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.
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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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