The idea that the fate of our universe is governed by forces that we can see was abandoned with the discovery of dark matter.

However, we now know that the evolution of our universe is driven by something even more mysterious-- dark energy.

[music playing] In the last two episodes, we talked about how the fate of the universe can be described using Einstein's general theory of relativity via the Friedmann equations.

However, there was a problem.

Observations show that out universe is infinitely expanding.

But it's also geometrically flat.

And this is only allowed if we introduce a new type of energy represented by the cosmological constant.

We call it dark energy.

But what does this dark energy thing actually do?

The answer comes from another piece of evidence of its existence, which itself came from an independent attempt to determine whether the universe would recollapse.

See, measuring the density of the universe is one way to determine its fate because the future expansion rate does depend on density.

However, so does is its past expansion history.

In fact, measuring the past expansion history should tell us the future expansion without ever having to count any galaxies.

That history is coded in every photon of light that reaches our telescopes from the distant universe.

See, as space expands, it stretches out the light that is traveling through it.

During that expansion, it increases the wavelength of these electromagnetic waves, resulting in what we see as redshift, cosmological redshift.

If we also know how long a given photon was traveling through that expanding universe, then its redshift tells us the total amount of expansion that happened during that time.

But how do we figure out how much time the light traveled for?

Well, we know the speed of light.

So we need to figure out how far it traveled, the actual physical amount of space the photon had to traverse to get to us.

To measure the expansion history of the universe, we need to measure the redshift-distance relationship.

We talk about that in detail in this episode.

But wait-- doesn't redshift tell us distance?

Well, sort of but only if we assume a redshift-distance relationship.

Redshift is the amount the universe expanded during a photon's journey, and distance is the amount of physical space it travelled through.

And the two are connected by the universe's expansion history.

Measuring many different redshifts and distances independently of each other tells us that expansion history.

No problem.

Just measure redshifts and distances for a bunch of things out there in space.

Well, not so fast.

Although it's not so hard to measure redshift, distance is one of the hardest things to get in astronomy, especially for things so far away that the universe will have expanded significantly in the time it took their light to reach us-- so billions of light years distant.

You know what would be really handy?

If something else happened to that traveling light that independently kept track of the distance it travelled.

Oh, wait.

There is.

Far away things are fainter than nearby things.

We just need some source of light out there whose true, intrinsic brightness is known.

That way, we can figure out how far away it is just by seeing how faint it looks to us.

We call such a magical source of light a standard candle, and we kind of got lucky there.

There's a very special type of supernova that's both spectacularly bright and for which we can figure out very accurate intrinsic brightnesses or luminosities.

It's a type Ia or white dwarf supernova.

Take a white dwarf, the leftover core of a dead, low-mass star like our sun, and let it cannibalize some of the material from a binary companion.

When the star reaches a critical mass, a runaway fusion reaction obliterates the star as a supernova.

These things explode with very similar and very high luminosities, so they're the perfect standard candle.

OK, so here's the experiment-- watch stars explode across the cosmos.

When you catch a white dwarf supernova, you know its distance and redshift.

Hypothetically, if the redshift for a given distance turns out to be on the large side, then that would mean the universe expanded a lot during the corresponding light travel time.

Now, that actually points to a more dense universe.

Why?

Because if the redshifts are large, then the universe was expanding much faster in the past, which means something would have had to slow it down to its current rate.

That something would be a high-mass energy content that could in the future cause it to recollapse.

So measuring a rapidly-expanding universe in the past points to it having had its gravity brakes on between then and now.

On the other hand, if the redshift at a given distance turned out to be on the small side, that would mean that the universe expanded less while that photon was traveling.

And so a lower density of matter would be needed to explain how the universe slowed down to the current rate of expansion.

The smallest redshifts you'd expect would be if the universe has always been expanding at the rate we see now, so almost no matter slowing the universe down.

Such a universe would certainly expand forever.

We can also flip this logic and say that for a given redshift, we would expect supernovae to be bright or closer in a high-density, recollapsing universe and faint or more distant in a low-density, infinitely-expanding universe.

Two separate teams of astronomers spent years catching white dwarf supernovae exploding in galaxies billions of light years away to measure the past expansion history of the universe.

They thought this would tell them whether the universe would expand forever or recollapse.

But what did they see?

In 1998, both teams announced that the universe was expanding even slower in the past than it is now.

The red shifts were way too low.

Or conversely, the supernovae were fainter than you'd expect, even for a universe that has no matter in it at all.

That means the expansion rate of the universe has actually sped up, accelerated, while that supernova light was traveling to us.

This discovery of the accelerating expansion of the universe earned both teams the Nobel Prize in 2011, and it's considered to be the discovery of dark energy.

See, this observation actually came before the discovery of the inexplicable geometric flatness of the universe that we talked about last time.

However, this accelerating expansion can be explained with the same bit of math, the cosmological constant, pointing to the same physics, dark energy.

Add the cosmological constant to the first Friedmann equation, and we reconcile the left and the right side.

But we also see that the constant nature of this term means that the larger the universe, the more of this stuff there is.

This lets us interpret the cosmological constant as representing a sort of vacuum energy, a property of space itself.

And it must eventually dominate the evolution of the universe.

But why should a constant vacuum energy cause the universe to accelerate?

Let's take a mathematical ride into the far future, when the galaxies will be so far away that the density of the universe will be basically zero.

We know that the universe is flat, so the curvature is also zero.

For that far-future universe, we can write the first Friedmann equation like this.

See?

Expansion will only depend on the cosmological constant.

So does that mean the expansion will become constant?

No.

See, it's not the expansion rate-- the A-dot-- that's constant in this equation.

A-dot over A will become a constant.

We also call this the Hubble Parameter, and it could be thought of as the rate at which the universe doubles in size.

The Hubble Constant is just the Hubble Parameter for the present day.

Typically, the Hubble Parameter becomes lower over time.

But with a positive cosmological constant, the universe will eventually have a constant Hubble Parameter.

And so we'll have a constant doubling time.

That's exponential growth, and it looks like an accelerating expansion.

Currently, there's still enough matter in the universe to influence the expansion rate, but we're already at the point where dark energy dominates.

In fact, the universe has been accelerating in its expansion for six billion years or so.

That's what we see in our white dwarf supernova measurements.

If the cosmological constant stays constant, we can expect an exponential growth to continue.

But will it stay constant?

Could it go down, up?

That all depends on what this energy of empty space really is.

For that, we'll need another episode of "Space Time."

In the last episode, we talked about how a general relativistic description of the expansion of the universe requires dark energy.

You guys had some excellent questions.

Pravar Parekh points out that we can't really know that the universe is flat because we can only see a small part of it.

This is absolutely true.

We can't rule out curvature below our current best sensitivity, which at the moment is 0.4% of perfect flatness.

The universe could be positively or negatively curved below that level.

If positively curved, that would mean a finite but very, very large greater universe with a volume at least 250 times that of our observable universe.

we talk about that in this episode.

However, the degree of curvature required by the first Friedmann equation to agree with the balance between expansion and density is much, much greater than our universe exhibits.

Even if the greater universe is curved, we still need dark energy.

Yeshwanth Vejendla would like to know how we can possibly measure the density of such a huge universe.

So the handy thing about a universe that's smooth on its larger scales is you don't have to measure the density of the whole thing, just of enough representative patches of it.

Our galaxy surveys have worked for decades to measure brightnesses, redshifts, stellar compositions, and more of many millions of galaxies.

And even then, they don't cover the entire observable universe.

However, they do sample a large enough fraction of it to tell us that matter in the universe is pretty smoothly distributed.

These surveys don't measure dark matter content of all of their galaxy clusters.

But again, we've weighed up the dark matter in enough of them to be able to extrapolate.

Thomas Waclav has a reasonable concern about just adding stuff to your math until it works.

Thomas, I hear you.

You can't just do that.

William of Ockham turns in his grave.

But when the theory-- general relativity, in this case-- is so thoroughly verified in so many other ways, and the addition of the cosmological constant works so well to describe the discrepancy, it's strongly suggested this addition describes something real.

As we saw today, the cosmological constant solves two measure discrepancies.

So at some level, it's right, even if we don't know what causes it or whether it's truly constant.

Austin Pinheiro likes to think that PBS stands for peanut butter sandwich for no apparent reason.

Don't sweat it, Austin.

People think silly things all the time.

Thanks to you for being honest about the strength of the evidence behind your belief structure.

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