Thank you very much and thank you for coming here. It's very nice to be able to give this this type of talk for this audience.
So what I'm going to talk about the string theory and how we derive predictions from string theory or string models.
But before starting off with discussing some work that we've actually done here over the past year,
I want just to take a step back and just contemplate the the scales involved in this problem,
sort of scales of of particle physics that we explored over the past century and is explore now
can be said to be in this range from the scale of atomic physics up to the acoustic scale,
the electroweak scale, the scale that is currently probed by the LHC survey.
We will later talk about some very high energy events coming from cosmic neutrinos, which is up here.
Further down we have the scale of the cosmological constant. So this this is a huge span of energy scales.
None of them include quantum gravity. The scale at which we expect quantum gravity to actually become important was mentioned by Saburo.
It's given by the Planck scale and it's up here. It's separated by from things that we know or are exploring by 14 orders of magnitude in energy.
That's a huge energy difference, of course.
So just to to get a sense of how huge that difference is, let us consider building an accelerator where current technology,
current LHC technology, the magnets that are to build it bigger.
So when we build it bigger, we can probe a higher energy because.
Oh, sorry. Uh, because, well, what we have here is the, what's keeping the, the protons circulating.
The ring will be the, the electromagnetic force from the magnetic from the magnets.
And this will give rise to a centripetal force so we can get an expression for the radius needed in order to probe a certain momentum.
And in particular, we can get a simple expression for the radius needed to probe the Planck scale energies.
So plugging into numbers and comparing with LHC, the scale of LHC, we see that we need a radius of 10 to 15 kilometres, 460 light years, so 50, 56.
So we should encompass, well, a good deal of the most visible nearby stars.
So this this shows that while accelerator experiments are not suitable to directly probe Planck scale physics,
if it's if it's actually sitting up at the Planck scale, it can still be important for cosmology and particle physics.
And this is the point I want to make now.
The point goes back to if you remember Serbia's slide about the standard model, he wrote it down as an effective field theory.
That's the concept that we'll use here. I also write down a Lagrangian, but it's given by just one field, Phi Phi here, some scalar field.
I won't be more specific about what it is and its energy is much below the scale.
We can write down an effective field theory and.
And this field theory will, it will capture the effects of the phenomena up here, but it will be valid down here.
So we'll integrate it out. All the effects up here, if you wish.
So this effective field theory for a scalar particle will be given by, well, the kinetic terms, and then some potential.
This potential will have some some well, some really realisable terms and then a tower of non renormalisation terms,
non renormalisation terms are suppressed by in this case then the Planck scale.
Now, it's an interesting fact that several of the proposed physical phenomena that are might be relevant in our cosmological history,
such as cosmic inflation, biogenesis and supersymmetry,
breaking are all sensitive to the structure of these coefficients called the Wilson coefficients.
And this gives a sensitivity to the theory in which those coefficients can be computed as the quantum gravity.
So this will be the framework in which one can probe quantum gravity.
I mean, we probe it indirectly, but its effect on the lower energy effective theory.
So then we're all set. We have a framework for testing quantum gravity.
It's just a three step process. We propose a consistent theory up at the Planck scale.
We we we scaled down two energies e and well below e e well below the playing field.
And we compute the relevant effective field theory of compute the Wilson coefficient c seven and we derive all the
cosmological and particle physics predictions and then we compare them to cosmological and particle physics data.
In practice, this is extremely challenging.
There's only one theory where you can even start, where you can even start computing those Watson coefficients.
And that string theory. And even this theory has proven very complicated to do this, to follow this procedure.
The fact that this is the case has even propagated out into popular culture where, well,
people are not physicists have elaborated on the point that it's really hard to go from point 1 to 2.2.
It's, of course, of a scandalous webcomic.
So in reality or in science, we think about it maybe a little bit differently.
But this, I think, can fairly be said about the status of string theory now.
Much of the initial excitement about the theory itself was sparked or spurred by a number of remarkable properties of the theory,
yet perhaps formal properties such as a highly nontrivial consistency.
Sex that was verified 30 years ago can be said to be the onset of of the first string theory wave.
It has an apparent lack of tuneable parameters, which gives us sense of uniqueness up at the core of theory at the Planck scale.
Without even asking for gravity, it encodes gravity. So it gives you quantum gravity right away, which is just spectacular.
There are a number of extremely powerful dualities connecting various formulations of the theory.
There are it that we can be used to gain some insight into the physics of the two micro physics of black holes.
None of this, though, tells you how to go from .12.2.
The issue here is that string theory has many solutions. These are called vacuna and I will use these words interchangeably.
And in these different back a these Wilson coefficients take different values and their cosmologies are completely different.
And this calls for a modified scheme so you can try to do it this way instead.
So you propose a consistent variable to Paxil that would be disturbing to you.
You find a vacuum and so a model and you compute in this model all the relevant predictions and the Watson coefficients,
and then you compare that with data. So this is still a hard procedure doing it explicitly, which has been done.
Well, it can be done. And models have been ruled out this way, but it's still hard.
The basic problem here is that there are many models say at least in one part, where you can do the counting reliably.
People have counted up to ten to the 500 models.
So you would have to go through the procedure like you start today with ten to the 500 after a few hours or down to 10 to 500 minus two and then ten,
four, five, five, and then, you know, it's the end of the day.
So it's it's pertinent to ask whether or not we can learn anything.
And, you know, it's just that goes beyond just saying that this one is nice and then you go on to the next one.
And that's the relevant questions to asking. And so trying to connect string theory to reality.
And there are ways to do that. A more efficient approach can be obtained by identifying consistency conditions for the low energy effective series,
which are very nontrivial, and see if the universe can be seen to to contradict those consistency conditions.
One can study large ensembles of vacuum statistically, and as I will discuss in this talk,
one can construct large classes of models with some common properties and then test these common properties.
And one can also derive generic predictions of the effective field theories and the corresponding cosmologies to make this more concrete.
In this talk, I'll discuss a new generic prediction motivated by a large class of string theory models,
and I'll discuss the observational signals that this prediction gives rise to.
And finally, I will mention something which is a little bit speculative, but it might turn out right.
I'll mention that these signals may already be seen. And our work on figuring out whether or not this is the case.
So the outline of the rest of the talk is like this. I'm going first to discuss how to construct a string model for string vacuum.
Second of all, I'm going to describe your cosmology, which is slightly different from the the standard picture of the early universe.
And then I'm going to discuss these predictions and go into the name of the extent of degradation of cosmic extreme background and,
and the cluster suffixes. So famously, string theory requires extra dimension in order to be consistent.
And we don't observe these extra dimensions, which means that they have to be hidden away somehow.
They have to be compact, defined. So if you compact it by an extra dimension to some small linear scale.
Ah, so that's the whole thing. So you have 6x2 dimensional volume, it's maybe our sixth power.
Then the energies you need to probe. That extra dimension skews inversely.
So you'll have a a compact ification scale here well below the pong scale.
So what we will be interested in will be the four dimensional theory well below the compact fabrication scale.
And that's well, this energy range, this compact ification scale is in in all interesting cases, still much above the electric scale.
Then having a complex application like that, then you can perturb the metric tensor of these extra dimensions.
So if you remember so we wrote down a metric for the Friedman Robeson Walker metric, the cosmological metric.
This extra dimensions will also have some structure.
So they're measured distances, they're measured by some metric.
And so when you write down a solution, you write down a metric, but you can perturb this metric.
So you make a slight deviation of the extra dimensions from their previous form.
And doing so one finds massless particles. These are called k k modes.
Sorry. The the massive masses of massive particles.
The massive particles are our k k modes. Well, the, the massless particles we call moduli.
And these particles or fields, the parameters, the size and the shape of this, this compact ification manifolds.
So you can increase the size of the manifold by varying the the value of one of these fields.
And I mentioned before that string theory had no free parameters.
A consequence of this is that in the low energy theory, all these Wilson coefficients that you want to predict,
they're not fixed before you fixed the values of these moduli fields.
Um, so it's, it's crucial to be able to fix them,
to be able to give them a potential where they sit and to be able to compute what your predictions in the low energy effect of theory are.
Before that, you can't really make very many predictions at all.
Fortunately, over the past decade, much progress has been made in this question.
And the understanding of how reliable potentials and masses can be generated.
There are many different complex applications scenarios, as they're called, and they give rise to two different detailed predictions.
For the well wasn't coefficients and effective series,
but there are several properties which commonly occur in large classes of solutions and and I'll discuss two of these specifically.
One of them is that the mass of of the light is modulus.
So it was massless and we gave it a potential and now it's mass. It will be of the order of 1036 giga electron volts.
This is assuming that we have super partner mass of at the t v scale.
So at the scale just about the electroweak scale. This is motivated.
This this footnote in the statement in a footnote is motivated by solving the hierarchy problem that should be alluded to earlier.
Bye bye supersymmetry. Furthermore, the second point is that additional light fields called accidents are typically present and can be much,
much lighter than the stabilised moduli. So accidents have a long history in particle physics, and I won't discuss this history at all in details.
The name was suggested from a detergent.
It was first suggested as a solution to what's called the strong C problem in particle physics.
What I will take away from this is just that in the string compact operations,
these particle typically arise and they have two salient properties that that that will be important.
The first one is that they're like scalar particles and they have very feeble interactions which are suppressed by some large mass scale.
Second, they can interact with gate fields through any interaction.
If you remember to gauge field strength, if you took relativity, this is a a matrix which encompasses the E and B fields.
The field sits on the F, not AI components, and the B field sits in a sort of middle.
And this is a dual in the end. If you do this for electromagnetism, what you get out is a dot b.
So this interaction will be important. But let me now turn to the second point.
What's the cosmology of this vacuum?
Just looking at this picture here from the left, going from the study of the cosmic microwave background from the sixties up until the present day,
it's quite obvious that observational cosmology has made remarkable progress over the past few decades.
In particular, studies of the cosmic microwave background have given evidence for a period of inflation,
cosmic inflation, or something very similar to it in the early universe.
So inflation can be accommodated in strip malls and studies of detailed string models as well as general arguments.
Habitat modulate genetically become displaced during inflation,
so they don't sit at the minimum where you stabilise them, they move away during inflation.
And just this fact as far reaching consequences for the cosmology of these models and I'll explain this pictorially.
So this is a brief discussion or a brief preview of a microsecond.
So what happened before inflation? You know, if we if we want to go to a time to equal zero, you know,
this is string theory is presumably a quantum consistent quantum theory of gravity.
So we should be able morally to go back to equal zero to see a resolution of, you know, the big bang singularity,
if there was one in which space was maybe not even a good quantity to start with that we can't do yet.
So I won't even discuss anything earlier than inflation.
So I'll start by having a model of inflation.
And as I said, during inflation, a moduli field here denoted by one will become displaced from its final vacuum.
So it might sit higher up in some potential, but it's not driving inflation, and inflation is driven by something else.
As inflation ends, this field will start to make it back to its to its the minimum of its potential.
And in doing so it will start oscillating around the minimum and just a damn simple harmonic oscillator.
So in this process, going from inflation to after inflation,
this is the period of reheating or the first stage of reheating that that should be mentioned.
And in this stage, you can create radiation and you can create well, you can create matter particles like like this modulus field is modulus field.
It will be a matter of particle. This oscillation period occurs during many, many equals.
And this means that the the the sorry not being equals.
But during a long time the the matter particle redshift like h cubed while radiation a redshift like eight to the fourth power,
which means that radiation will become more and more so, less and less important as time goes on.
It's easier to see this. There's why this scaling is so matter.
Redshifts like a cube. Because, you know, if you have these particles in a box, they have some certain energy and the box grows.
Then the box closed with a factor of eight cubed. Well radiation you apart from the box growing you also stretch the wavelength
of the particle and as a stretched of wavelength they become less energetic.
And that explains the difference in power there. Okay.
So now we're sitting and we have modulus which which oscillate around a vacuum.
At some point it will decay. It's weakly coupled to essentially everything else.
And one can compute the decay time.
The decay time is given by this expression so that the relevant feature here is that it's it's less like one over M today,
cubed one and cubed of the mass.
So the lightest modulus will live the longest, but eventually it will decay into two, say, other particles.
And the typical timescale here is ten to the mine, minus 6 seconds, so microsecond.
And eventually, after this final period of reheating, we're back at at the minimum of the potential.
So now I'm going to talk about this stage here, which is important for for the rest of the cosmology.
So at this final status stage, overheating the light as modulus can decay into visible sector particles,
as we call photons, Higgs particles, quarks, if you wish.
As well as any additional light particles. For instance, these actions that I mentioned earlier,
if weakly coupled light actions and the remainder of this talk will solely focus on this occasional modulus decaying into two axioms.
One immediate observation that one can make is that one works out.
If one works at the temperature, that's that the case of photons, of the decay of the modulus into photons and and and existence.
So get. So this is the receipt temperature. It looks like.
Like this. So it's around 0.6 V for the masses of interest.
While the accidents there are created by a true body decay, they don't thermally they interact to regulators thermally.
So they will keep on having the energy that they had at the decay.
So half that of the mass of the of the modulus.
So the the observation here is that this expression here, the mass divided by two, is much, much larger than just one.
This one is suppressed by a factor of the mass of the modulus of the mass over implying a square root.
So this changes the cosmology of the early universe.
So this was the figure that Trubridge showed earlier.
The picture that I've just described or the cosmology that I've just described, would instead look like this.
So before. Okay. So we're here now. Up until well past Nucleosynthesis and all the way back to ten to the minus 6 seconds, it's the same as as we see.
Then we have the onset of Big Bang cosmology when this model is decay.
Before that, you know, even if we extrapolate back, this actually never happened in our previous history.
This was when Big Bang cosmology, as we know it started.
And up here we had instead modulus, dominator or matter domination.
And then again, we had inflation up here. And and past that, we don't know.
The point, though, about these actions, as I said, they were energetic.
So they will be created at this time when the module is the case and it will be created with a higher energy.
Subsequently, they will redshift just like the radiation. So they will keep on being, say, a million times more energetic than the CMB photons.
So this is extra radiation. It's radiation that we don't see. Because these actions act like radiation and.
So this relativistic action would completely contribute to what we call dark radiation as opposed to dark matter.
But dark matter before that was matter particle non relativistic nanoparticles.
This is actually the relativistic version. So this is relativistic particles.
So it's called dark radiation. Um, and there are some hints at the 1 to 2 and a half sigma level of dark radiation in a universe coming from a
variety of different experiments involving looking at the CMB and bearing acoustic oscillations and the BBN.
Uh, so uh, abundances from from Big Bang nucleosynthesis.
What I want you to take away from this is that there are some hints of it, but it's, there's no firm evidence.
We don't know whether or not there is dark radiation in the universe yet or not.
But it could be the end. Oh, sorry. Thank you.
Thank you very much. So the question was, what is an effective here?
And effective is a measure that cosmologist uses, which is the effective number of neutrino species.
So we know that there are three neutrinos, actual neutrinos, we think, in the sun.
Well, in the standard model, there are three neutrinos. And and they affect the value that one gets out from this animal.
When we're doing a full computation of thermal, the coupling is a little bit higher.
So it's here. This is the standard model value. And, uh, deviations from this value can be created by any dark radiation.
So the important thing is the difference between this dashed line and the.
So perhaps this is caused by some sonic degradation.
So let's let's think about the consequences of this. So this exotic, dark radiation would be still present today.
And one can compute the typical energies. The typical energies would be around 200 electron volts.
And each square centimetre would be penetrated by around a million of these particles per second.
One can compute to the spectrum that these particles would have today.
The spectrum comes from some of them that came a little bit earlier, some of them a little bit later.
So there they have a difference in Redshift when they reach us.
So in analogy with the C and B, we call this action background, the cosmic action background or C, a, b.
Now it's a relevant question to ask whether or not this can be detected or if we're just postulating something that's just implausible.
And this is the relevance of the coupling that I wrote down before, namely the coupling of the action to EMV or EDP,
so that this coupling makes it possible to take actions here denoted by wise arrows,
propagate them through some field, and then in the end, some of them have a probability of converting into photons.
So in this energy range, photons are soft X-rays, so they're in the soft end of the X-ray spectrum.
So we could we could find a cab by looking for these soft X-rays in more detail.
Um, the computation to compute the probability starting from, from this, uh, this interaction is very similar to,
to solving a Schrodinger equation for, well, it looks like a three level system here, but it's actually a two level system if you simplify it.
Um, and I won't use any full solution of it, but for a homogeneous domain so of size.
L So say that this is less. L uh, the probability in a particular approximation is just given by this expression.
So it's scales with a magnetic field, times the coherence length squared.
So what we should be looking for then is, is strong magnetic fields, which are coherent over large length scales.
Strong magnetic fields. Well, they occur. Um, perhaps.
Well, you can create strongly new fields in the lab, for instance, but they're not coherent or very large scales.
And we haven't yet found a way to efficiently detect these particles that way.
But there are other places where one can find magnetic fields, for instance, in clusters of galaxies.
This is a picture of a coma cluster. Clusters of galaxies typically have magnetic field of micrographs strength, but so that's kind of weak.
But then they are coherence over several kilo parsecs, so several thousands of light years.
And since it's B or L that matters, this is an important fact.
So clusters of galaxies provide an interesting laboratory to search for this background.
Now, interestingly, by looking at galaxies, this is a picture of coma in x rays in an axis above.
The expected background has been found by a number of experiments ranging from from EUV in 1996, in a large number of galaxy clusters, including coma.
So what we want to ask now is, you know,
could it be that this excess that has been seen actually are the particles that that we predicted that have been converting,
that that would be a, well, spectacular and interesting consequence of the theory.
So, of course, you can't just say that you have to actually work out the details.
And it's, uh, it both takes, uh, work with pen and paper and computer time to actually figure out whether or not this is the case.
So recently we did a study using a stochastic model for the coma cluster magnetic field,
which was consistent with what's called Faraday rotation measurements.
So in some sense, measurements of the magnetic field in a cluster.
And, and then we computed a conversion probabilities that these actions would have when they propagated here.
We did this by simulating a 2000 cubed lattice. So we took coma this year, testing to 2000 cubed points.
And at each of these we had a magnetic field which was consistent with Faraday rotation.
And then we propagated those actions through by solving this, showing an equation that shows and the results can be summarised like this,
you have more probable regions to propagate in red and less in blue,
and 25 electron volts is a little bit on the low end of the actions that we consider.
But I'll show you a few more energies. So the 50 electron volts, the probabilities change.
Also, the morphology changes a bit at 100 changes.
And as I said, it was blue in the in the centre before and now it's red when I'm up at 600 electron volts and then it can propagate through.
Oh, yeah. Okay. So we can compare whatever we get.
From these simulations with the actual data of the soft access, soft X-ray access that's done in this figure for the case of coma.
The data here are these red points. And the axis here is the radial distance and arc minutes,
meaning it's a distance out from the centre of the cluster going out to two, 500, 500 kilometres.
The models here are different predictions that we derive depending on.
Well, I told you it was a magnetic field model, but it's a magnetic field model,
which is a parameter degeneracy, which means that is actually not one model is a class of models.
So we have to explore different ends of the spectrum of these models.
And in some cases it looks like it's not a very good approximation in in other cases,
it certainly looks like it's, it's relatively well described by death.
Um, but it's cosmic actually in background converting to photons.
So we have more studies underway. This was a stochastic model.
It's essentially modelling the magnetic field as a gauss, a divergence, less Gaussian random field didn't have dynamics in it.
It wasn't created by actually creating a cluster.
So what we're doing now is working with some some very skilled people in astrophysics who have actually
taken and simulated the formation of clusters through magnetic magneto hydrodynamics simulations.
And they also have the structure of the magnetic field of clusters of the types of this type.
So we will work with them and see whether or not there's a big difference between this model and their model for, for, for the self us.
And we'll continue to explore this also in other clusters and of course to see whether or not this exclusionary explanation works.
Now, I want to go back to the string theory. Make their way back.
This is my final slide.
And the question that I would like to ask is that suppose we discover this cosmic background, could we learn anything more than okay,
there was a cosmic text in background, maybe a model and string theory predicted it, but it still gets the cosmic action background, so we don't know.
Well, I'm going to make the two two assumptions first, that we can measure the mean energy of this cab.
So then we can measure some ratio of I mean, then we have the ratio of this energy to the temperature of the CMB.
As you saw these lines, the line of action and the line of the temperature of the CMB, the decreased.
Similarly in this plot I had before so that then this ratio will stay the same throughout the cosmological history.
Up to two small modifications. And second of all, I will assume that one can measure the spectrum here.
And by measuring the spectrum, which is non thermal, one can establish that it was very likely to have come from the decay of of some field.
In that case, the reheating temperature will be determined by this expression.
Here. Here. I haven't assumed that there's a suppression.
Scale of this new physics is implying.
I haven't assumed that this is quantum gravity, but it's just suppressed by some scale lambda, which I want to determine.
So we can then use that successful big bang nucleosynthesis requires that this temperature is sufficiently high.
So particles have have had to have had had to be created sufficiently early on in order for BBN to work.
And this gives the constraints on the mass and a constraint on the scale.
In particular for for the case of modulus with a mass of ten, 2 to 6.
This constraint implies that the mass is should be larger than around 40 V but also the scale,
the suppression scale should be up to the up of around 10 to 17 GB.
This is pressing and plug.
So what this would mean if you could do the two measurements that have assumed here is that you would have seen a particle which
came from the decay or a particle which interacts with Planck suppressed operators or essentially Planck suppressed operators.
But that's what we call moduli. So in some way it's hard to derive general predictions valid for all bacteria.
But definitely falsifiable predictions can be made from large classes of bacteria, and that's what we work on.
Sexy dark radiation is just an example of this, which is it's valid for a large class of evacuates, a prediction of large classes,
of accurate and precise measurements of the radiation content of the universe as
parameters but as an F parameter provides direct constraints on this string also.
More model dependently psionic dark radiation can be detected through this action
photon conversion that are discussed and and converted photons in magnetic fields.
The cloth clusters of extra access may in fact be one of the first signals of a string theory cosmic in background.
And would we detect a severe beating that would strongly suggest the existence of Moduli?
One. That's one of the few generic predictions of string theory since it comes just when a compact ification.
So with that, I would just like to say and thanks.