Can we try to predict the fate of the universe?

Amazingly, yes, we can.

Yet our efforts to do so have revealed the existence of a strange influence called "dark energy."

[theme music] Einstein's general theory of relativity allows us to describe the behavior of the cosmos on the largest scales-- of a volume of space vastly beyond our capacity to physically explore and at a time billions of years in the future.

But attempts to constrain the predictions of this theory with real astronomical observations tell us that the fate of the universe is governed by something we call "dark energy."

To truly understand dark energy, we're glimpsing into the workings of Einstein's theory on a cosmic scale.

In the last episode, we looked at how general relativity, expressed in the first of the two Friedmann equations, can describe the cosmic balance between the outward expansion of the universe and the resistance to this expansion due to the gravitational effect of everything it contains.

Seriously, you have to pause now and watch this episode if you haven't already.

OK, ready?

So it turns out that this cosmic conflict will be won by expansion.

And this is true even though we haven't taken dark energy into account yet.

By weighing up all of the matter in the universe, astronomers have figured out that there just isn't enough of anything to turn the universe back on itself.

There will be no Big Crunch.

And the universe will expand forever.

There are two powerful and completely independent measurements that can test this prediction of the fate of the universe.

Today, let's look at one of these measurements-- the geometry of the universe, which points to a discrepancy in the first Friedmann equation.

We know for sure that, the left side of this equation, the sum of the expansion and density terms don't cancel out to zero.

In fact, they come out positive, which means that the expansion term wins over the inward-pulling density term.

The universe is too low-density to recollapse.

Right.

So the left side of this equation, as we wrote it, is positive, which means the right side should be, too.

See?

Equals sign.

But that right side actually talks about something completely different.

It describes the curvature of space.

And it hinges on that k thing.

k is, in a sense, the shape of the universe-- its spatial curvature, as well as its spatial extent, finite or infinite.

Notice I said "spatial" curvature.

Spacetime will be curved, no matter what.

Which is what gives us the expansion described here.

But the spatial geometry of the universe at a fixed instant in time can be flat or curved.

And it's pretty straightforward.

k can be plus 1, minus 1, or zero.

"k equals plus 1" means the universe has a positive-curvature spatial geometry.

Spatial snapshots of the cosmos at an instant in time will be curved like the surface of a sphere-- except the 3D surface of a 4D hypersphere.

In a universe like that, geometry is weird.

The angles of triangles add up to more than 180 degrees.

And circles and spheres contain more internal area/volume than their circumferences or surfaces should allow.

But the total spatial volume of such a universe is finite.

And we call that a "closed geometry."

If k is minus 1, the universe is the 3D version of a negatively curved hyperbolic plane.

Triangles add up to less than 180 degrees.

And surfaces hold less volume than in flat space.

Such a universe is infinitely large, or "open."

But "k equals 0" means the universe is flat.

Zero spatial curvature, at any given time.

Geometry works just as you learned in school, and a flat universe is still infinite-- open-- in all three spatial dimensions.

But check it out-- this gives us a way to independently verify what we got on the left side of the first Friedmann equation, when we measured the universe's density.

The left side has to equal the right.

So, assuming we got the equation correct, then the shape of the universe should be intrinsically tied to its fate.

An overdense, recollapsing universe should have a spherical geometry.

An underdense, infinitely expanding universe should be hyperbolic.

And only a universe with exactly the right density, that's expanding at exactly its escape velocity, one that will slow to a stop over infinite time, should be flat, with the both left and right sides coming out to zero.

OK, cool.

That's something we can test.

See, we can measure the shape of the universe and, so, measure k, just by checking how geometry works on cosmic scales.

Now, if we got everything right so far, the geometry should turn out to be hyperbolic.

Because that gives us a positive right-hand side to match the positive left-hand side we got from weighing our universe.

In fact, we already talked about this in our episode on inflation.

Check it out.

Observations of the size of the cosmic [inaudible] background features allow us to verify that the longest triangles in the universe have angles that add up to exactly 180 degrees.

That's the straight-up geometry of a flat, Euclidean universe-- flat to within 0.4%.

The right side of the first Friedmann equation has to be very close to zero.

This is totally inconsistent with the level of positive curvature we'd expect from an infinitely expanding universe.

So, did we miss up our measurements?

Is general relativity wrong?

No.

But when we tried to describe the universe by reducing the Einstein field equations into the Friedmann equations, we missed something.

We missed the cosmological constants.

We also talk about this in inflation.

The very same addition to the Einstein field equations that can describe cosmic inflation can also fix this little problem with the first Friedmann equation and geometry.

When we derive the first Friedmann equation with the cosmological constant included-- that's the lambda symbol, here-- we end up with this little extra something on the left.

Assuming the cosmological constant is positive, this works on the side of the density term to help bring the left side down to zero, to flatten the universe.

So, even though the density is still too low to reverse the expansion, with this new player in the game, geometry is no longer tied to the fate of the universe.

A flat, k-equals-zero universe can expand forever.

But what does this cosmological-constant thing actually do?

The expression "cosmological constant" is a clue.

This term, as we commonly interpret it, is constant.

As the universe expands, regular matter and energy get diluted away.

The weird stuff described by the cosmological constant doesn't do that.

Its density stays constant.

So the bigger the universe, the more of this energy.

We call it "dark energy," and we interpret it as an energy possessed by empty space itself-- by the vacuum.

When the universe gets large enough, the density of regular matter will, at some point, drop below that of this vacuum energy, as described by the cosmological-constant term.

At that point, dark energy will govern expansion.

But when will this happen?

Billions of years from now?

No, it's already happening.

In fact, the universe reached that tipping point pretty recently, on cosmic time scales.

We now live in a universe dominated by dark energy.

How do we know this?

And what are the possible consequences?

Soon, we'll get to the second and most compelling piece of evidence for dark energy and for the cosmological constant.

And, along with it, the second Friedmann equation, which will give us the insight we need to understand dark energy's effect on the future of spacetime.

Some of the topics we've been diving into lately have been pretty high-level.

If any of you are looking to brush up on your basic physics, or you're looking for some more great physics content, PBS Digital Studios has an awesome new show for you.

"Crash Course Physics" is hosted by Dr. Shini Somara, a mechanical engineer and fluid dynamicist.

We've got a link to it in the description.

Go ahead and check it out.

Now, last week we talked about the fate of the universe.

Let's see what you had to say.

OK. A number of you were curious to know, on what scales of space is the universe really expanding?

So the universe is only expanding on the largest scales, not at all inside atoms, inside humans, the Earth-- even inside the Milky Way.

Within these regions, the shape of spacetime is dominated by the gravitational field of the densely packed matter.

And expansion is not occurring.

In fact, you need to get millions of light years from the Milky Way for the gravitational field of the Milky Way and Andromeda to not dominate the shape of local spacetime.

Only outside that influence does expansion become significant.

Now there are certain models of dark energy that could have space on smaller scales expand, resulting in the so-called Big Rip.

We'll get to that.

Mychelly Goulart would like to know whether the density we use in the Friedmann equation includes dark matter.

Absolutely.

The density that we calculate when we figured out the fate of the universe does include dark matter, which we can measure by its gravitational effect in several independent ways.

Even with dark matter, the universe is just not dense enough to recollapse.

Tomek Wooff would like to know what the job prospects for bachelor's or master's graduates in physics.

Hey, Tomek-- great question.

So actual research jobs in physics typically require a PhD.

But if you have a knack for math and a passion for physics, that shouldn't deter you.

However, you can do pretty well with just a bachelor's or masters in industry.

Various tech fields have a high demand for bachelor's or masters physicists, like medical imaging or radiology, energy industries, meteorology, science education, science journalism, and definitely information technology of all types.

And, if you choose, you can always sell your soul for the big bucks in finance, business consulting, patent law, et cetera.

Physics graduates are hot recruits, due to their killer problem-solving skills.

And, in fact, in 2009 the National Association of Colleges and Employers found that new graduates from physics-major programs have starting salaries higher than any other science major.

Mr. B is asking for our outtakes of apple mishaps.

Well, I'm sorry, Mr. B, but this is a very serious science-education show.

We don't stoop to blooper humor.

And, besides, we get every take right the first time.

If I throw it at 11 kilometers per second-- [bonk] [thud] --per second-- [bonk] [thud] [bonk] [thud] Is that the good-- I mean, the up throw, there?

Or-- or should I be really doing something-- [clap] --at 11 kilometers per second-- [bonk] [thud] [thud] MAN: Great!

That was good.

And we destroyed the apple.

MAN: Action.

Now, before we do any general relativity-- MAN: Start again-- had some eyebrow stuff doing on.

That was my acting.

MAN: [laugh] [laugh] [theme music]