbit.

In that reference frame, it's the velocity perpendicular to the centripetal acceleration that resists radial infall.

But centrifugal force is easier to say, and it's still accurate.

A couple of you asked about the shape of a black hole and its accretion disk based on the spin of the black hole.

OK.

So first, the accretion disk that forms around the black hole can either be very flat or fatter, but probably more toroidal than spherical.

Yet that doesn't have much to do with the spin of the black hole itself.

It depends more on things like the rate of accretion, the viscosity of the material, the way angular momentum is lost by that material, stuff like that.

Although the magnetic field of a spinning black hole can also play a part here.

However, the shape of the event horizon of the black hole itself does depend on spin.

And indeed, a rapidly-rotating Kerr black hole is flattened-- it's an oblate spheroid-- while a non-rotating Schwarzschild black hole is a perfect sphere.

Omicron Vegra asks if I can please do the Blue Steel face from "Zoolander."

I'm sorry.

I only do Magnum.

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