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Capability. Once again, everybody. And a very warm welcome to this set of Saturday Morning Theory lectures.

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This is actually the third set of of of these lectures.

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And I'm very glad to see that their popularity is not waning.

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It's great to see so many people here here this morning.

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Now, this this lectures is about cosmology, which, of course, these days is the, you know, one of the forefront fronts of of physics research.

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But it wasn't always like that. And 100 years ago, the the the forefront of physics research was somewhere else.

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It wasn't actually in Oxford is the first thing one should be fairly honest about.

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And so Oxford University famously had the opportunity to hire a Helmholtz to one of its senior senior chairs and instead hired a guy called Clifton.

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Ring any bells? Who sort of blocked the entire system for about 50 years as he sat in his chair?

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But it all changed in the early years of of the 20th century.

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And I think that the thing that changed the psychology was was a guy called Henry Moseley,

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who was the person who established the relationship between atomic number and the central charge of the nucleus by doing X-ray spectra experiments.

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So many of you may vaguely remember seeing Moseley's graph somewhere up in the in the Clarendon Laboratory.

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Now, Moseley was killed in the First World War in 1915, so his hundredth anniversary is is coming up.

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And this is really by way of a trailer. So so in order to to honour Moseley's legacy.

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And, you know, so I think make the point that, you know, we're here now doing all these things,

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you know, partly because of a mindset which was going around. Then we'll be having, you know, a number of events to to celebrate Moseley's centenary.

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Of course, we're not celebrating his death, but we're set up, which was very sad, but we're celebrating the achievements, his scientific achievements.

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So there will be a number of sort of Moseley specific events over over the next couple of years.

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And the physics department in his college, which was Trinity College and in fact the University Museum of Science,

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we will be working closely together to make sure that we, you know, do it in the best possible way that we can.

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Now, those of you who were at the alumni weekend in the autumn will remember that we've also launched the Henry Moseley Society,

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which is a sort of basic society for people who want to support the physics department and its and its work in the future.

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And if you weren't here that alumni weekend to want to learn more about it, you can do some leaflets.

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There'll be some leaflets outside. And there are also details about what well, how it works on on the website.

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So so back to back to today.

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So we're doing doing cosmology. And we're going to start with the spear who it looks like somebody in a balloon

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on the left hand side and some very high tech picture on the right hand side.

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So severe. So that John says today's theme is the interface between particle physics and cosmology.

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I'm the head of the Particle Theory Group.

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And as you would see in the talks that follow, we have diversified immensely from what you might consider to be the code of particle activity.

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We impinge on our neighbouring sub departments, on astrophysics and on particle physics.

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We are garnets, we go wherever the action is and we try and apply the same underlying core principles that you have heard

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about in the last couple of lectures through the problems that we now encounter at this interface.

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So the last two sessions are of course going to be a hard act to follow, and I'm very happy to see that so many of you have come, nothing else.

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It keeps the room warm. We have switched of the heating to safe, but actually I've just turned the air conditioning on, so it should be all right.

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And the other departure from the previous format is that instead of having all the talk given by senior staff today,

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I've asked one of my graduate students released on offer who is from Heidelberg and is just finishing here to talk about dark matter.

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And he will be followed by Dr. David Marsh, who's a postdoc working in a group, is from Cornell University of the Swedish Belgian.

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And I hope that you will then get a feel about what we actually work on.

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So these won't just be grand overviews of the subject. We'll try and give you a flavour of the kind of problems we're engaged with.

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So that means necessarily that it will not be as accessible at every moment as when, for example, the first talks.

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But I hope you will understand that our purpose is really to try and convey some of the excitement at the coalface, as it were.

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Okay. So on with the show of James Binney has asked me to give an overview to the all the three dogs because they

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will be focussed on specific topics and I think that's necessary and I'm already 8 minutes into my time,

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so I'll go even quicker than I had done when we rehearsed it yesterday.

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But let's see. So the motivation for what we are doing is starts about 100 years ago, 1912.

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That gentleman on the left is an Austrian physicist, Victor Hess, who got into a balloon those days.

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There were nice suits to do experiments and went up and discovered cosmic rays, particles that are impinging on us from all directions.

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And space was origin is still a mystery and which extend up to very high energies.

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That's how particle physics started. And I would say that was the birth of what has come to be called astroparticle physics,

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which is this intersection, as I indicated there, and the particles.

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Physics, of course, has reached its pinnacle now in the Large Hadron Collider at CERN,

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about which I hope there'll be a future dedicated session someday.

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And cosmology is represented here by this map of the sky, as taken by the Planck satellite and the microwave radiation,

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which was the first evidence that we live in a universe that at one time was hot and dense and therefore

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subject to the same laws of fundamental physics that we study today in accelerators such as this.

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So you see this prophetic statement by Viktor Hess on the occasion of his receiving the Nobel Prize.

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And the other one, which I also like and which has motivated me considerably, is Yakov,

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which pioneering Soviet cosmologist and father of the Soviet hydrogen bombs.

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He never got out much. He recognised as soon as the microwave background radiation was discovered that we could in fact study

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the universe as a whole and try and infer things of interest to fundamental physics from there.

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Okay, so let me take you on a whirlwind journey through this interface, which has been very active for, I would say, the past 30 years.

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That's how long I've been working in it anyway, and try to give you a flavour and context for the talks that are to follow.

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So very quickly, you saw what Mr. Hess, Mr. Hess carried two counters of with him.

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These are ionisation chambers. They showed that in addition, instead of falling off as you went up, actually went increased,

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which is not what you expect if it does due to radioactivity in the ground.

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And just as we have two experiments at CERN today, Atlas and CMS had two chambers.

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Okay. It's always good to have good information. And it was a amazing discovery.

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And what it really triggered, that's what intrigues us theorists was further work.

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You heard about the Dirac equation from James Binney in the first session,

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the Relativistic Wave equation that in fact gave you a solution that suggested that for every particle that we know,

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there is another one of opposite charge and the C mass and Dirac himself couldn't

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figure out whether this was really true in nature until a man called Carl Anderson

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at Caltech observed that a a particle going through a plate and therefore slowing

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down was actually curving the wrong way from what you would expect for an electron.

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And certainly we had doubled the number of particles in the universe in the same

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way that today people talk about perhaps invoking supersymmetric partners.

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So you been there before a mathematical equation, predict something that turns out to be what nature has chosen to be.

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This is miraculous when we see it and we witnessed it again last year with the discovery of the Higgs.

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So this is what gives us the confidence that we are doing the right thing. We are on the right track.

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And of course, the parallel developments in experimental physics were equally crucial in order to make these discoveries possible.

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I know that several of you are experimentalists or have worked in the area.

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Then of course you know the story you call up predicted the presence of existence of mesons, heavier particles mediating the strong force.

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Initially, another particle which looked like the pion was found.

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It turned out to be just a heavy cousin of the electron.

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And the question that Rabi asked allegedly in a Chinese restaurant who ordered that still holds today?

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We don't know the answer. That's the notorious flavour problem while the three generations of particles that look identical.

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And then this series went on to bore the word when a series of discoveries, one of the brothers, the U.K. physicist, played a notable role in them,

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not least, Don Perkins was the professor of particle physics here for many years, and all that has now resulted in a magnificent edifice.

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But let's go back to what theorists were thinking around the same time,

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and I thought I would show you something that you may not be so familiar with because this Russian physicist did not live very long.

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As you see, he was executed by Stalin,

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but he recognised that the three dimensional couplings that had been talked about already that mentioned four constants of nature.

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Absolutely. The action quantum of the action that Planck had given us,

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the speed of light that we already knew from Maxwell as emerging out of the unified electromagnetism that he had constructed.

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And of course, Newton's constant that these corresponded to various aspects of the magnificent theoretical edifice that he urged us all to pursue,

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to unify quantum theory and special relativity and gravitation into what today we would call the theory of everything.

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And so this has come to be called Brownstein's Cube. You see, if at the origin we have Galilean or classical mechanics,

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Newtonian Newton rules so the in the speed of light but infinitely sea goes to zero.

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Then you added are the. I'm sorry. Otherwise, you would have to be living here at the Theory of Special Relativity.

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If you marry that with gravitation, you have general relativity.

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If you marry that with quantum mechanics, you have quantum field theory.

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Perhaps the greatest intellectual construction of the past century.

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But we still have this other vertex here to get to, which is where you all these three constants play a role.

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And the scale of that or the energy scale of that is parameterised by the combination of this constants,

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which is that anomalously high energy, the Planck scale.

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And I'm setting this up so that David Marshall talk about superstring theory and its possible observable consequences.

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You know that we are following the same program that was outlined for us nearly 100 years ago.

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But today we have, of course, the standard model which most of you know about.

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This deserves a talk by itself, which I'm not going to give you.

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But you have heard and you have read that the last missing piece of the standard model of unified

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electroweak interactions and the strong interactions had one missing piece the Higgs boson.

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That, through the mechanism of spontaneous breaking of a gate symmetry gives masses to

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the W and Z bosons which mediate the weak nuclear force that has was missing,

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it says, yet to be confirmed,

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and now it has been spectacularly found through processes that create the Higgs boson through in the Large Hadron Collider.

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And you observe here that it's decayed to four leptons through this Feynman diagram.

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And then we observe its decay due to photons through this other Feynman diagram.

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And the two giant experiments with 4000 people each have managed to carry out this

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amazing endeavour of showing that a mathematical trick that Peter Higgs discovered,

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which enabled him to satisfy two loopholes that had to be plugged, namely the existence of massless particles that were not seen,

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and that this need to give masses to the Higgs boson so we can fractions which to explain why they're short range,

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that this could be achieved in an extremely elegant and economic way,

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which however, until two years ago,

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even provenance theorists I think I'm thinking for example of there are two hooft did not quite believe and yet that exists.

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Richard has once again chosen to obey the dictates of the mathematics that we can construct.

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I find it quite awe inspiring that this is actually the case, and we now know that this famous Mexican hat potential,

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which has a centre of symmetry but the universe live somewhere on that,

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didn't go vacuole, which are degenerate,

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that we are sitting somewhere out on the ring and we know the potential, we know the height of that potential.

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We knew the vacuum expectation value of the Higgs. We know everything about it now, and it looks just as predicted in the standard model.

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The couplings are proportional to mass. This is amazing.

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But this is, of course, just the beginning. This has been talked about for the last 40 years.

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That's how long it took to find that particle. What is next?

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So here I have to be slightly more technical, but please bear with me because you can see how this feeds into the talks that will follow.

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We have a Lagrangian for the standard model now, which are written in very schematic form.

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We have been introduced to the gradients earlier and you will recognise that there are terms here which look like credit terms.

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There are things that look like the potential, the size of fermions, the find, the Higgs field.

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This is the coupling that gives masses to the fermions, to the so-called couplings.

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This is the for example, it could be the electromagnetic field. It could be the electroweak field.

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These are the reasons that mediate forces, and we have very normalised opportunity.

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In other words, one in which you can calculate quantities to very high level of position by a trick of cancelling infinities off against each other,

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which nonetheless gives numbers.

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But this somewhat dodgy approach which agree with experiment to now eight or nine decimal places you got to seeing is believing.

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Okay, but this is not all. What we now recognise is that this is just the tip of the iceberg.

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You can write an infinite number of other terms which you can add to the Lagrangian of the standard model which are not normalised.

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But. They reflect physics, new physics, which violates the symmetries of the standard model.

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The standard model, for example, has the barrier number of particles conserved.

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It's a global so-called global quantum number, but we know that it cannot be exactly conserved because it is not a gauge quantum number.

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There are no longer influences government barbarians bought from gravity, of course.

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And that means that I can write down a term that makes protons leaky.

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And we know that protons must decay at some level because otherwise they could not have been born.

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That's what a philosopher once told me.

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And I think that there's a point there, and the proof don't have to be born because we are here to prove that they have.

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They didn't exist earlier and now we are here. And similarly, neutrinos carry ID number four, lepton number, quantum number, which is also violated.

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And that allows a neutrino to be its own antiparticle because it's a neutral particle gain in so-called majorana models.

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And here is a term that allows for that. We believe we might have seen this not definitively.

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We have seen neutrino oscillations.

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That means that the mass the race is now on to find out if they really had their own antibody to live their masses of the majorana nature.

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So these are just technical terms and throwing them out.

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I have no time to explain them in detail, but I hope you are getting a idea of the vast landscape of phenomena into which all these things intersect.

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And we understand why these quantities are so slow or so small,

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because the purpose of the purity of the cut off in the denominator, this is the energy scale at which new physics will emerge.

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We don't know what that scale is, but what we do know is that there is a tension within the theory that tells us that

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that new speed must be within reach of colliders such as the Large Hadron Collider.

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How do you know that? Because in order to keep these guys small, m has to be large.

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But there are two terms in the theory which are of dimension less than four.

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So they are super normal move. And this term shows that the Higgs particle,

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which is the fundamental particle asking the particle the first to be first fundamental scheme is to have been found.

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It propagates through the vacuum and sees everything in the universe, all particles that go through them through their mass.

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So, for example, it covers the top quark and gets a mass correction to its own, which diverges as the square of the cut-off.

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And this is not tolerable. The fusion would not make sense.

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The measurements are not make sense. If we can attain that quantity and you can see that the only way to do that

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is to have the aim of ordering TV so that the Higgs mass is within control.

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And then, of course, we have the opportunity to look for processes that might be new Windows beyond the standard model.

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Without actually having to construct large machines, we can get access to high energy scales through these real processes.

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And one of the ways to cure that problem is to invoke another symmetry between bosons and fermions,

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which contribute to the opposite sign to that divergent laws so that they cancel out.

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And that's called supersymmetry, which I'm sure you have heard about.

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But the race for finding these particles is very urgent, and we are definitely expecting the next run of the Large Hadron Collider in two years time.

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We'll either find them or show that we have been barking up the wrong tree and we

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are really the weirdest people in the universe that when you are proved wrong,

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we actually quite enjoyed. It's nice to be wrong. It's nice to be reminded that there are yet more wonderful ideas to discover, right?

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As long as somebody funds us to do these experiments.

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Now, the link to cosmology that I'm trying to highlight here is that this new physics provides candidates for new,

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stable particles in nature other than the ones that we are made of,

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the ones that we have lived with all these years, the ones that astronomers have been concerned with for most of recorded history.

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We now understand that dark particles, dark matter, dark energy makes up most of the universe,

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and their identity must be sought for a new physics beyond the standard model.

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And that, of course, is what physics will talk about following me.

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I also want to point out the biggest embarrassment we have in theoretical physics that

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there is one more term which is allowed by all of the symmetries that we know of,

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which is the vacuum energy of the theory. And as you can see from here, the scale is at least of order 1000 GB to the fourth power.

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That's a trifling matter of 60 orders of magnitude larger than the maximum that is tolerable from cosmology.

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So I think it's a safe understatement to make that we don't really understand how gravity governs to the standard model,

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and nonetheless, we have to pursue the goal of constructing quantum gravity where presumably the clue lies.

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We still do not have a clue. And that, again, is something which one might see.

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Weinberg calls it The Bone in our Throat, which I think is a rather apposite description.

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But it is also the beacon for the next generation of theories to attack.

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So I think we'll leave it there. So let me very quickly, in the remaining few minutes and through the general construction of cosmology, then again,

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we have some assumptions, except that these have not been as well tested as the standard model of particle physics.

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We assume the simplest possible kind of spacetime, which is called the Friedman Robertson Walker metric,

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after the people who first came up with it, which basically looks like the metric of special relativity.

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You can see the square minus square. You are familiar with that, except that this is not time.

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This is something called conformal time, because the metric is just a sheet of graph paper which allows you to measure things.

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But this graph paper, somebody's stretching it. And the scale of the graph paper we call the scale factor of DX.

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And that means that this innocuous little substitution means that all your information about how spacetime and booleans behave is now

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going to be examined because this gives rise to a dynamical situation where the scale of spacetime itself is changing with time.

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And that means I rather put it that way than, say, the universe is expanding, because that begs the question of what is it expanding into?

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And the answer is nothing. The metric is all that there is. Mathematically, we have to deal with the metric.

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We should not ask questions like, What is the universe expanding into?

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But we can certainly draw a picture of what I'm talking about, which shows us that the centre of the universe,

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where we of course belong and the Big Bang is this dashed line surrounding us.

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The radial direction is what's called redshift, which is, as you know,

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the movement of spectral lines towards that end of the spectrum, indicating that the scale of the universe is smaller and smaller.

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As you went out, it was infinitely small that thanks to this mapping, it is a finite surface here and a photon from the Big Bang,

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good sort of random walk there until it got to the point where the universe becomes transparent because it's expanding and becoming more dilute.

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And at that point, it can come straight to us and that.

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Typical structure on that last scattering surface, you can see,

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is such that only points which are about a degree apart, can be causal contact at this point.

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At this point cannot have been in close contact. And yet when you look at the sky, it looks totally smooth.

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And that raises fundamental questions about how that happened in the early universe around here, which we call inflation.

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And I'll talk about that in a second. But meanwhile, by combining this metric with this description of the dynamics,

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according to Einstein, which takes this metric, constructs objects from it,

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called the curvature tensor and relates them to the energy density of matter,

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which is the quantity here, coupled through Newton's constant that this simplifies it.

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This is very, very complicated, but it simplifies into a simple equation that an undergraduate can solve.

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And we do. And that can be written in terms of the energy density of matter, the curvature of spatial sections,

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and this cosmological constant which allows it, which allows for general coordinated invariance.

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We have to add it because we have to reflect the symmetries of the theory and that then describes itself into this simple equation here,

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which tells us how the universe evolves.

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And then when astronomers go out and measured the universe, we find that it is in fact in conformity with this.

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But it is very, very hard. It's not what we expected.

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Atoms, the stuff here made off with shine and emit light that are mainly in clusters of galaxies.

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You'll hear about that from David Moss. They are only 5% of the universe.

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We can take a good census from Big Bang Nucleosynthesis the formation of the elements and the famous 3 minutes up to the Big Bang.

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And that raises yet another mystery.

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There are no empty variants, although all the laws of physics that we know are pretty much symmetric between variants and antibody ons,

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and yet there are just no antiquarians. Okay, big mystery.

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Then there is the mystery of dark matter, which is about six times more.

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Felix Karloff would talk about this and you have plenty of evidence for this from gradation curves of galaxies,

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from gravitational lensing by clusters, from the formation of structure in the universe.

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[INAUDIBLE] talk about it in detail.

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And then we have evidence that most of the universe is in the form of some mysterious fluid with negative pressure,

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which is causing accelerated expansion that we see here in this Hubble diagram of supernovae in distant galaxies,

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and from observations of the fluctuations in the cosmic microwave background and the large scale distribution of galaxies

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that this we do not yet have direct evidence for that is inferred from that equation that you just saw in the last slide,

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which I have now written as the sum rule.

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So we measured this and we measured this, and from that we inferred that this guy is one minus point three -0, i.e. about 2.7.

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Okay?

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But all this raises issues about this new physics that must lie beyond the standard model in order to give us possible candidates for dark matter.

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And this, of course, touches on the cosmological constant problem.

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So I'm personally not yet convinced that it actually exists.

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We need to do further experiments, make more detail observations to find dynamical evidence for dark energy.

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But we certainly are able to do better when you go to the early universe, because the early universe is very simple.

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It's just a ball of radiation.

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The radiation comes to dominate over matter because as you go back to the universe, the energies of photons and other monstrous particles increase.

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Just as the rich shift, the universe expands the also redshift upwards when the universe contracts and therefore it takes over.

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And we are therefore able to construct a permanent history of the universe and

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put the energy scales that we know in physics on superimposed on top of that.

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So here is the transition between three quarks and gluons and nuclei, which is nucleosynthesis.

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Here is the transition between a plasma and a neutral atoms.

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That is the last scattering surface of the microwave background. And when you go back,

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these experiments at the at CERN have allowed us to extrapolate back to an

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unimaginably small time shortly after the big bang into the minus 10 seconds.

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Although our direct evidence stops here at about a minute after the big bang or maybe a second.

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But we do know this physics beyond that, however, is just extrapolation and speculation, which is fun.

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And that's exactly what we do, because we can confront ideas about new physics here with their consequences for the universe,

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and we can confront that with the data and ask if it measures up.

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Okay. So in addition to the Large Hadron Collider, we do need known accelerator experiments as well in order to throw light on this.

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And one of the most important of those is the picture that you have seen earlier,

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the picture of the microwave background, which is has been called the Rosetta Stone of cosmology.

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And indeed it is because it is those fluctuations that you see in the microwave radiation that go through gravity in.

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A sea of dark matter that dominates the universe to give us the large scale structure that we see today.

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And we'll hear more about it later.

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And the amazing thing is that our current picture of how those fluctuations arose is that there are quantum fluctuations

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as big as the universe of a massless field that came to dominate the expansion of the universe at very early times.

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Now, this sounds like a fantastic story, and obviously it needs to be demonstrated that this is actually true.

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But mathematically it holds together, even though, again, it impinges on this cosmological constant problem, which is as yet understood.

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But we do know this is in cartoon form, that that phenomenon can blow up a small universe into a large universe and explain

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that horizon problem I alluded to earlier as to why different parts of the sky,

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which could not have been causal contact, apparently were clearly in close contact.

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That's because we are assuming that the expansion did just go smoothly.

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But what if it had gone up exponentially at one time?

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Now, inflation is something those of you who work in the city are familiar with in a different context.

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We actually like inflation because it solves problems. It creates something called DC space, which is very interesting.

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Mathematically, it turns the curvature to zero, as is shown in this cartoon,

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and the microwave background shows that the picture is in fact that the spatial

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sections of the universe are flat rather than being positively or negatively curved,

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because then this picture would look different, and we know that the universe looks like that.

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So these are all magnificent achievements in delineating the nature of the universe,

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which have come to a real head last year with the release of this blog maps,

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which again you would have seen in the newspapers,

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people wonder what what the significance of that is that you understand when you expand it in spherical harmonics and you plot the power spectrum.

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And this power spectrum, let me just point out one feature,

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which is that the present universe and everything it contains would be contained within about one degree of that map.

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Okay. And that is why most of the fluctuations you are seeing in that map are on one degree scales.

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This multiple corresponds to one degree. Okay, these are all other universes.

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Of course, we don't see them because they are outside of Horizon now and we are of course inside of the universe.

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So it's kind of bit weird to try and think about it.

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And remember of course, that when we think of this micro photons coming to us, they're not actually coming to us.

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We get there as well. We everything we had made of everything that we know, it was all did in the same place.

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But it was going away from each other so fast that it has taken 10 billion years for that photon that started out right there to catch up with me.

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Okay. It's a fantastic thought and I try not to think about it.

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It's sort of it's sort of rather mind blowing to you over use a commonly used word.

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But we can actually test the theory of inflation by studying this pattern in some detail.

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And that's what our colleagues, for example, in astrophysics are engaged on, as are we,

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because those fluctuations, as I said, go into the large scale structure of galaxies.

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And I only have time to flash to this, which Felix will talk about later, which shows that the full spectrum of Galaxy clustering,

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measured from large surveys of galaxies using fancy techniques,

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is in very good agreement with the theory that I have presented to you somewhat sketchily.

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And I just have one word to say. This is to provide a lead to the talk by David Marsh that this inflatable field is meant to be a scalar field,

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which has its own potential, just like the Mexican hat potential you saw for the Higgs, which it evokes down.

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And then then it falls into the minimum, it oscillates there and it transfers this energy to ordinary particles of the standard model.

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It's just a problem. Undergraduate put salt book upward oscillators like two simple harmonic oscillators.

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And in that process you create the hot big bang that we know and love.

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And then these starts the history of the universe.

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And during this process, I have no time to explain how the fluctuations that are created of quantum fluctuations get

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stretched out to astronomical length scales and are then responsible for creating the galaxies,

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the clusters of galaxies, the silver clusters that we see today.

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So let me wrap up. We have this timeline that I already presented to you starting from today,

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15 billion years after the big bang, going back to the formation of galaxies, the universe turns opaque.

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At this point, we cannot see beyond that form because it's ionise and the electrons and protons are tightly coupled.

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But then there is the synthesis of the elements at 3 minutes, which created helium made stars possible,

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made life possible, and then earlier, still, we don't have a direct window, but we have physics.

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We have calculations on the lattice or computers which allow us to understand this transition,

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and we can also understand the electric phase transition now thanks to the discovery of the Higgs.

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But beyond that is speculation. And we don't know this physics.

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That's what you are engaged in.

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And as it says here, although we can account for a vast body of observations and I justifiably can be proud of what we have achieved,

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we should also be ashamed that we have no idea about this initial condition problems that we have thereby brought up.

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Why is the universe asymmetric between matter and anti-matter?

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What is the dark matter? How do you solve the cosmological constant problem and explain dark energy?

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This is what we are struggling with right now. And the journey, of course, is the reward.

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But I think since we are in the Danish drama lecture theatre and I came to Oxford 32 years ago to work with Denis,

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who in fact turned me on to this subject. That was the best professional advice I've ever had in my life.

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He said something which I'd rather like. None of us can understand why there is a universe at all, why anything should exist.

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That is the ultimate question. But why do we cannot answer this question?

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We cannot just make progress of the next simpler one of what the universe as a whole is like.

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So what I'm trying to say is that for us, the journey is the reward, and I hope we will make that clear in the talks to follow.

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Thank you.