- Of all the unlikely ends to the universe the big rip has to be the most spectacular.

Galaxies ripped to shreds, stars obliterated, cats and dogs living together, and then tragically separated by the infinitely accelerating expansion of space on subatomic scales.

Good thing it's not going to happen.

Or is it?

(upbeat playful music) The universe is expanding, and that expansion is accelerating, and we don't know what's causing that acceleration, but that hasn't stopped us from giving it a name.

We call this unknown influence dark energy.

The observed acceleration is for the most part nicely described with a constant density of dark energy, the same amount of this stuff in every block of space which means if you increase the volume you increase the overall amount of dark energy, hence the accelerating expansion.

Mathematically we describe a constant energy density with the cosmological constant in the equations of Einstein's general theory of relativity, but what if dark energy is not constant?

What if the energy density in each patch of space increases over time?

In that case, the acceleration itself would be accelerating, but that would be bad.

As long as the rate of acceleration doesn't increase, the accelerating expansion of the universe isn't a big deal, at least for those of us safe and sound in nice galaxies like the Milky Way.

Here the galaxy's gravitational field is plenty strong enough to resist the minuscule effect of dark energy.

It's in the vast tracts of space between galaxy clusters over countless trillions of cubic light-years of emptiness that dark energy adds up.

The sum of this outward push ultimately overcomes the inward gravitational pull between the galaxies.

Galaxies will eventually be so far apart that they can't see each other, let alone feel each other's gravity, but as long as dark energy doesn't increase, there'll be no expansion inside those lonely galaxies.

They'll be safe to fade to heat death as we cheerily discuss in this episode, and in fact that's probably what will happen, but it's fun to think about even worst-case scenarios.

Also there's a tiny bit of very circumstantial evidence that we might not be so safe from dark energy after all, but before we get to the potential disaster of an increasing dark energy and the big rip that follows, let's do a quick refresher on how dark energy works in the language of Einstein's general relativity.

I say refresher because we spent a whole playlist delving into the mysteries of dark energy.

We actually used math, the Friedmann equations.

We're not gonna go so deep here, but we are gonna take a quick mathy detour.

Feel free to review that playlist before or after if you're into that sort of thing, or take a nap, and wake up when the pretty pictures come back.

This beautiful thing is the second Friedman equation.

It's basically the equivalent of Newton's law of gravity for the whole universe describing the acceleration or deceleration of the expansion rate which depends on how much stuff there is in the universe.

Because this is Einstein's gravity, not Newton's, gravity is influenced by mass and energy density, but also by pressure.

Both mass energy density and any positive pressure act to decelerate the universe to cause it to re-collapse.

In fact for regular matter the effective density is much higher than the effective pressure.

The ratio, pressure over density, is basically zero By the way, in cosmology we call this ratio, pressure over density, the "equation of state."

It's a simplification of the good old equation PV equals nkT, relating pressure, volume, temperature, and the amount of stuff.

Anyway, the upshot is that positive energy density and no real pressure leaves the right side of the equation negative, so negative acceleration.

Matter on its own can only cause deceleration of the expansion rate.

What goes up must come down.

Okay, let's add dark energy in the form of a cosmological constant.

It usually hangs out outside the brackets because it's emo, but we can make it join the party.

We can express our lambda as a sort of equivalent mass and pressure.

In fact, let's make it an emo party and get rid of regular mass and pressure.

After all, in the future, dark energy will completely dominate the expansion.

So we have the energy density of the vacuum and the pressure that it exerts, but now that pressure term is important.

The equation of state of dark energy is pressure divided by density equals negative one.

That just means that as volume increases, density does not go down, the basic definition of the cosmological constant.

So now the pressure term is A, negative and B, because of this factor of three, it's a bigger influence than the density.

So this whole party in the brackets becomes negative.

So emo.

That cancels this negative sign, and makes the right side of the equation positive.

The acceleration is therefore positive which means dark energy is pushing outwards to increase the expansion rate.

In fact, any equation of state parameter less than negative one over three would cause that effect.

It would mean the stuff is diluted away a little less quickly than the universe expands.

In fact, if the parameter is below negative one over three, but larger than negative one, that's still accelerating expansion, but in that case the dark energy is decreasing over time.

The popular idea for that scenario is called quintessence, and it's something for a future episode.

For today, let's push things to the limit.

What if we make the equation of state parameter smaller than negative one?

How about negative 1.5, negative three, negative 1,000,000?

That's the case where the density doesn't just stay constant as the universe expands, but it actually increases.

The result would be that the acceleration increases over time.

Offhand, that doesn't sound so much crazier than regular old dark energy, except that it is much crazier.

As the rate of expansion increases and with no gravitational bodies left to resist the expansion, all points in space will eventually be racing apart from each other faster than the speed of light.

That faster than light recession of space is already happening, but right now for patches of space very far apart like many billions of light years.

If two patches of space are moving away from each other faster than light, then they can never communicate with each other.

The distance from us to the nearest inaccessible region of space is called the cosmic event horizon.

Now if the expansion is accelerating, then over time the distance between patches of lightspeed space gets smaller, and that is actually happening.

Your cosmic event horizon gets closer and closer.

Eventually, we won't even be able to see the nearest galaxies because they'll be moving away too quickly.

But as long as we have a nice gravitationally bound galaxy to live in, the cosmic event horizon can never shrink to a size smaller than that galaxy.

That's not the case if dark energy increases.

After our galaxy is disrupted by the increasing dark energy, there's no protection from the encroaching cosmic event horizon.

The final result is that no particles will be close enough to interact with each other ever.

So protons and neutrons will be separated into their component quarks.

That is the big rip scenario.

It happens when the cosmic event horizon is smaller than the smallest possible structure.

What could cause something like this?

No idea.

No one has any idea.

That doesn't stop us from giving it a name.

We call any dark energy that increases in strength, so with an equation of state less than minus one, phantom energy.

That name seems to have been coined by dark myth physicist Robert Caldwell in a seminal 2002 paper, "The Phantom Menace," and that was three years after the theatrical release, and I guess we still thought it was a sign of the end of the universe.

So let's see what this made up math has to say about when the big rip would happen.

Any equation of state parameter smaller than negative one means a big rip.

The smaller the parameter, the sooner it happens.

Caldwell does this calculation for the case of W equals negative 1.5.

In this scenario, the big rip happens in 22 billion years from now.

Things don't get really messy until near the end.

Around a billion years before the big rip galaxy clusters are ripped apart.

At 60 million years and counting, the Milky Way is shredded.

Now, this doesn't mean that the cosmic event horizon is quite inside the Milky Way just yet, just that the effect of phantom energy is stronger than the gravity binding the stars together.

In fact, at this point the cosmic event horizon is still about 200 million light years away.

And so there should be a handful of galaxies still visible to us.

There are some millions of years of fun as we watch those galaxies disassemble, and the constellations of stars in the Milky Way fly apart.

The final deadly stage only happens in the last month or so when the solar system is pulled apart.

In the last 30 minutes, phantom energy is strong enough to overcome Earth's own gravitational binding energy, and the planet is disrupted.

Moments later at the 10 to the negative 19th of a second before absolute disruption, it will overcome all chemical bonds, then the forces binding atoms together, then nucleons, and then presumably anything smaller.

In its final state, a big rip universe will be nothing but hopelessly isolated elementary particles separated by infinitely expanding space.

That's a hell of a story.

How sure can we be that it won't happen?

Well, somewhat, mostly.

Our efforts to understand the nature of dark energy are focused on measuring the value of this equation of state parameter thing.

We can do that by combining all of the clues to dark energy's behavior, for example, in the patterns of the cosmic microwave background, in the baryon acoustic oscillations, and in supernovae.

We've talked about all of these thing before.

Combined with a few other measures these tell us that the equation of state of dark energy is very very close to negative one.

The Plank Science Team calculate negative 1.028, plus or minus, 0.032.

Phantom energy is still a faint possibility, but even at its most extreme from the Planck estimate, the big rip would be around 75 billion years away.

Time to get our affairs in order.

But more likely is that W is exactly negative one, meaning dark energy is constant for three reasons.

First, it seems too much of a coincidence that it should be so close to negative one without being negative one.

Second, there's a plausible physical explanation for a constant dark energy that the vacuum has a set amount of energy per volume.

There are at least some physical ideas for that.

As far as I know, there aren't serious ideas for an increasing dark energy.

And the final reason to hate on phantom energy, it violates energy conservation in a way far worse than regular dark energy.

It violates the same energy conditions of general relativity that prohibit negative mass and time travel.

Okay, so after all that hate, let's finally get to the one significant result that suggests dark energy may be increasing after all.

In fact, we've already covered it in our recent Journal Club episode.

The acceleration rate measured using distant quasars hints at an equation of state parameter slightly less than negative one, although not yet with enough significance to overturn all other results.

Probably, probably the universe will still end in a long cold heat death in which the stars of our galaxy wink out, become black holes, and then evaporate over an unthinkably long future.

But maybe if you believe in phantoms, it'll all be over much sooner when the universe is ripped to shreds by the infinitely accelerating subatomic structure of space-time.

(tonal music)