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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.

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So what I'm going to talk about the string theory and how we derive predictions from string theory or string models.

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But before starting off with discussing some work that we've actually done here over the past year,

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I want just to take a step back and just contemplate the the scales involved in this problem,

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sort of scales of of particle physics that we explored over the past century and is explore now

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can be said to be in this range from the scale of atomic physics up to the acoustic scale,

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the electroweak scale, the scale that is currently probed by the LHC survey.

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We will later talk about some very high energy events coming from cosmic neutrinos, which is up here.

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Further down we have the scale of the cosmological constant. So this this is a huge span of energy scales.

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None of them include quantum gravity. The scale at which we expect quantum gravity to actually become important was mentioned by Saburo.

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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.

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That's a huge energy difference, of course.

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So just to to get a sense of how huge that difference is, let us consider building an accelerator where current technology,

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current LHC technology, the magnets that are to build it bigger.

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So when we build it bigger, we can probe a higher energy because.

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Oh, sorry. Uh, because, well, what we have here is the, what's keeping the, the protons circulating.

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The ring will be the, the electromagnetic force from the magnetic from the magnets.

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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.

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And in particular, we can get a simple expression for the radius needed to probe the Planck scale energies.

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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.

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So we should encompass, well, a good deal of the most visible nearby stars.

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So this this shows that while accelerator experiments are not suitable to directly probe Planck scale physics,

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if it's if it's actually sitting up at the Planck scale, it can still be important for cosmology and particle physics.

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And this is the point I want to make now.

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The point goes back to if you remember Serbia's slide about the standard model, he wrote it down as an effective field theory.

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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.

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I won't be more specific about what it is and its energy is much below the scale.

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We can write down an effective field theory and.

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And this field theory will, it will capture the effects of the phenomena up here, but it will be valid down here.

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So we'll integrate it out. All the effects up here, if you wish.

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So this effective field theory for a scalar particle will be given by, well, the kinetic terms, and then some potential.

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This potential will have some some well, some really realisable terms and then a tower of non renormalisation terms,

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non renormalisation terms are suppressed by in this case then the Planck scale.

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Now, it's an interesting fact that several of the proposed physical phenomena that are might be relevant in our cosmological history,

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such as cosmic inflation, biogenesis and supersymmetry,

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breaking are all sensitive to the structure of these coefficients called the Wilson coefficients.

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And this gives a sensitivity to the theory in which those coefficients can be computed as the quantum gravity.

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So this will be the framework in which one can probe quantum gravity.

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I mean, we probe it indirectly, but its effect on the lower energy effective theory.

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So then we're all set. We have a framework for testing quantum gravity.

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It's just a three step process. We propose a consistent theory up at the Planck scale.

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We we we scaled down two energies e and well below e e well below the playing field.

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And we compute the relevant effective field theory of compute the Wilson coefficient c seven and we derive all the

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cosmological and particle physics predictions and then we compare them to cosmological and particle physics data.

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In practice, this is extremely challenging.

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There's only one theory where you can even start, where you can even start computing those Watson coefficients.

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And that string theory. And even this theory has proven very complicated to do this, to follow this procedure.

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The fact that this is the case has even propagated out into popular culture where, well,

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people are not physicists have elaborated on the point that it's really hard to go from point 1 to 2.2.

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It's, of course, of a scandalous webcomic.

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So in reality or in science, we think about it maybe a little bit differently.

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But this, I think, can fairly be said about the status of string theory now.

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Much of the initial excitement about the theory itself was sparked or spurred by a number of remarkable properties of the theory,

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yet perhaps formal properties such as a highly nontrivial consistency.

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Sex that was verified 30 years ago can be said to be the onset of of the first string theory wave.

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It has an apparent lack of tuneable parameters, which gives us sense of uniqueness up at the core of theory at the Planck scale.

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Without even asking for gravity, it encodes gravity. So it gives you quantum gravity right away, which is just spectacular.

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There are a number of extremely powerful dualities connecting various formulations of the theory.

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There are it that we can be used to gain some insight into the physics of the two micro physics of black holes.

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None of this, though, tells you how to go from .12.2.

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The issue here is that string theory has many solutions. These are called vacuna and I will use these words interchangeably.

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And in these different back a these Wilson coefficients take different values and their cosmologies are completely different.

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And this calls for a modified scheme so you can try to do it this way instead.

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So you propose a consistent variable to Paxil that would be disturbing to you.

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You find a vacuum and so a model and you compute in this model all the relevant predictions and the Watson coefficients,

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and then you compare that with data. So this is still a hard procedure doing it explicitly, which has been done.

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Well, it can be done. And models have been ruled out this way, but it's still hard.

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The basic problem here is that there are many models say at least in one part, where you can do the counting reliably.

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People have counted up to ten to the 500 models.

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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,

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four, five, five, and then, you know, it's the end of the day.

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So it's it's pertinent to ask whether or not we can learn anything.

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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.

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And that's the relevant questions to asking. And so trying to connect string theory to reality.

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And there are ways to do that. A more efficient approach can be obtained by identifying consistency conditions for the low energy effective series,

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which are very nontrivial, and see if the universe can be seen to to contradict those consistency conditions.

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One can study large ensembles of vacuum statistically, and as I will discuss in this talk,

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one can construct large classes of models with some common properties and then test these common properties.

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And one can also derive generic predictions of the effective field theories and the corresponding cosmologies to make this more concrete.

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In this talk, I'll discuss a new generic prediction motivated by a large class of string theory models,

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and I'll discuss the observational signals that this prediction gives rise to.

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And finally, I will mention something which is a little bit speculative, but it might turn out right.

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I'll mention that these signals may already be seen. And our work on figuring out whether or not this is the case.

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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.

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Second of all, I'm going to describe your cosmology, which is slightly different from the the standard picture of the early universe.

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And then I'm going to discuss these predictions and go into the name of the extent of degradation of cosmic extreme background and,

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and the cluster suffixes. So famously, string theory requires extra dimension in order to be consistent.

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And we don't observe these extra dimensions, which means that they have to be hidden away somehow.

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They have to be compact, defined. So if you compact it by an extra dimension to some small linear scale.

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Ah, so that's the whole thing. So you have 6x2 dimensional volume, it's maybe our sixth power.

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Then the energies you need to probe. That extra dimension skews inversely.

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So you'll have a a compact ification scale here well below the pong scale.

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So what we will be interested in will be the four dimensional theory well below the compact fabrication scale.

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And that's well, this energy range, this compact ification scale is in in all interesting cases, still much above the electric scale.

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Then having a complex application like that, then you can perturb the metric tensor of these extra dimensions.

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So if you remember so we wrote down a metric for the Friedman Robeson Walker metric, the cosmological metric.

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This extra dimensions will also have some structure.

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So they're measured distances, they're measured by some metric.

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And so when you write down a solution, you write down a metric, but you can perturb this metric.

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So you make a slight deviation of the extra dimensions from their previous form.

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And doing so one finds massless particles. These are called k k modes.

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Sorry. The the massive masses of massive particles.

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The massive particles are our k k modes. Well, the, the massless particles we call moduli.

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And these particles or fields, the parameters, the size and the shape of this, this compact ification manifolds.

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So you can increase the size of the manifold by varying the the value of one of these fields.

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And I mentioned before that string theory had no free parameters.

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A consequence of this is that in the low energy theory, all these Wilson coefficients that you want to predict,

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they're not fixed before you fixed the values of these moduli fields.

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Um, so it's, it's crucial to be able to fix them,

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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.

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Before that, you can't really make very many predictions at all.

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Fortunately, over the past decade, much progress has been made in this question.

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And the understanding of how reliable potentials and masses can be generated.

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There are many different complex applications scenarios, as they're called, and they give rise to two different detailed predictions.

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For the well wasn't coefficients and effective series,

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but there are several properties which commonly occur in large classes of solutions and and I'll discuss two of these specifically.

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One of them is that the mass of of the light is modulus.

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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.

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This is assuming that we have super partner mass of at the t v scale.

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So at the scale just about the electroweak scale. This is motivated.

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This this footnote in the statement in a footnote is motivated by solving the hierarchy problem that should be alluded to earlier.

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Bye bye supersymmetry. Furthermore, the second point is that additional light fields called accidents are typically present and can be much,

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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.

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The name was suggested from a detergent.

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It was first suggested as a solution to what's called the strong C problem in particle physics.

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What I will take away from this is just that in the string compact operations,

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these particle typically arise and they have two salient properties that that that will be important.

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The first one is that they're like scalar particles and they have very feeble interactions which are suppressed by some large mass scale.

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Second, they can interact with gate fields through any interaction.

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If you remember to gauge field strength, if you took relativity, this is a a matrix which encompasses the E and B fields.

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The field sits on the F, not AI components, and the B field sits in a sort of middle.

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And this is a dual in the end. If you do this for electromagnetism, what you get out is a dot b.

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So this interaction will be important. But let me now turn to the second point.

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What's the cosmology of this vacuum?

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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,

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it's quite obvious that observational cosmology has made remarkable progress over the past few decades.

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In particular, studies of the cosmic microwave background have given evidence for a period of inflation,

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cosmic inflation, or something very similar to it in the early universe.

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So inflation can be accommodated in strip malls and studies of detailed string models as well as general arguments.

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Habitat modulate genetically become displaced during inflation,

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so they don't sit at the minimum where you stabilise them, they move away during inflation.

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And just this fact as far reaching consequences for the cosmology of these models and I'll explain this pictorially.

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So this is a brief discussion or a brief preview of a microsecond.

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So what happened before inflation? You know, if we if we want to go to a time to equal zero, you know,

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this is string theory is presumably a quantum consistent quantum theory of gravity.

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So we should be able morally to go back to equal zero to see a resolution of, you know, the big bang singularity,

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if there was one in which space was maybe not even a good quantity to start with that we can't do yet.

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So I won't even discuss anything earlier than inflation.

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So I'll start by having a model of inflation.

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And as I said, during inflation, a moduli field here denoted by one will become displaced from its final vacuum.

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So it might sit higher up in some potential, but it's not driving inflation, and inflation is driven by something else.

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As inflation ends, this field will start to make it back to its to its the minimum of its potential.

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And in doing so it will start oscillating around the minimum and just a damn simple harmonic oscillator.

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So in this process, going from inflation to after inflation,

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this is the period of reheating or the first stage of reheating that that should be mentioned.

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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.

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It will be a matter of particle. This oscillation period occurs during many, many equals.

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And this means that the the the sorry not being equals.

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But during a long time the the matter particle redshift like h cubed while radiation a redshift like eight to the fourth power,

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which means that radiation will become more and more so, less and less important as time goes on.

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It's easier to see this. There's why this scaling is so matter.

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Redshifts like a cube. Because, you know, if you have these particles in a box, they have some certain energy and the box grows.

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Then the box closed with a factor of eight cubed. Well radiation you apart from the box growing you also stretch the wavelength

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of the particle and as a stretched of wavelength they become less energetic.

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And that explains the difference in power there. Okay.

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So now we're sitting and we have modulus which which oscillate around a vacuum.

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At some point it will decay. It's weakly coupled to essentially everything else.

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And one can compute the decay time.

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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,

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cubed one and cubed of the mass.

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So the lightest modulus will live the longest, but eventually it will decay into two, say, other particles.

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And the typical timescale here is ten to the mine, minus 6 seconds, so microsecond.

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And eventually, after this final period of reheating, we're back at at the minimum of the potential.

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So now I'm going to talk about this stage here, which is important for for the rest of the cosmology.

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So at this final status stage, overheating the light as modulus can decay into visible sector particles,

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as we call photons, Higgs particles, quarks, if you wish.

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As well as any additional light particles. For instance, these actions that I mentioned earlier,

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if weakly coupled light actions and the remainder of this talk will solely focus on this occasional modulus decaying into two axioms.

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One immediate observation that one can make is that one works out.

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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.

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So get. So this is the receipt temperature. It looks like.

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Like this. So it's around 0.6 V for the masses of interest.

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While the accidents there are created by a true body decay, they don't thermally they interact to regulators thermally.

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So they will keep on having the energy that they had at the decay.

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So half that of the mass of the of the modulus.

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So the the observation here is that this expression here, the mass divided by two, is much, much larger than just one.

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This one is suppressed by a factor of the mass of the modulus of the mass over implying a square root.

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So this changes the cosmology of the early universe.

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So this was the figure that Trubridge showed earlier.

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The picture that I've just described or the cosmology that I've just described, would instead look like this.

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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.

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Then we have the onset of Big Bang cosmology when this model is decay.

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Before that, you know, even if we extrapolate back, this actually never happened in our previous history.

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This was when Big Bang cosmology, as we know it started.

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And up here we had instead modulus, dominator or matter domination.

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And then again, we had inflation up here. And and past that, we don't know.

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The point, though, about these actions, as I said, they were energetic.

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So they will be created at this time when the module is the case and it will be created with a higher energy.

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Subsequently, they will redshift just like the radiation. So they will keep on being, say, a million times more energetic than the CMB photons.

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So this is extra radiation. It's radiation that we don't see. Because these actions act like radiation and.

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So this relativistic action would completely contribute to what we call dark radiation as opposed to dark matter.

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But dark matter before that was matter particle non relativistic nanoparticles.

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This is actually the relativistic version. So this is relativistic particles.

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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

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variety of different experiments involving looking at the CMB and bearing acoustic oscillations and the BBN.

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Uh, so uh, abundances from from Big Bang nucleosynthesis.

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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.

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We don't know whether or not there is dark radiation in the universe yet or not.

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But it could be the end. Oh, sorry. Thank you.

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Thank you very much. So the question was, what is an effective here?

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And effective is a measure that cosmologist uses, which is the effective number of neutrino species.

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So we know that there are three neutrinos, actual neutrinos, we think, in the sun.

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Well, in the standard model, there are three neutrinos. And and they affect the value that one gets out from this animal.

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When we're doing a full computation of thermal, the coupling is a little bit higher.

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So it's here. This is the standard model value. And, uh, deviations from this value can be created by any dark radiation.

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So the important thing is the difference between this dashed line and the.

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So perhaps this is caused by some sonic degradation.

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So let's let's think about the consequences of this. So this exotic, dark radiation would be still present today.

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And one can compute the typical energies. The typical energies would be around 200 electron volts.

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And each square centimetre would be penetrated by around a million of these particles per second.

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One can compute to the spectrum that these particles would have today.

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The spectrum comes from some of them that came a little bit earlier, some of them a little bit later.

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So there they have a difference in Redshift when they reach us.

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So in analogy with the C and B, we call this action background, the cosmic action background or C, a, b.

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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.

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And this is the relevance of the coupling that I wrote down before, namely the coupling of the action to EMV or EDP,

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so that this coupling makes it possible to take actions here denoted by wise arrows,

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propagate them through some field, and then in the end, some of them have a probability of converting into photons.

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So in this energy range, photons are soft X-rays, so they're in the soft end of the X-ray spectrum.

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So we could we could find a cab by looking for these soft X-rays in more detail.

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Um, the computation to compute the probability starting from, from this, uh, this interaction is very similar to,

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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.

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Um, and I won't use any full solution of it, but for a homogeneous domain so of size.

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L So say that this is less. L uh, the probability in a particular approximation is just given by this expression.

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So it's scales with a magnetic field, times the coherence length squared.

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So what we should be looking for then is, is strong magnetic fields, which are coherent over large length scales.

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Strong magnetic fields. Well, they occur. Um, perhaps.

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Well, you can create strongly new fields in the lab, for instance, but they're not coherent or very large scales.

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And we haven't yet found a way to efficiently detect these particles that way.

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But there are other places where one can find magnetic fields, for instance, in clusters of galaxies.

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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.

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But then they are coherence over several kilo parsecs, so several thousands of light years.

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And since it's B or L that matters, this is an important fact.

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So clusters of galaxies provide an interesting laboratory to search for this background.

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Now, interestingly, by looking at galaxies, this is a picture of coma in x rays in an axis above.

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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.

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So what we want to ask now is, you know,

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could it be that this excess that has been seen actually are the particles that that we predicted that have been converting,

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that that would be a, well, spectacular and interesting consequence of the theory.

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So, of course, you can't just say that you have to actually work out the details.

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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.

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So recently we did a study using a stochastic model for the coma cluster magnetic field,

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which was consistent with what's called Faraday rotation measurements.

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So in some sense, measurements of the magnetic field in a cluster.

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And, and then we computed a conversion probabilities that these actions would have when they propagated here.

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We did this by simulating a 2000 cubed lattice. So we took coma this year, testing to 2000 cubed points.

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And at each of these we had a magnetic field which was consistent with Faraday rotation.

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And then we propagated those actions through by solving this, showing an equation that shows and the results can be summarised like this,

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you have more probable regions to propagate in red and less in blue,

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and 25 electron volts is a little bit on the low end of the actions that we consider.

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But I'll show you a few more energies. So the 50 electron volts, the probabilities change.

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Also, the morphology changes a bit at 100 changes.

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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.

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Oh, yeah. Okay. So we can compare whatever we get.

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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.

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The data here are these red points. And the axis here is the radial distance and arc minutes,

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meaning it's a distance out from the centre of the cluster going out to two, 500, 500 kilometres.

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The models here are different predictions that we derive depending on.

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Well, I told you it was a magnetic field model, but it's a magnetic field model,

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which is a parameter degeneracy, which means that is actually not one model is a class of models.

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So we have to explore different ends of the spectrum of these models.

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And in some cases it looks like it's not a very good approximation in in other cases,

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it certainly looks like it's, it's relatively well described by death.

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Um, but it's cosmic actually in background converting to photons.

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So we have more studies underway. This was a stochastic model.

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It's essentially modelling the magnetic field as a gauss, a divergence, less Gaussian random field didn't have dynamics in it.

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It wasn't created by actually creating a cluster.

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So what we're doing now is working with some some very skilled people in astrophysics who have actually

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taken and simulated the formation of clusters through magnetic magneto hydrodynamics simulations.

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And they also have the structure of the magnetic field of clusters of the types of this type.

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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.

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And we'll continue to explore this also in other clusters and of course to see whether or not this exclusionary explanation works.

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Now, I want to go back to the string theory. Make their way back.

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This is my final slide.

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And the question that I would like to ask is that suppose we discover this cosmic background, could we learn anything more than okay,

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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.

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Well, I'm going to make the two two assumptions first, that we can measure the mean energy of this cab.

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So then we can measure some ratio of I mean, then we have the ratio of this energy to the temperature of the CMB.

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As you saw these lines, the line of action and the line of the temperature of the CMB, the decreased.

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Similarly in this plot I had before so that then this ratio will stay the same throughout the cosmological history.

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Up to two small modifications. And second of all, I will assume that one can measure the spectrum here.

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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.

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In that case, the reheating temperature will be determined by this expression.

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Here. Here. I haven't assumed that there's a suppression.

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Scale of this new physics is implying.

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I haven't assumed that this is quantum gravity, but it's just suppressed by some scale lambda, which I want to determine.

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So we can then use that successful big bang nucleosynthesis requires that this temperature is sufficiently high.

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So particles have have had to have had had to be created sufficiently early on in order for BBN to work.

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And this gives the constraints on the mass and a constraint on the scale.

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In particular for for the case of modulus with a mass of ten, 2 to 6.

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This constraint implies that the mass is should be larger than around 40 V but also the scale,

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the suppression scale should be up to the up of around 10 to 17 GB.

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This is pressing and plug.

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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

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came from the decay or a particle which interacts with Planck suppressed operators or essentially Planck suppressed operators.

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But that's what we call moduli. So in some way it's hard to derive general predictions valid for all bacteria.

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But definitely falsifiable predictions can be made from large classes of bacteria, and that's what we work on.

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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,

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of accurate and precise measurements of the radiation content of the universe as

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parameters but as an F parameter provides direct constraints on this string also.

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More model dependently psionic dark radiation can be detected through this action

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photon conversion that are discussed and and converted photons in magnetic fields.

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The cloth clusters of extra access may in fact be one of the first signals of a string theory cosmic in background.

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And would we detect a severe beating that would strongly suggest the existence of Moduli?

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One. That's one of the few generic predictions of string theory since it comes just when a compact ification.

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So with that, I would just like to say and thanks.