Our universe began in a state of ultimate heat and compression in what we call the big bang.

And it will “end” by expanding forever towards a state of perfect cold and emptiness.

It’s incredible that we could figure this much out, but we should not get too cocky - big questions remain open.

Like, what happened before the big bang?

What, if anything, happens after our universe?

I’m about to give you the most outrageous hypothesis so far that may actually be right.

Conformal Cyclic Cosmology is a story of the origin and the end of our universe from great mathematical physicist Sir Roger Penrose.

It’s goes like this: the infinitely far future, when the universe has expanded exponentially to to an unthinkably large size, and every black hole and particle has decayed into faint radiation .... that infinite stretch of space and time is identically the SAME THING as the infinitesimal and instantaneous big bang of a new universe, and our universe is just one in an endless chain.

We know this is an outrageous proposal because Roger Penrose himself called it that.

And as with all outrageous proposals it’s probably wrong.

But if there’s a faint chance that it’s right it’s so bizarre that we should definitely know about it.

OK, so, conformal cyclic cosmology, CCC.

Here, conformal is for the “conformal scaling” needed to turn your gigantic end of the universe into a tiny new big bang.

A conformal transformation is just some mathematical function that you apply to a geometric space which preserves all of the angles in that space.

An example would be if you had a sheet of rubber and drew some lines on it, then expanded the rubber evenly in all directions - the lines would get longer and further apart, but the angles at their intersections would stay the same.

This is perhaps the simplest conformal transformation - just multiplying or dividing all dimensions by the same scaling factor.

We would say that our universe has conformal invariance under scale changes - so the angles don’t change if you change the size smoothly.

But other things sure do change.

It makes a big difference whether every atom in the universe is right next to each other or a billion light years apart.

But let me try to give you a sense of a situation where scale might not matter.

A conformal scaling of spacetime means scaling both space and time.

For example, consider a universe that’s one light-second across, and it exists for the span of a single second.

Light has time to travel across it once.

Scale it up by around 30 quintillion times to describe a second universe that’s a billion light years across and lasts a billion years.

Again, light crosses it once in that time.

Let’s say these universes contain no matter - only photons - light.

They both contain the same number of light rays, which begin traveling in the same direction, although obviously they’re packed much closely together in the smaller universe.

Over the life of both universes, those rays trace out the same pattern - all the angles between them stay the same, and the rays pass close to each other the same number of times.

Now these clearly aren’t the same thing.

Light takes 30 quintillion times longer to cross one than the other.

But who’s to say that?

Remember, the universes contain only light - no observers and no clocks.

And there’s the key point: light does not experience the flow of time.

For those photons, the beginning of their journey is the same as their end, and these universes are equivalent.

So there’s a crude notion of how a tiny early universe could be equivalent to a gigantic late universe.

It was pretty loose compared to the formal explanation of conformal cyclic cosmology.

More “street” cyclic cosmology.

But let’s get a bit more rigorous - we’ll call it business casual cyclic cosmology.

To really compare the sizes of two chunks of spacetime we need to grid them up with rulers and clocks.

Surely, then, the big universe will have more length and time ticks.

We’ll simplify things by gridding up an imaginary universe with only one dimension of space on the x-axis and one dimension of time on the y, and we choose our axes so that light travels at a 45 degree path - the graph spans either 1 second in time and 1 light second in distance, or a billion years and a billion lightyears, depending which universe we’re talking about.

Either way, light travels a 45 degree path.

This is a spacetime diagram.

Let’s take two instantaneous events in this universe, separated in both space and time.

The separation between them can be determined by the number of gridlines of space and time you pass on your journey.

Now in Einstein’s universe it’s not quite that simple.

Lines representing constant distance or simultaneous times shift with the velocity of the observer.

If I draw the line of constant time for all possible travelers passing by my position, I get these nested curves - hyperbolas.

They show how time will tick for any constant-velocity observer passing through this point.

By the way, our episode on the geometry of causality goes into all of this in more detail.

The best way to define the separation between two events in spacetime is by the travel time of something taking the most direct path between them - a path of constant velocity that reaches that point in space at the right instant in time.

This is the so-called spacetime interval, and it’s equal to the amount of time that passes on the clock of the traveler - or the proper time of the traveler.

It’s the number of these hyperbolic intervals crossed.

So it turns out that we grid up the universe by the rate of ticking of the clocks of its travelers.

But what if the universe has no clocks?

That would be the case of a universe that contained only light.

Light follows these tracks in between the time grid, and never, ever cross contours that mark even a single tick of a clock.

For light, or any light-speed particle, the beginning and end of every journey is the same.

Both space and time lose meaning for a photon.

As Roger Penrose puts it: in order for time, and hence space to be meaningful, a universe must be able to build a clock.

A clock must see the spacetime grid - and to do that it must travel at sub-light speed.

And in order to do that, the clock must have mass.

So if you have even a single electron in the universe you can build a clock and can tell the difference between the one light-second and the billion light-year sized universes.

But with only light or other light-speed radiation there’s nothing internal to those universes that can tell them apart.

They’re identical under the conformal transformation of rescaling.

So how does this apply to our universe?

Well, it may be that in the extreme far future our universe will contain only radiation.

Eventually all stars will die and their remnants will decay - black holes will evaporate by Hawking radiation, and particles of matter will decay into their lightest possible components.

In the case of the proton that’s speculative, but it may be the case that we’re left with only a universe of photons, electrons and positrons, and neutrinos, as well as gravitons - the quantum particles of gravity.

The photons and gravitons are massless - you can’t build clocks with them.

But the others do have mass, so presumably there’s still a way for the universe to tell that it’s gigantic.

Penrose speculates that mass itself may not be a fundamental property, and may eventually decay to leave massless electrons, etc.

The standard model of particle physics predicts eternal electrons.

But it’s not absurd to imagine their mass decaying.

The masses of the elementary particles are not some fundamental property of those particles - they come from the interactions of those particles with quantum fields - the Higgs field in the case of the electron.

I’ll come back to why we might expect the mass granted by the Higgs field to change over time.

So that’s the late universe.

Filled with only timeless radiation, it would possess no spacetime grid, so perhaps could be considered sizeless.

But what about the early universe?

Surely it was full of particles.

Well yeah, but those particles were effectively massless also.

Two ways to think about this: A particle's energy is a combination of its kinetic energy and rest mass energy.

Kinetic energies were so high at the big bang that rest mass energy was completely negligible - all particles behaved like light-speed particles.

And that’s precisely true for things like quarks and electrons, which gain their masses from interactions with the Higgs field.

But that only works below a certain temperature - in the extreme temperatures of the Big Bang, the Higgs field could not grant mass.

There’s a previous episode, obviously.

By the way, a change in the nature of the Higgs field - if it decayed to a lower energy - could eliminate elementary particle masses in the late universe also.

In the first tiny fraction of a second we can think of the universe as being full of effectively or actually massless particles.

Hence the concept of time is as meaningless as in the late universe.

But does that really mean we can equate the two?

For the black-tie formal answer we’d need to delve into the math of the conformal equivalence of the beginning and end of time.

But we’ll just do it semi-formally without the math.

Maybe cocktail cyclic cosmology?

One of the other things Roger Penrose is famous for is his Penrose diagrams - these are ways of mathematically transforming our grid of spacetime to fit infinite distance and time into the one map, while at the same time preserving the 45 degree path of light.

The edges of this map represent “conformal infinity” - where infinite space and time are compressed onto an edge.

That’s for one dimension of space and one dimension of time.

For the full 4-D spacetime the edge becomes a 3-D “hypersurface” in which infinite distance and time are compressed or “conformally rescaled” into a finite space.

Similarly, the infinitesimal or “zero-sized” point of the Big Bang can be rescaled into a finite space.

This was actually a discovery by one of Penrose’ colleagues, Paul Tod, and Tod’s work inspired Penrose to follow this idea in the first place.

So you stitch these rescaled “conformal hypersurfaces” together and you get this endless chain of universes.

Penrose calls each universe in the chain an “aeon”.

By the way, one important aspect of all of this is that in order for the ends of time to be stitched together by this sort of conformal rescaling, the universe needs a positive cosmological constant.

That means it needs dark energy.

Which our universe has, so no problem, but it’s interesting that it worked out so neatly.

Penrose also says that CCC naturally gives you dark matter - but we’ll skip that for now.

Only radiation - light and other massless particles - can cross over this conformal boundary from one aeon into the next.

Because radiation can pass between universes, conformal cyclic cosmology gives a natural explanation for the extreme smoothness that we observe in the early universe.

This was actually Penrose’s motivation in the first place: to explain the apparent smoothness of the early universe.

In particular, to explain its extremely low entropy.

If entropy can only rise over time, per the second law of thermodynamics, how did it get so low at the start?

There is a standard explanation for the smoothness of the early universe - its cosmic inflation - a period of extreme exponential expansion that smoothed things out in the first fraction of a second.

But Penrose insists that this does not explain the low entropy of the big bang.

Paul Tod’s conformal transformation of the Big Bang singularity helped Penrose to demonstrate that the smallness of the entropy at the Big Bang is due to the tiny entropy in the gravitational field at the time.

That then inspired this daisy-chaining of universes, which eliminated the need for inflation.

In CCC, all of the energy - and, importantly, the gravitational field - is smoothed out over infinite time between aeons.

Inflation isn’t needed because the inflationary period is equivalent to the rescaled late-time forever of the previous universe, where exponential expansion was fueled by dark energy.

For the daisy-chain-verse to give you low entropy big bangs, you need to actually clean the entropy slate between aeons.

To do that, black holes must swallow entropy - and destroy information.

This is another issue with the CCC model - most physicists think quantum information can’t be destroyed.

But Penrose isn’t so sure.

OK, so how do you test an idea like this?

Wait infinite time and see if you find yourself in a big bang?

Well actually, Penrose has proposed a test - and in fact conducted it and claimed convincing evidence.

If radiation can travel between universes, and if the end of the previous universe was not completely smooth that could lead to features in the cosmic microwave background radiation.

Penroses proposes that the collisions of super massive black holes in the previous universe may leave rings on the sky in the next.

And in a paper with Vahe Gurzadyan he claims detection of just such features.

Others have questioned the statistical methods of that study, which were non-standard, and they say there are no statistically significant features.

Penrose and Gurzadyan have one more somewhat awesome speculation.

They wonder if civilizations might be able to communicate between universes.

It turns out that, as well as photons, gravitational waves should be able to pass between aeons.

If a super-duper-ridiculously advanced civilization could manipulate the dances of gigantic black holes, they could potentially send information between universes.

So far no evidence of that.

But wouldn’t it be cool if we found a message scrawled on the sky?

Like, hey guys, try not to mess up your aeon, remember to eat your greens, and try to have fun in this infinite chain of conformally rescaled spacetime.