In this series we explore competing models for 
what happened at or even before the Big Bang.
The dominant paradigm for
 Early Universe Cosmology is Inflation.
The idea that the early universe underwent 
a stupendous growth spurt,
doubling in size every 10⁻³⁷ seconds.
But in this episode,
 we'll explore an alternative paradigm,
which assumes that it wasn't the expansion rate 
of the universe that was enormously larger than today,
but instead it was the speed of light that was
 inconceivably faster than its present value.
The theory known as Variable Speed of Light, or VSL, 
challenges the very foundation of Physics.
But its proponents argue that such a radical step is needed 
if we're to explain the many mysteries of our origin.
"Before the Big Bang: Episode 8"
"Variable Speed of Light (VSL) Cosmology"
So, I'm given detention in high school,
and there was a lady who was 
overseeing us and she said,
"Listen, go read a book. 
Find a book and read this book".
So, I went to the back of the library,
 trying to find something,
and I discovered this book about 
Albert Einstein.
So, when I was a kid I was interested—
If I think far back, I was interested in
 cars and then planes,
and then bigger and bigger
 spacecrafts going into space.
And then that kind of developed into the biggest, 
farthest things you can get to,
which was like stars and galaxies.
I got into Astronomy as a teenager, basically.
I got into Physics, 
or theoretical Physics I should say,
when when my father gave me a book
 when I was around 11 or 12,
called "The Evolution of Physics", 
by no less than Albert Einstein and Leopold Infeld.
It's a very narrative book, it's popular science, 
there was not any formulae,
but it's completely full of the idea of
 thought experiments.
The idea that you can in your mind
 conceptually play experiments which
probe whether things are one way or another.
I was in Paris at the age of 17 for a year.
The only student of the now
 famous painter Serge Poliakoff.
And I started reading popular science books.
I was the first theoretical physicist at Trinity College at the time 
to take a PhD with an undergraduate degree.
My supervisors were Fred Hoyle, Abdus Salam.
And then I started seriously studying 
Einstein's General Relativity and Unified Theory.
And I wrote two papers on his Unified Theory
 and sent them to Einstein in Princeton.
And he actually responded.
Because I made some critical comments
 about his work which he took seriously.
The idea that the constants of nature 
might in fact not be constant
did not begin with modern VSL theory.
It goes a way back, and I think,
 it goes a way up to Dirac.
Dirac is probably the person who framed 
this question the best in the modern setting.
Around the time there was all this big issue about 
whether we could explain the constants of nature.
And this led to, you know, relating constants
 to things like the number pi,
a bunch of numerological identities and 
things that became more and more mystical.
And I think Dirac at some point just said,
"Well, maybe they're not constant at all",
and then you can play this game ad aeternum,
and you can even claim
 nothing is really constant in Physics.
Einstein thought about the speed of light 
varying already in 1911,
before he developed his
 Gravitational Theory of General Relativity.
Suggesting that some of the constants
 may change is one thing.
But the speed of light is no ordinary constant.
I mean, it's true that within Relativity the 
speed of light is as it were the center constant.
The central constant.
Everything revolves around the speed of light, 
and not just as the physical speed of light.
It's the speed of a lot of other things,
what we call "massless particles".
It's also a speed limit.
It sets out the causality 
limitations of the universe.
So why did we do it? 
It wasn't of course gratuitously.
It wasn't just questioning
 for the sake of questioning.
We had some kind of clues from Cosmology
 that this might be a desirable feature.
These clues from Cosmology are known as the Horizon, 
Flatness, and Origin of Structure problems.
The same problems that Cosmic Inflation
 is thought to solve.
The Horizon Problem is an observational fact,
which is that when we look back 
at the early universe and look at
when the universe was permeated
 by radiation—
It's called the Cosmic Microwave 
Background Radiation.
About 14 billion years ago, it appears that these photons are correlated
 to have the same properties and the same temperature, ok?
That would actually be out of causal contact.
It seems to require faster-than-light travel
 for this to happen.
In Inflation, the Horizon Problem is solved by rapidly expanding
 a tiny patch of space that was in thermal equilibrium.
So, how does VSL do it?
Instead of taking a small patch of the universe
 and making it very big,
you keep the same universe but make the speed of propagation, 
the speed of communication, much faster,
and then everybody can talk to everybody.
It's like saying that you switch from, say, 
snail mail to e-mail.
I was out there walking one day
and I said to me, it's obvious.
If the speed of light is much larger than
 its measure today in Special Relativity,
then trivially it solves the problem.
But the problem then was to develop a
 mathematical theory
that could seriously support this idea.
You can't just walk in along and say,
 Oh, well, obviously, the speed of light is— You know?
"Obvious"?
Well?
You have to construct the theory that works.
Another problem is the Flatness Problem. 
So the universe is incredibly close to flatness.
This goes back to Gauss.
Gauss had this idea, maybe we can experimentally 
test the geometry of the universe with triangles.
We can triangulate the universe.
Are the triangles flat?
Do the angles add up in some way that suggests
 they're flat or are they actually curved?
Or are they like of squashed this way?
That's the Flatness Problem.
And the problem is that the flatness
 isn't stable in Relativity.
If the universe is very slightly deviating from flatness,
 it will deviate even more.
There is this thing in Einstein's equations 
called the "critical density" of the universe,
which at a given time, at a given expansion rate, 
is the density which is just right to make the geometry flat.
This instability in the Big Bang Theory means you 
either tuned this density to be critical to a very high precision,
or else you have some other mechanism beyond traditional 
Einstein's equations and traditional Big Bang model.
And in Varying Speed of Light theories, at least in 
some of its formulations, the most radical ones,
it turns out that not only do you violate
 energy conservation,
you create energy or you destroy energy,
but you actually do it in a way that's tied
 to this critical energy density.
In a way, if you are slightly more dense 
you take away energy.
If you are slightly under-dense you create energy, 
so you push towards the critical density.
And this is how these crazy thing—
"Universe might not satisfy energy conservation"
 solves the Flatness Problem.
It turns out in the Theory of Relativity, 
and this is a purely classical statement,
there is no such thing as 
conservation of energy.
So, the energy is locally conserved.
That means that if I look at, say,
 particles that are colliding in a small room,
then the energy doesn't change.
But if you look at everything as a whole,
 when the universe is expanding,
of course, things, for example, cooled down.
Cosmic Microwave Background used to be 6,000 K 
when photons separated from baryons, but now it's 3 K.
So, where did that energy go?
Locally you could say that this is redshift,
because of the expansion of universe
 photons basically cooled down.
But, of course, globally, where the energy went,
 there's no good answer to that.
In General Relativity, you work space, you work time,
 so that if you look at things globally,
if you if you "fill" the whole spacetime,
conservation of energy is really never there,
 but it is there locally.
And if you don't actually fill the whole space,
 it is there.
Whereas in Varying Speed of Light theories, 
it isn't.
So, you actually—
At that scale, on the scale of the local things,
conservation of energy is intimately tied to the fact 
that the laws of Physics don't change in time,
that they're the same everywhere 
and at all times.
So the idea is that if you do violate that precept, 
the principle, you also violate energy conservation,
because they come hand-in-hand.
VSL represents a radical challenge to Relativity,
and so it's not surprising that it's emergence 
as a rival to Inflation was far from smooth.
I wrote a paper and submitted it for 
publication to the Physical Review.
And the referee was very quite unhappy.
He said, Moffat is claiming the speed of light
 is very large in the early universe,
and he's violating Special Relativity. 
We know we can't do this.
And he rejected it.
So, I sent it to a journal in Europe, 
International Journal of Modern Physics,
and they've published it without a word.
Then I more or less forgot about it for a while.
John Moffatt's version of VSL was mostly ignored.
But several years later, the idea would resurface.
Funnily enough, I was quite hung over on that day.
It was in Cambridge, it was a while ago.
For many years I'd been trying to find 
an alternative to Inflation.
Trying to solve the puzzles which we knew Inflation had solved,
 but without resorting to the idea of inflation.
Just for the sake of finding an alternative.
And, yeah, I just fell from the sky.
And then, of course, what took a long time 
was to find the right collaborator,
and funnily enough it was one of the 
forefathers of Inflation, Andy Albrecht.
He also had been for many years trying
to find an alternative to Inflation,
partly because he was one of the 
forefathers of Inflation,
and wanted to know whether it was 
true or not.
So, we kind of hooked up together--
We took like two years or so 
to come up with a final product.
And it took another probably a year—
Probably another year to get it published.
It was a nightmare to get the thing through
 the refereeing process.
I was scrolling through the abstracts one morning 
and I saw the abstract of this paper and said,
"Oh! That's what I did"
 Okay?
So, I corresponded with him—
Corresponded with Joao and he was very—
He was very good about it.
They put in a recognition in their 
published paper that I did this.
Just to find later on that actually,
someone had had a very similar idea before us.
John Moffat had actually been there before.
And he had also had trouble getting it published
 in Physical Review and actually lost the battle.
His idea was very different from ours.
 It was independent.
Anyone who reads the papers will notice.
We do solve the Horizon Problem, Flatness Problem,
 blah-blah-blah, what inflation solves and so on.
That's the spiel we gave everyone and the spiel gave ourselves
 when we started but I think it's much more than that.
It really is questioning the foundations of Physics.
I yet tend to have radical ideas.
The Physics community is not—
is uneasy, as it should be, because
one has to be conservative in Physics,
and you don't change the laws of Physics 
unless you absolutely have to.
We found that the minimum criterion for 
solving all these problems
was to add 32 zeros to the current 
speed of light
and say this is the speed of light in the 
early universe.
But this is like the minimum.
It could be anything above that.
And if you don't want to be too fine-tuned,
 you might as well just say, well, it's infinite.
So there was a transition between
 infinite speed of light and finite speed of light,
which is much more dramatic, 
but also less fine-tuned.
Many years later there was this thing 
called Hořava-Lifshitz theories in which
this phenomenon is actually predicted.
And as you go into higher and higher energies, 
the speed of light does go to infinity.
Adding at least 32 zeros to the speed of light,
violates Relativity,
which Inflation does not.
So why should we consider VSL as a serious
 alternative theory for the early universe?
We have to go beyond General Relativity 
and maybe start thinking about
how General Relativity speaks to 
Quantum Mechanics or Quantum Gravity.
And there opens up the possibility that 
the speed of light might—
That that assumption might have to be
 relaxed.
The problem with Inflation is—
Inflation was very successful in the sense 
that there were some problems
and we came up with an idea 
to solve those problems.
But then this cycle of basic going back,
 making more predictions and testing them,
somehow doesn't cause real inflation because 
there are basically too many inflationary theories
that could solve the problems that we start with.
And then beyond that they can make 
any prediction you want, basically.
It's very difficult to rule out Inflation,
which to my mind raises issues about 
its credibility as a scientific theory.
Whereas Varying Speed of Light theories
 are actually falsifiable.
I don't think that's bad. 
I think that's science.
And maybe the only way is to rule out
 all alternatives,
and it turns out that maybe one of those 
alternatives cannot be ruled out,
and hopefully one of those alternatives 
may be more predictive than Inflation.
When we look at the oldest light in the universe,
 the Cosmic Microwave Background,
we see that it is uniform to one part 
in 100,000.
But beyond that fluctuations 
in temperature appear.
These fluctuations are said to be 
the seeds of galaxy formation.
Inflation creates these seeds by
 stretching quantum fluctuations.
So an alternative theory like VSL needs to explain
 how these fluctuations came about,
and also predict their magnitude.
Fine-tuning problems are terribly 
overblown sometimes,
and people think they're important
 and not.
At the end of the day what you really want to explain
 is the fluctuations in the universe.
It's not exactly homogeneous, it's—
There are these fluctuations in the early universe, 
which became mass nowadays.
Can we explain them?
And I think Varying Speed of Light theories initially 
were not even a model for that.
So, curiously the time at which the press
 became crazy about this—
We're not competitors at all in this thing which I think
 is really the most important one, but now we are.
Since 2007 there's been a lot of work which really pushes
 Varying Speed of Light theories into competitors of Inflation.
And there I think we're better,
 because we're more predictive.
It's very similar to the Inflation,
 except that instead of
quantum fluctuations, 
you have thermal fluctuations,
and the other is that you don't really 
inflate this everything.
You just say that—
Everything communicates so fast that 
you have basically thermal equilibrium,
and thermal fluctuations on the same scales.
Radiation has this property, 
if you have like an oven,
the temperature is, you hope, very constant, 
but you always have like convection flows even there.
You have thermal fluctuations.
These are very different in origin to 
quantum fluctuations.
In Varying Speed of Light theories 
you have this option,
which I think is superior,
because you're actually capable to pinpoint
 one kind of fluctuations you would get.
When water freezes, it can imprint 
certain structures like cracks in ice.
Some have hypothesized when the 
universe cooled from the Big Bang,
it might have left thin filaments of exotic objects,
 called "cosmic strings".
In the context of VSL,
could these cosmic strings be a way to realize 
the science fiction dream of interstellar travel?
It would be really convenient to have like
 corridors of high speed limit
to move around the universe.
So the Horizon Problem is not 
just a problem in Cosmology.
It makes our life very dull
 in terms of trying to travel around.
That's quite interesting to come up with this solution that
 cosmic strings really are corridors of high speed limits.
And then—
And whether this could be ever used or not,
you know, for space travel is a different issue.
In a way, they're not very different conceptually
 in some sense from wormholes.
Except wormholes are generated by curvature 
and by the twisting of the manifold,
and by the fact there might be these shortcuts.
Whereas this is really something 
which would affect the speed limit.
If a critique of Inflation is that there are
 too many inflationary models,
why doesn't the same problem apply to VSL?
It is true that there are many models of 
Varying Speed of Light theories
the same way there are many models of 
Inflation.
But I think whereas Inflation is just 
variations on the same theme,
in which you have a potential and
 you withdraw this potential ad nauseam
with more fields, more things, more details.
But it's always effectively the same thing
 conceptually.
Whereas this is the case with Inflation,
 with Varying Speed of Light theories
the different models are really 
conceptually quite different,
and in one case you might say the 
speed of light and gravity is different.
So we have two structures in spacetime,
 or spacetimes, one for matter and one for gravity.
In others you say that the speed of light changes with
 the energy and goes to infinite for very high energies.
In others, still, you introduce preferred frames
 in the universe, preferred times.
You break all the concepts of symmetries of Physics.
 In others you do not do this.
So, all these theories have different predictions,
 but clearly I would say they're different theories.
A key goal of contemporary Physics is to combine 
General Relativity with Quantum Mechanics.
Can VSL be embedded in such a
 Quantum Theory of Gravity?
String Theory is one of the leading 
candidates for such a theory,
and Stephon Alexander has shown 
how VSL can be derived from its dynamic.
Imagine this two-dimensional surface. 
We call it a "brane" or a "brane world",
not B-R-A-I-N, but B-R-A-N-E.
So this two-dimensional thing 
will be a "membrane"—
So imagine this this is a projection of 
a three-dimensional world.
It turns out that there's a pretty beautiful 
solution of String Theory
that if you have a 
five-dimensional black hole—
So imagine that this is
 my little black hole here,
and our world was a three-dimensional 
spatial brane—
So, all of the fields of the Standard Model 
were localized on this brane,
they only lived on this brane, and—
There are solutions— 
stable solutions of String Theory where this 3-brane,
(3+1)-dimensional, "1" is time,
is hovering in a stable orbit 
around this five-dimensional black hole.
It turns out that the radius that—
Between—
In this fifth dimension, between this 3-brane—
 that I found solutions such that,
as the distance varies,
an observer in this three-dimensional brane 
sees the speed of light varying.
So the idea of the early universe cosmology, 
but it gets more interesting than that.
When an observer actually moves in this direction,
you get an expanding universe.
So you get both an expanding universe, 
as this brane moves closer into the black hole—
The speed of light varies, right? 
The universe expands,
and then what happens is that if you end up
 in a stable orbit around this black hole,
the speed of light gets fixed.
The varying speed of light was not 
implemented just for the sake of it.
Actually that came out of trying to 
address another problem,
which is that brane worlds 
suffer from a flatness problem.
So, in other words, why is a brane so smooth 
and not very not curvaceous, right?
So, it turns out by—
Giving the brane dynamics in this extra spacetime
addressed the Flatness Problem,
and what came out of that as a byproduct,
 was that the speed of light varied in that scenario.
But that was the first time that VSL 
naturally came out of String Theory.
One of the world's leading string theorists
 is Petr Hořava.
In 2009 he created a new theory of 
Quantum Gravity
which has become known as
 Hořava-Lifshitz gravity.
This theory breaks the symmetry known as
 Lorentz symmetry
between time and space in Relativity,
and implies the speed of light is only a constant 
at low energies where the symmetry is respected.
Another way to think of Lorentz invariance 
is to say that if the speed of light is absolute
then space and time must be relative.
Hořava-Lifshitz gravity differs from 
General Relativity in that
no longer is time and space democratic,
 that I can rotate freely from time to space
using the Lorentz transformations,
but, actually, that symmetry between
 space and time is actually broken.
When you do that, actually, it resolves 
some problems, actually having to do with
what we call the renormalizability of gravity.
The idea that you that you can get infinities 
when you look at the propagat—
When you look at perturbations of the graviton, 
you know, the quanta of gravity.
And in Hořava-Lipschitz some of those infinities go away,
whereas in General Relativity it doesn't go away.
What I like about Hořava-Lifshitz gravity is that you're not really
 introducing new tooth fairies to solve your problem.
You just stick with what you got, but—
But basically ask what is the minimal thing
 that you have to do.
And in some sense that's similar to
 Loop Quantum Gravity.
They are both very minimalistic in their approach.
So we have broken fundamentally this 
Lorentz invariance which equates space and time,
which allows by some time to be—
Any foliation could be done.
Results would be the same.
Once you've done these you have broken
 this symmetry.
You have a special foliation of spacetime
 into space and time.
And what you get from these?
You get a bunch of nice results in quantum gravity.
Things that used to blow up and become infinite,
but infinite in really nasty ways you couldn't remove—
Well, they're actually finite.
So Loop Quantum Gravity and Hořava-Lifshitz gravity 
do it in different ways.
Loop Quantum Gravity does it by making everything discrete, 
so you just basically think about a lattice or graph.
In  Hořava-Lifshitz gravity you violate
 Lorentz symmetry.
So you say the speed of light is not really
a fundamental constant.
It's really just something that you have on
low energies or large scales in time.
At higher energies, or smaller scales, 
the speed of propagations becomes very very big.
And then the result of that is that you essentially don't 
worry about things that are propagating very fast,
because you need too much energy to excite them.
So that makes your predictions fine—
You get rid of the infinities,
because basically things that propagate 
very very fast, they decouple from you.
Hořava-Lifshitz theories do have a varying 
speed of massless particles,
typically the graviton,
but a "Lifshitz scalar", which is kind of jargon 
for matter that behaves like the graviton in Hořava-Lifshitz,
has the same properties, and—
That's an example.
 It was clearly not what we—
Well, this was before.
No VSL preceded Hořava-Lifshitz,
so, we never thought there would be 
a connection there.
I think there's been a much better relation, 
not just sociologically, but also scientifically,
with Loop Quantum Gravity.
Because really  there's been this understanding that somehow 
these emergent properties in Quantum Gravity,
which lead to a semi-classical approximation
 in the universe like we see today,
carry this property that actually 
Lorentz invariance is emergent.
Consequently, the speed of light 
is an emergent concept,
and that consequently there can be 
variations
when you go from this transition period 
between one and the other.
So this is really the relationship and I think,
 to my mind, more recently—
I think the ideas we entertained initially 
were incredibly naive,
and maybe we should have just jumped
 straight into Quantum Gravity.
It's a bit daunting to go into Quantum Gravity,
 but it's partly because it's done by mathematicians—
Mainly mathematicians, and—
And we shouldn't be afraid of that.
I mean I think it's their problem that 
they are mathematicians,
and that they complicated things 
unnecessarily,
and then they lost track of Physics
 quite often.
In many theories of Quantum Gravity spacetime is
 treated as being discrete rather than a continuum.
It's often said spacetime has an atomic structure with a
 fundamental length scale known as the Planck length.
But this brings with it a difficult puzzle.
In Relativity, objects undergo Lorentz contraction.
In other words, the length of an object 
reduces as it moves faster.
If you want to atomize space and time—
It's more complicated than this because it's
 kind of a fluctuating structure, and so on.
If you want to give it some kind of
 physical meaning,
then you do have this problem that the Planck length 
and Lorentz contraction really don't mix very well.
Because then you could have a situation in which 
two different observers disagree on whether something
is in that realm or not on that realm.
So if you have these structures, these granular structures, 
they must be absolute to avoid contradictions.
Certainly contradictions with the principle of Relativity
 of equivalence of all the observers.
So in a way It's the other postulate of Relativity, 
that of constancy of "c",
that has to give way to make sure
 Relativity is preserved.
It goes back to this thing that maybe 
if you want to have an invariant Planck scale—
Planck length, for example, you should have an 
infinite speed of light at the Planck length,
because with infinite speed of light you've got 
 Galilean theory and the lengths are not contracted.
In 1998, it was discovered the universe
 is accelerating,
and this is thought to be driven by a 
cosmological constant or dark energy.
But the true nature of this dark energy 
remains controversial.
VSL raises the issue of whether dark energy 
may impact on singularity theorems
proven by Penrose and Hawking and by
 Borde, Guth, and Vilenkin,
both of which have been used to argue
the universe must have had a beginning.
There was one thing in which we were
superior to Inflation,
which was we could address the
 cosmological constant problem.
The way we did it initially was really quite naive,
which is the energy in the cosmological constant 
depends on speed of light.
So, you kind of in a way, you deflate that.
You get rid of that other energy and you couldn't 
put that energy in the matter.
But then, you can actually—
You know, if you don't do it completely,
and if what we see nowadays, 
the acceleration nowadays,
is a residue of that phase,
and if it is actually the dominance of the 
cosmological constant that
produces variations in the speed of light,
 you can kind of create a cycle
in which you have big variations in "c",
which cause great big variations in the
 energy in the cosmological constant,
which generate a Big Bang.
Then you wait to bit until the Big Bang
 dies down,
and the cosmological constant resurfaces,
 and you just start the cycle.
And that was a picture which 
I realized very early on wasn't that original.
I mean this goes back to Zel'dovich, to Tolman.
This idea of cyclic universes have 
appeared and reappeared.
Everyone can come up with a model of that
 in their favorite theory.
So in that respect, I wasn't—
I never published that because 
I didn't think it was that original.
The singularity theorems that Hawking and Penrose
 proved relied on certain assumptions.
One assumption is, of course, 
General Relativity.
The other assumption is their 
"certainty energy conditions"
that need to be satisfied.
But if you include VSL in that picture you find that
some of these assumptions go out of the window.
For example, the "strong energy conditions",
depending on what version of VSL you're talking about,
no longer applied.
The strong energy condition is just a complicated way 
of saying that gravity is always attractive.
Basically, there's no other way to matter to
 produce gravity other than attracting.
VSL theories that are embedded in String Theory
 do not use General Relativity,
they use extensions of General Relativity.
And so it's plausible that the singularities that
 you would find, for example, for Inflation,
Borde, Guth and Vilenkin may not apply.
I have kind of mixed feelings about this 
Borde and Vilenkin singularity theorem because
unlike Penrose and Hawking's singularity theorem,
this Borden and Vilenkin's singularity theorem has one
 obvious counterexample, which is a De Sitter space.
A De Sitter space is an inflationary universe, 
but one that's not flat.
It has positive curvature, okay?
So, in that universe you could have basically things
 which go infinitely past, infinitely  back in time,
but then in early times things are slowly collapsing,
and then at some point they stop, and then they expand.
So, there's nothing wrong with that and—
As far as we know all the inflationary
 models could start that way.
The problem with this 
singularity theorem is that,  first of all,
it assumes universe has always been expanding, 
but that doesn't have to be the case.
It could have been collapsing.
And you don't really need to violate Relativity
 or any any obvious—
Just the simple inflationary model can do that,
 if you toss curvature.
And the other assumption is that it's classical,
but of course, I mean,
the whole point of having inflation is to generate 
the universe out of some quantum beginning.
So, yeah. So, in—
I don't think it has as much power—
I don't think I'd really rule out Inflation or say that 
there must be a singularity to begin with,
but that's kind of besides the point, 
we need to have some quantum theory of gravity.
Even if there is no singularity at the 
very early universe,
but you still don't have a 
quantum description of gravity yet,
then you're missing something,
 and you can get wrong results.
It depends on what kind of structures you think
 that might have existed initially.
The example I like to give is exactly the
idea of quantum time,
or the example of quantum space,
the example that you don't actually 
have a smooth manifold.
You'll actually have geodesics in usual sense.
So, how can these theorems, which really are based 
on a very smooth spacetime idea,
which is one we see here and now,
how can this be extrapolated all the way
 to the beginning of the universe?
I think it does affect Inflation,
because inflation is meant to be
something that doesn't depend on 
quantum gravity.
So, if you're gonna use inflation
 to solve these problems,
you really haven't solved them 
because you haven't been radical enough.
And if you're prepared to violate 
Lorentz invariance, varying "c",
even to quantum foam, spacetime, 
that kind of thing,
then I think these theorems are completely—
They're obviously not valid, but—
Basically these things contradict the 
very, very basic assumption of the theorem.
I think you can prove anything.
Theorems are very strange things.
Because you can have a theorem to prove anything,
 as long as you assume the right things.
In a way, that's the problem.
And, you know, you can violate any theorem
 as long as violate the assumptions.
Some commentators have thought if we remove 
the singularity and have an infinite past,
we are lead to contradictions,
 due to the strange results of infinite set theory.
That would be a contradiction 
if you're a sloppy with the language.
Of course, infinities existed in Mathematics
for centuries, and mathematicians
by definition they're doing consistent Physics—
 Consistent Math, basically.
The whole thing is a logical framework, 
which is Math.
So, infinity itself doesn't imply 
inconsistency or contradiction,
1 over X, when X goes to 0, goes to infinity. 
That's not a contradiction.
So, infinity itself is not a problem, 
the problem—
I mean, it comes to physical prediction.
The problem is that if your theory 
somehow breaks down,
or your  theory cannot give you a
 unique prediction for something.
Ideally a model of the early universe should explain 
why the entropy of the Big Bang was so low.
Some of the scientists that we've 
interviewed in previous episodes,
such as Alan Guth and Sir Roger Penrose,
have argued that this can be understood
 in the context of a past eternal universe,
generating dynamics that put the entropy 
of the universe into a low state.
But others have argued that entropy 
considerations rule out a past eternal universe,
as the entropy would have increased
 to an intolerable level.
So, I showed that when the
 speed of light was very large,
the entropy was very low 
at the beginning of the universe,
because the speed of light is very large.
So, the universe does—
therefore, there's a mechanism
explaining why entropy was very low 
at this very early microfractions of seconds.
And then when I do a phase transition, 
or whatever physics transition I have,
to the present speed of light,
which happens very quickly,
in fractions of seconds,
then the speed of light comes down
 by orders of magnitude
and the entropy grows enormously.
There you have it.
So, this explains the 
second law of Thermodynamics.
These arguments about entropy are
 a little bit funny because, of course,
if you think our universe is infinite,
 the entropy is infinite, so—
Of course, infinity isn't bigger or smaller
 than infinity.
I don't know how to make the comparison.
When people think about entropy 
they'll make this argument.
They're thinking about a finite patch of 
the universe,
but exactly which finite patch we're looking 
and then how that goes through the Big Bang
is not clear,
because we don't really know which patch of the universe you match to the other, which other patch.
At the face of it, I don't really buy that argument
 because it assumes some finite universe,
but as far as we know universe is not.
To my mind the problem is that 
we've been too classical.
We have this idea of time as something,
 which is our human experience.
And it has gone out the window a long time ago. 
Time doesn't flow in Relativity.
It's like ontologically on the same level of space.
In fact, you can transform the two, what we have is
 a worldline, and you don't have something flowing
along this worldline.
It's more abstract, but it's what Physics gives us, 
and in Quantum Gravity time disappears altogether.
So, it could be the case that, actually,
these arguments are not even true because
 the concept of time, let alone the arrow of time,
has disappeared.
So, it could actually be that these phases,
 these cycles,
go through a quantum time phase
 in which
it really doesn't make any sense to try 
and have this linear idea of time,
and try to project these cycles into an 
idea of time,
and it is a problem, really.
By far the most controversial aspect of
 Inflationary Cosmology
is that it seems to predict the existence of
 a multiverse,
which can solve certain difficult issues 
in Cosmology,
but it can also lead to the problem of a 
lack of predictivity.
These physicists claim that we've forced the 
anthropic principle into the multiverse.
That they have different bubbles of inflation.
Each bubble corresponds to a universe.
And, uh—
I don't like this.
I don't like the multiverse.
I don't think it's Physics.
VSL is not forced into a multiverse.
It doesn't have this problem.
This may be considered a positive feature.
The whole subject is really controversial.
Some scientists claim that the constants
of nature are delicately fine-tuned for life,
and one way to solve this problem 
is to invoke the inflationary multiverse.
With so many universes, it's no surprise
 the one we live in is conducive to life.
But if there is no inflationary multiverse, 
what do we do about the issue of fine-tuning?
I don't know about the fine-tuning thing.
First of all, the whole thing seems
 very prejudiced.
Certainly we live in a maximum of the 
probability for life,
but given the life we know, when given the constants
 we know, and the Physics we know.
So, it could be a local maximum.
These selection arguments are incredibly tight,
or are very limited perceptions of what life can be
 and what an observer can be.
I never really bought these fine-tuning arguments
 in the first place.
I find them interesting when they do
 generate interesting physics,
when they motivate interesting physics.
And in that respect, yeah, why not? 
You know.
I have written papers on anthropic principle 
with Barrow and so on,
but I don't really take it seriously.
Whether some constants are too small or not,
I think the evidence that there is fine-tuning
 is very subjective.
Constants are what they are.
You experimentally determine what the are,
so what's the problem?
I don't think this is really science and I think
 it's quite curious how people somehow
find these fine-tuning problems incredibly relevant, 
but then when you ask them, for example,
then why are the fluctuations in the 
microwave background 10⁻⁵?
And then the answer is, well, 
we have to explain the height of this table.
Why is that fine-tuned to a better height?
I'm sorry but, you know—
I actually find that 10⁻⁵ in the microwave background 
much more interesting to explain than
these fine-tuning issues,
which are really metaphysical issues.
People talk about naturalness.
At least it's one way the physicists 
try to quantify fine-tuning.
But, of course, naturalness implies
 that you know, what is natural.
But as we are kind of developing the 
theories of nature,
how do we know what is natural
l and what is not a natural?
The work that I published with Marcelo Gleiser
and my former PhD student, Sam Cormack,
we wanted to address the issue of
 fine-tuning in nature.
So, the question is:
"Is there a mechanism in the early universe
that controls—
that controls the—
why the coupling constants are what they are?"
And, so, what we discovered was that if the 
universe undergoes cycles of, you know,
contraction into a bounce, 
which is what you might want to call a Big Bang,
back into an expansion and contraction—
What we found is that mathematically 
the coupling constants naturally vary
at the moment of the bounce
and randomize in their variation.
And as it emerged out of the bounce,
 it stabilizes, so—
It's kind of interesting that the expansion of the universe 
actually stabilizes this coupling constant.
And then when you go back into a Big Crunch,
the coupling constant have a chance to
 randomize again,
and so you can imagine having a universe
 that's eternally cyclic.
One way of addressing this this fine-tuning problem,
 why the coupling constants take their value,
is to allow them to vary,
 including the speed of light,
and realize that actually we're living in
 an epoch of the universe
where the coupling constants are what they are, 
but in some future universe
and in some past universe it had different values.
While speculations on the ultimate origins 
of the cosmos are fascinating,
ultimately science needs hard data to determine 
which model of the early universe is correct.
In order to have a direct verification of inflation 
or this variable speed of light (VSL),
you need to go back to the beginning of 
the universe,
and at the Big Bang,
 or just fractions of seconds afterwards,
you look up at the sky with our
 colleague standing with you,
and the colleague says, 
"No, spacetime is expanding exponentially fast".
And I look up and I say, "No, it isn't!"
"Spacetime is what it is."
"It's expanding in the normal way in Cosmology."
"But, look, the speed of light is enormous!"
So, can we ever have this enacted?
Of course not.
We have to infer the consequences of 
these two hypotheses,
two ideas,
today on observational data.
Recently Joao Mageijo and Niayesh Afshordi
have made a precise prediction 
that a number called "N.S." is equal to 0.96478
But what is "N.S."?
I'm very proud of that number, I should say, yes.
So, N.S. in the simplest terms is really 
the color of the universe on the largest scales.
If N.S. is one that would be basically 
like a color of white, if you want,
which basically means that every 
wavelength has the same power in it.
The idea is that the universe literally is not white,
because our eyes are sensitive to only
 micron-sized wavelengths.
But if you actually could see wavelengths 
that were MPc or GPc in size,
on very very large scales,
our universe is very close to white.
If N.S. is less than one they usually call it red,
or we call it red, which means that
longer wavelength has more power 
than a smaller wavelength.
The same as the color red that you see
with your eyes.
We've known for almost 10 years now that
 N.S. is not one exactly.
We've known that it was very close to one
 for 20-30 years now.
And about 10 years ago, 
we discovered that—
About 15 years ago, we discovered 
it's actually slightly below one.
So, universe is almost white, but it's slightly red 
if you look at very, very larger scales.
And then it's been a challenge for Early Universe theories 
to predict exactly what that number is.
And, of course, the ones that predicted the 
wrong number, they've been kind of thrown out.
Our, at least the one we came up with,
 predicted just the right number.
So, that's what we're very proud of.
There are some simple inflationary models
 that happen to give these values,
and that's good for them.
The one problem in Inflation is
 there is always some uncertainty in it,
because you have to transition from an 
inflationary phase to a radiation-dominated phase,
or hot plasma, which we know
the early universe looked like,
and that transition is another level of 
model dependence,
and that's why all—
Even the simplest inflation models, they always 
have a few percent uncertainty in this prediction.
The nice thing about our model is that 
because you don't actually need this transition,
because our model was always hot,
 you never had to actually heat up [the] universe
to to reach this radiation-dominated
 or hot plasma.
Our universe was always in a hot plasma.
Then we can be more precise.
That's why we have more significant
 digits there.
There are a lot of experiments,
 cosmological experiments—
There are additional cosmic microwave 
background experiments,
the  fourth generation of cosmic microwave 
background experiments.
And then there are other galaxies surveys that are looking
 at the structure of the universe on very larger scales.
So, the hope is that they're going to 
shrink the error bar from 1%
to probably a factor of 2 or 3 smaller,
 at least in the next 10-15 years, I would think.
So, depending on where they land and whether
 they can actually deliver what they promised,
then they could rule out our prediction.
Because we don't have any free parameters in it 
that is in a minimal model.
In the last 20 years, there have been claims that 
a constant of nature related to the speed of light,
known as "alpha",
has been observed to vary.
Could this be related to VSL?
Well, "alpha" is a constant which relates the electron charge
 with Planck's constant and the speed of light, and—
And yeah, there was an early claim, 
like some 10-15 years ago,
that there was observational evidence that
 it had changed in the last few billion years.
So, not quite in the beginning of the universe.
On cosmological scales, quite recently.
But, yeah, there were variations on 
the order of a part in 100,000.
These claims, I don't want to judge them, 
because I am not really an astronomer,
and I think you should ask 
the experts to clear this, and—
They always sounded a bit 
too good to be true to me.
It was the first time that these claims for
 variability of constants
experimentally became detections
 rather than upper bounds.
So this was fascinating, and—
We had ways of—
You know, in Varying Speed of Light theories clearly 
there's a "c" there, because of varying alpha, right?
Clearly we could arrange ways to accommodate these, 
but we were really dealing with the early universe.
You could create situations in which there was a
 residual until nowadays that explained this effect.
It was really kind of, in a way, an add-on.
Conceptually it was interesting, of course, but
you were not really testing the early universe
 part of the theory.
So, it was always two disjoint things.
It was interesting, but the theory didn't really 
predict this.
It's controversial whether the data really 
supports alpha varying or not,
but, you know, future experiments eventually 
will come to some decision about it
Recently LIGO detected gravitational waves
 through colliding black holes.
But are their gravitational waves from 
the Big Bang itself?
Inflationary Theory seems to predict 
they should be there.
What about VSL?
We predict no primordial gravitational waves out there.
Of course, gravitational waves could be generated
 at late time from binary black hole mergers,
but primarily gravitational waves would be 
gravitational waves that come out of the Big Bang.
There was an excitement a few years ago
  from BICEP that maybe detected it.
And a lot of alternative-to-inflation people got upset, 
but that went away, so we're happy again.
If you take the Quantum Gravity versions 
the amount of gravity waves
is really just a ratio between the speed of light 
and the speed of gravity at very high energies.
And hopefully this could be predicted as a number
 in Quantum Gravity, but it hasn't been.
So it's a free parameter just because 
we cannot compute it.
Now, we could add something that 
does produce gravitational waves.
I have mixed feelings about this is a
 right thing or a wrong thing because, ultimately,
we have to have a correct theory of Quantum Gravity 
and that might actually produce gravitational waves.
And what we did was just General Relativity 
plus this varying a speed of light construction.
But if you actually modified gravity itself,
that could produce gravitational waves.
So, that's something that could change the story,
basically.
After detecting the first black hole mergers,
 LIGO went on to see neutron stars merge,
which importantly, leave a visible trace.
This enables scientists to compare the speed of light
 with the speed of gravity over large scales.
So far the data says they have the same speed.
So what does this mean for VSL?
Absolutely nothing because 
as I said before
these big differences between the
 speed of light and the speed of gravity,
which do explain these fluctuations in
 the microwave background,
that's just restricted to the early universe.
And you can actually work out the residual,
 and it's tiny.
10 to the minus thirty-something, or so.
So, you would never expect to detect a appreciable difference
 between the speed of light in the speed of gravity
nowadays on these times scales.
It all takes place fractions of seconds 
after the Big Bang,
and the Bimetric Gravity theory does not
 affect Einstein's Gravitational theory today.
Cosmologist George Ellis has claimed that it's only meaningful
 to talk about Dimensionless constants varying.
And since the speed of light has units
 it doesn't qualify.
He'll never learn anything.
I think it's a strange statement because 
these people have talked about varying "G",
[the] gravitational constant, 
all their lives, and "G" has units.
It's not dimensionless.
So, it's only when you talk about varying "c" 
that people get all worked up.
You cannot talk about varying constants with units.
And in fact, it's not true at all.
The problem is that you don't see these 
things in a void.
Any kind of statement about what are the units, 
and therefore what is varying and what is not,
comes with the dynamics,
 with a proposal for dynamics.
And it's within that dynamics that 
you talk about varying whatever.
To say that you can only measure dimensionless constants is okay, I agree with that.
But when you put it into a theory 
and make that the constant a field,
then all of this becomes a 
misunderstanding.
And if you try to explain the value of constants clearly, 
you have to look at dimensionless things.
Because, you know, when you change the unit 
you change the number while you are trying to explain it, right?
Whereas dimensionless things are pure numbers.
So therefore it makes sense trying to explain 137, 
 not 300,000 kilometers per second,
because put it in miles per second 
and it'll be different number, right?
It's in that sense that dimensionless constants 
are the things to explain, if they are constant.
Because those numbers, if they're constant, then they
 have a meaning regardless of how you set up the units.
Whether things vary or not, 
then varying things with units happen all the time.
If George Ellis' statement is real then we couldn't talk
 about varying acceleration of gravity.
We'd still be stuck in Galileo, right?
Newton, you know—
George will go to Newton and say, "You cannot talk about
 varying the acceleration of gravity because it has units!"
VSL theories are more than 20 years old.
So what's next for these ideas?
Perhaps the most recent development in 
these Varying Speed of Light theories
is the idea that the speed of light 
and the other constants of nature,
such as the cosmological constant, etc,
might actually be quantum,
and therefore subject to uncertainty relations, 
like position and  momentum.
Variables in quantum mechanics appear in pairs.
They don't like to be precise at the same time.
One very important constant in nature, 
which is the cosmological constant.
And the question still remains,
why does it seems to be so tiny?
When we account for how this cosmological constant, 
otherwise known as vacuum energy,
It should be a lot more, okay?
Orders of magnitude larger than 
what we observe.
We realize that, actually—
That in some versions of quantum gravity, 
in particular Loop Quantum Gravity,
there's a time that seems to know
 about the—
There's a time called the Chern-Simons time,
and that this Chern-Simons time, actually, does—
There's an uncertainty in that time variable
 and the cosmological constant.
This is one internal way of defining time,
a sort of problem to defining time in quantum gravity.
You have to be more intelligent than
 just having a standard clock.
In other words, the more certain you know
 about the flow of time,
this Chern-Simons time,
which knows about the global property of
 space and time,
the less you're certain about the value 
of the cosmological constant.
In this framework both the cosmological constant
 and this time are allowed to vary.
And so, this theory actually might also have something 
to say about a varying speed of light as well.
But this is an interesting new avenue of research
that we're still learning about,
that might help us to address actually
 the cosmological constant problem.
Now the Horizon Problem is the statement that
 you go forward in Chern-Simon's time,
and solving the Horizon Problem is the statement 
that as you go back in Chern-Simon's time.
So inflation makes actually Chern-Simons time 
loop backwards.
It could be though that this looping 
backwards happens
precisely because of this uncertainty relation between
the cosmological constant and Chern-Simon's time.
So, we flow forward if you have matter around— 
At some point the cosmological constant kicks in,
and what actually happens is that you become delocalized
 in time so that the leap backwards is possible.
In Episode 6 of this series,
 we interviewed Richard Gott
who proposed the universe could create itself
 by using closed timelike curves,
a solution to Einstein's equations that
 allows for time travel into the past.
I think there is a connection between Gott's idea,
 just simply because—
If you start having this issue like, you know,
 bouncing universes or anything,
anything which has a past, you know, 
how many cycles before,
it really is a timelike tower of turtles
 what you're building, and—
Imagine that suddenly there's no time.
The problem with all these arguments is this idea 
there's an omnipresent timeline throughout the whole universe,
presiding over the whole universe.
What if you become delocalized in time 
because of the laws of Quantum Mechanics?
Then clearly all these arguments break down,
 philosophically break down.
Most recently I've been very excited 
about black holes,
especially light of black hole mergers that have
 been observed in gravitational waves, so—
One interesting thing about VSL is that it could actually
 give you an explanation for black hole entropy.
That's been written about.
And this could also solve the so-called
"firewall paradox",
which is this problem of understanding 
where the information
that falls into a black hole goes 
when it evaporates.
So, if you have varying speed of light—
I can tell you what's the problem with black holes,
it's kind of similar to the problem with the Big Bang.
If things get very close to the black hole,
 they have to fall into the black hole,
and then information is lost,
and then black hole evaporates, and then you ask, 
"Okay, where did it go? What happened?"
Information in Quantum Mechanics 
doesn't disappear.
But Relativity tells us everything that gets close
 to the black hole should fall in and then it's gone.
[In] VSL you could actually get information out
because things can propagate faster 
than the speed of light.
And we have constructions that basically 
don't have horizons in these VSL-like theories.
That means that they don't have to trap information,
 information can come in and can go out.
And that's one thing that you can actually
 test now, because
now that we see mergers of black holes 
we could see these horizons,
or what we think our horizons of black holes,
 merging together,
and then we can ask, "does something come out?"
Because if it's in GR, horizons are points of no return.
So, the horizons may hit each other but nothing can come out
 because these are places where everything falls in.
But if you have material that can propagate 
faster than the speed of light,
then you could get things things that come out 
and we actually look for them in data.
This is what we call "echoes".
We call them "echoes from the abyss".
And we have some tentative evidence in the data.
So that's a very different direction of looking for VSL 
by looking at gravitational waves from black hole mergers.
In less than a year, basically starting maybe in February, 
there will be the third run of the LIGO/Virgo collaboration.
and they are supposed to be—
If their promise holds, they're supposed to be 
much more sensitive.
So we'll have many more abyss events.
So, if these echoes are there, 
I think we're gonna definitely confirm them.
So the thing I am expecting is that 
the spectral index,
this N.S. for the fluctuations of the 
microwave background, which is .96,
now gets two, three more figures and that 
those figures are the ones we have predicted.
Because that will be a remarkable prediction,
a remarkable indication of the theory.
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