Into the Impossible With Brian Keating - Do We Live in a Mirror Universe? Oliver Philcox (#292)

Episode Date: January 26, 2023

Also available as a video on Youtube: https://youtu.be/y0_ePN7c1gw What is parity and how can it be violated? A striking asymmetry in the arrangements of galaxies in the sky has been announced. If confirmed, the finding would point to features of the unknown fundamental laws that operated during the Big Bang. “If this result is real, someone’s going to get a Nobel Prize,” said Marc Kamionkowski, a physicist at Johns Hopkins University who was not involved in the analysis. Brian Keating and Oliver Philcox discuss the large scale structure of the universe and how enigmatic space tetrahedrons, drawn between galaxies, may map out some key features of the most poorly-understood phases of early big bang cosmology. Oliver Philcox is a theoretical physicist interested in statistical cosmology. He obtained his Bachelor’s and Master’s degrees in Cambridge’s Institute of Astronomy before spending a year in Harvard’s Center for Astrophysics. He is a Junior Fellow in the Simons Society of Fellows, hosted at Columbia University. More: https://www.quantamagazine.org/asymmetry-detected-in-the-distribution-of-galaxies-20221205/ Connect with Professor Keating: 🏄‍♂️ Twitter: https://twitter.com/DrBrianKeating 📸 Instagram: https://instagram.com/DrBrianKeating  🔔 Subscribe https://www.youtube.com/DrBrianKeating?sub_confirmation=1 📝 Join my mailing list; just click here http://briankeating.com/list ✍️ Detailed Blog posts here: https://briankeating.com/blog.php 🎙️ Listen on audio-only platforms: https://briankeating.com/podcast Subscribe to the Jordan Harbinger Show for amazing content from Apple’s best podcast of 2018! https://www.jordanharbinger.com/podcasts  🎧 On Apple devices, click here, https://apple.co/39UaHlB scroll down to the ratings and leave a 5 star rating and review The INTO THE IMPOSSIBLE Podcast. Other ways to rate here: https://briankeating.com/podcast Support the podcast on Patreon https://www.patreon.com/drbriankeating  or become a Member on YouTube- https://www.youtube.com/channel/UCmXH_moPhfkqCk6S3b9RWuw/join Learn more about your ad choices. Visit megaphone.fm/adchoices

If you had never seen the universe and I gave you A, the universe, or B, the universe that I'd flipped in a mirror, you wouldn't be able to tell which one was which. They both look statistically indistinguishable. And the reason that they should be indistinguishable is because primarily the universe is controlled by gravity, and gravity doesn't care about parity. Anything that's not parity symmetric in the universe tells us that some other force of interest going on. And if we were to see something like that in the universe on super large scales, it would tell us that something weird and new is going on that isn't just gravity. Welcome, dear listeners, to this episode of Into the Impossible with your host, Brian Keating and theoretical physicist Oliver Philcox. Be forewarned, this episode dives deep and may awaken latent curiosity and thinking at cosmological scales. Does the universe obey fundamental principles of symmetry?

Is there a hidden tetrahedral asymmetric geometry that could reveal details of cosmogenesis? How does one even begin to test theories at the scale of a million galaxies with billions of tetrahedro relationships? As Brian and Oliver stretch your imagination to new dimensions, please consider telling us what you think with a review and by adding an asterism of five stars to our ever-expanding galaxy. So for now, lean forward, listen carefully, as Brian Keating and Oliver Phil Cox discuss what could be one of the great cosmological observations of asymmetry in the universe. Any sufficiently advanced technology is indistinguishable from magic. Open the bud-bay doors, please, help.

So Oliver, what is parity? I'm used to hearing about that in the context, particle physics properties. What does it have to do with astronomy, of anything? Absolutely. So parity is fundamentally one of the big symmetries we think about in the universe. So fundamentally, this is the symmetry of mirror. reflections. So basically if something looks the same if you swap left and right round or reflect something in a mirror. So on a human scale the example is the human

body. If you look at it from afar you'd think okay humans look the same if you reflect them in the mirror you swap say that left and right shoulders but if you look in more microscopic detail you'd see when you do that the heart would move from one side of the body to the other. So a human on a human scale internally is not perisometric. So cosmologically this is also super relevant and in this case we're thinking not about reflecting a human in the mirror but reflecting the entire universe in a mirror if I say and in this case we actually expect that things should be symmetric so another way of saying this would be if you'd

never seen the universe and I gave you a the universe or B the universe that I've flipped in a mirror you wouldn't be able to tell which one was which they both look statistically indistinguishable and the reason that they should be indistinguishable is because primarily the universe is controlled by gravity and gravity doesn't care about parity so gravity is the same if things are moving to right or right to left and such. Anything that's not parity symmetric in the universe tells us that some other force of interest going on.

Like, say, on super small scales, we can get interactions from the weak force, which, as particle physicists have known since the 60s, does violate parity. And if we were to see something like that in the universe on super large scales, it will tell us that something weird and new is going on that isn't just gravity.

And have there been other credible, you know, kind of observations of parity violation in astronomical context before? Yeah, so it's an interesting question. So there's been a couple of different routes with which to explore it. So actually there was a famous one about looking at the directions of spins of galaxies, galaxy rotations, it's looked at, I think, in galaxy zoo images. And that was actually a particularly interesting experiment,

because they found out that most of the images, if I remember correctly what identified as it was kind of rotating towards the left, the spiral arm was moving to the left rather than the right. And that's this kind of parity asymmetry, left and right on equivalent. In that case, that was actually eventually put down to some psychology, and the human brain likes to identify patterns in one direction rather than the other direction. So in the end, that was incredible. But there have been some other kind of very intriguing things from cosmology.

One of the big ones is cosmic bio-referringence. So it's measuring polarization data from the cosmic microwave background. Right now, that's giving some sort of tentative evidence that might be something interesting going on. But exactly what and whether that will continue to hold up in future data is quite hotly contested at the moment. Yeah. In the late 90s, there was a famous claim of a detection of radio galaxy polarization orientations that were preferentially biased in one elicity state. In that case, it was left and right, circular polarization that were claimed to be asymmetric. And then the person who actually had the theory that would have predicted such an effect, Sean Carroll, past four-time guest on the podcast, he actually had the most to gain, perhaps Nobel Prizes. And he, he actually had the most to gain, perhaps, Nobel Prizes. And he, was one of the chief architects to refute this claim almost as soon as it came up in the late 1990s.

So these claims can be quite perilous, and that's why, you know, Mark's, you know, very, very, almost brazen for Mark Kamienkowski. So it has to be very, very interesting and provocative, hence your appearance here. So you have some wonderful images and slides that you were going to show. I wonder if you can share them with the audience and kind of walk through it. And my audience is, as you know, the brightest and the known. corner of the multiverse. So don't be afraid to geek out and I can get into the details. Fantastic. Great. So you should hopefully now be to see the screen. Yeah. Yeah. So just do a couple of details about this sort of work. And it's actually where these slides are from. I'm going to

discuss mostly the new stuff with galaxies, but also maybe comment a little bit more about this cosmic birefringents, which I just mentioned a minute or two ago, because it's still sort of quite hotly contested thing. So I think, obviously, to anyone listening to this, it's obviously an exciting topic to have made it onto Brian's podcast. And it made it into a couple of other science magazines, which is quite exciting. New scientists described the universe as surprisingly lopsided. And so that was about sort of the recent work. It's also this article by CITC Daily saying it's hints of new physics in the early universe. So it's obviously something exciting. And hopefully I'll be to unpack a little bit more about why it's exciting and what

could possibly mean. And also a little bit realistic. Do we think it's actually real? What else could cause it? Obviously, we need to be good scientists and think, is it new physics, or is it something we haven't thought about yet in our analysis? I think it's worth considering both of those pretty carefully. So I said a little bit about parity before. So I'll go quite quickly here, but so parity symmetry is symmetry if you reflect something, so left and right switch, as we've said. And one of the fundamental things about particle physics is that it doesn't have to obey parody symmetry, just as we said, the human is not parity symmetric, the weak force isn't parity symmetric, but generally everything we know about in physics, and the standard model is

charge parity time symmetric, or CPT symmetric. And this basically means that if you do an experiment and you flip left and right, but you also flip plus and minus, and you flip the direction of time, you end up having a symmetry, like stuff like the weak force surveys the symmetry. And you can sort of ask what would that mean in cosmological contexts? Well, for something like gravity, gravity doesn't care about charge and gravity doesn't care about time. So that itself means this CPT symmetry is automatically going to mean the gravity is going to be parity symmetric. So what I was alluding to before. So as I said, cosmology should be parity symmetric and the main manifestation of that is images of the universe which are flipped in a mirror, like this image

in the top and the bottom here, which is in fact I think a realization of the illustrious TNG simulations. These should be statistically indistinguishable. So I shouldn't be able to tell you which is which, if I hadn't seen them before. Obviously, if you have two next to each other, you can say, okay, this one's flipped version of the yellow one. But if I only had one of them, I wouldn't be able to tell you, is this the flipped one or is this not the flipped one? So a lot of the work in this has been to kind of ask the question, can we make any robust statistics and measurement tools, which are able to actually say, do we have something flipped or unflipped? Can we try and create a test for this whole parity symmetry? So I said parity violation exists in

nature. And it also exists, we think, in cosmology. So one of the big example of this is barrier genesis. So in this case, this is about the formation of a matter in the universe and how we have predominantly mostly barons and very few anti-barons. So we have mostly protons, very few antiprotons. We have electrons, not positrons, etc. And that itself is a slightly interesting process. So there's a really nice work by Yem Sakharov in 1967,

which basically said there's a couple of conditions in order for this sort of process to happen to be able to generate this anti-symetry. And one of the big conditions is that we, we need to break charge parity symmetry. So I said before charge parity time is a symmetry, but charge parity doesn't have to be. And that we need some process which breaks that in the early universe. And if it's something that doesn't care about charge,

that could mean it's gonna break parity symmetry. So the reason I bring this up is really to say that by virtue of the fact that we see matter in the universe and not antimatter, we already know some interesting parody phenomena are going on in the early universe. So it's not beyond the range of possibilities that we could have something interesting going on

that we could observe today, say in the distributions of galaxies or in the cosmic microwave. background. So in cosmology, where could we actually get this manifesting? So the formation of matter against antimatter is something we normally affixed to the super early universe. In general, there's actually a couple of different times that we could have some kind of parity-violating process. So cosmic inflation is one of the big ones, this hypothesized super-luminal expansion in the first 10 to the minus very small seconds, or 10 to the minus a lot seconds. But that's not the only option. We could also have things happening at the end of inflation, and where chaotic period could reheating,

we really don't understand well. And in general, in fact, these first two bullet points are not well understood theoretically. We have hints from late data about what the early universe did, but we don't have sort of good observational probes to it. And we're really trying to extract as much information as possible to try and uncover the secrets to this a little bit. The other option is something weird in the late time. So for example, some kind of modified gravity. Maybe we have some version of gravity which doesn't respect sort of things being invariant under left and right switches. So often when we do this, we actually require, some kind of vectors or tensors in the universe. So generally a lot of physics is scalers,

so whether that's sort of the temperature of the C&B or the number of galaxies, it's just a number. It doesn't have any kind of direction attached to it. And because these parities necessarily involve left and right-handed things, we often require some kind of left-and-handed elements in order to generate this asymmetry. So maybe we have some kind of vector field in the super early universe during inflation. The dynamics of that vector field could leave some kind of parity violation in the universe. So I'm just showing this graphic at the top. The green line is a left-handed vector field.

You can see the green lines showing the direction of the field are going left-handed round the line moving to the left. And in the bottom, the red panel here is showing the right-handed one. So if you only had just left-handed ones in the universe, you could make a measurement of parity because let's say I had a universe with just left-handed things,

and when I observed it, I only saw right-handed things. That would tell me that I wasn't looking at the original universe, I was looking at the mirror-flipped universe. because we know it should all have been left and it's now all right, etc. So that really begs the question, how do we look for this in data? So we need to find some kind of statistic which is different between the standard universe and the flipped universe. So measuring the sort of vector fields in the universe is quite a nice way to do this,

but we don't really have many vector fields, which makes our lives quite difficult. A lot of our standard statistics are things like power spectrum, by spectrum and the tri-spectrum. At heart, these are really giving correlations of particles. So they're saying, on average, how far apart are too, galaxies or on average how far apart are three galaxies or four galaxies and it's an interesting question about which of these are actually parody sensitive so which of these can tell us something interesting your summer starts now with Memorial Day deals at the home depot it's time to fire up summer

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book on Hilton.com or the Hilton app and save up to 20% to get the stay you expected. When you want savings, not surprises. It matters where you stay. Hilton, for the stay. I'll talk a little bit about scalar observables. So these, in particular, the main ones of interest are galaxies and C&B. There are a couple of other ones, like 21 centimeters and lines from the sort of metals absorbed in galaxies. But I'm mostly talking about these guys because they're kind of the big players in cosmology right at the moment in terms of data.

So the simplest we can do is look at something called the two-point correlation function. And the two-point correlation function is just the distribution of pairs of galaxies. So I pick two galaxies and I say, how far apart are they? Unfortunately, this doesn't really tell us anything. Because if you imagine taking a pair of points and you flip them, so you flip from the left, flip from A in front of B to B in front of A, they're still exactly the same distance apart. So here, parity is actually the same as just rotating my two points around. And the consequence of that is that there's no interesting signal.

So parity inversion and rotation are the same, which means my two-point functions can't tell us anything. So if we want to look harder, maybe we want to look at, say, three-point functions. So this is a little cartoon of what a three-point function looks like. We've now got three galaxies, and we're now asking the question, what shape do these three galaxies make? If I depict three galaxies at random, they're going to be separated by some distances, sort of the lengths, R1 and R2 here. What are those distances? And what distances are most or least likely? So we can play the same trick again here to think,

let's look at these galaxies on the left, and then let's just flip them in a mirror and look at the ones on the right. Do they look the same? And unfortunately, we once again have a problem, because in this case, flipping the diagram on the left looks like the right, but you could also imagine rotating the diagram on the left

and getting the diagram on the right. So if you imagine sort of taking your triangle, pulling it out of the page, turning it over and pushing it back in again, we have the diagram on the right. And this tells us that once again, the three objects, parity inversion and rotation is the same. Thus, if you're just, if you're going to be the same. the universe is rotationally symmetric, which we think it is, we're not going to see anything

about parity with a three-point function. So at this point, you can kind of guess where I'm going. To we just see anything interesting with parity, we actually need a four-point function. So this can either be done with a C&B, or also with Galaxy Surveys. It's a nice paper by Bob Kahn, some other collaborators of his pointing us out back in 2011. So in this case, you now have four galaxies in the universe, and you pick four at random, form a tetrahedron with them, and they form kind of this, on his shape shown in the left. here, when you flip it on a mirror, you get something on the right. And these are interesting because as long as the four points don't all lie on the same plane,

so as long as I can't draw them all on a bit of paper, parity inversion and rotation are physically different things. So basically there's no way to get from the left to the right diagram. So if I were to do something simple, like say, count the number of tetrahedra on the left and the number on the right, I can learn something about parity. So effectively I would say, I'm going to count the number of left tetrahedra, subtract off the number of right tetrahedra, and say, is the answer zero?

is the answer zero. Like obviously when you do this in practice there's all sorts of noise going on. We only have a finite number of galaxies so everything's kind of random, but you can sort of ask statistically do I have more left-handed tetrahedra than I have right-handed tetrahedra and is this a significant more? Is it much more than I expect simply from random charts? So that's really the essence kind of one of the big statistics of parity violation that we've been exploring of either with the four-point correlation function or the tri-spectrum, which does the same thing but slightly more furrow transforms involved. And so the C and B turns out. to be slightly better. I will briefly say the other thing which is tensor parity

violation. So if we have access to things in the universe that have directions as well as just numbers associated to them like polarization, we know that has kind of it's a tensor, it has two directions associated with it, or the shapes of galaxies, so called galaxy shear, or even the spins of galaxies. It's been some nice work on that recently. We can do a couple of different tests. And the reason for that, I'm going to go out a little bit wonky here, But when we have a vector or a tensor observable, once we flip something in a mirror, we also flip the directions in the mirror. So something that was sort of left-handed before we flipped it is now right-hand. And the consequences of that are that with a two-point function, we can now see parity violation if we have some interesting vector.

So the big consequence, the standard thing used here is the two-point function of temperature and polarization of the cosmic microwave background, the CLTB here. And this has been known about for quite a long time, and there have been attempts to measure this and from different sources. One of the main ones I've talked about in a little bit, birefringence is sort of quite interesting at the moment, has some interesting implications. So to summarize this bit, if I'm just looking at scalers, like number of galaxies or the temperature of the C&B, I'm forced to use sets of four galaxies or sets of four points on the C&B, which makes the computation kind of difficult. If I'm using vectors or tensors, I can just use two points, but that calculation still kind of is difficult, mostly because, because we normally need things like B modes, and we haven't made a good detection of B modes in the universe from primordial sources at this point.

Tell me about it. Although, of course, Brian knows a lot about that. Yeah, tell me. Okay. So, now let me talk a little bit about what we've actually seen. So the first observation, cosmic birefringents. So the credit to this absolutely goes to a bunch of people, I think, mostly in Munich, Aikirio Komatsu,

and the authors give another bottom here. So in this case, the authors looked at the correlation of polarisation, from cosmic microwave background. In particular, the correlation of E-modes and B-modes from the C&B. This is kind of a very difficult measurement to make, which is basically why we're seeing it mostly now, rather than when the Plunk data release first came out. The authors have been very carefully calibrating for every possible systematic and some really intriguing new methods for how they do this. But the result seems to we would get a signal, and we shouldn't get a signal if the universe is parity symmetric. Basically, anything with B-modes and something that isn't B-mode should always cancel.

So something weird is happening. So the hypothesis with this is that in the early universe, we have the C&B and it's parity symmetric. It doesn't have any weird physics. But as the little photon moves from the C&B, sort of 380,000 years ago, or 380,000 years after the Big Bang, until the observer today,

it interacts with matter going from early universe to the late universe, and the action of that is it rotates the polarization of the photon. So even though it was originally parity symmetric, some interesting rotation effects means that when we observe it, it's not parity symmetric.

If this is real, this would be super exciting. So it's rotated by an angle which is pretty small. It's about 0.3 degrees. And it's roughly detected, I think right now is about 2.7 sigma. There's been a couple of different analyses. This is one of the recent ones I think that Diego Palothwell has been. So what could be causing this? Well, in this case, it's possible that we can have the cause of an axion in the universe

connected to these C&B photons. So this axion is just sort of a weird scalar particle. It's existing in the universe and not really doing too much until it encounters the photon. And axions have a particular ability by what's known as the churn-simons coupling to interact with a photon and rotate its polarization, giving exactly the signal that we think we might get to see in the data. So this will be a simultaneous detection, not just a parity violation, but also of axions in the universe. We've never been into directly detect them, although a lot of theories are hypothesized. Unfortunately, there are complexities with this. So the major complexity in this case is dust in the universe.

So we've been talking about polarization rotation from axions. Unfortunately, we can also get polarisation, rotation and parity violating radiation itself emitted from dust. It's a little bit different kind of the standard CMB mode thing, because now we have to have parity violating stuff. But the galaxy has dust everywhere. It's not rotationally symmetric. It's not spatially symmetric. So it's very likely a priority that we could have similar sorts of signals coming from dust. So is this the end of the story?

Well, people don't really know. There's been a lot of papers saying yes and saying no. I think the most recent results say we need better data and we need better. understanding of dust. So in fact this plot here is showing you the sort of signal that we could expect from dust in some forecasts, some of the other ones I think, in black and in blue that measured signal we were seeing, that 0.3 degrees rotation. And you can see the dust kind of could be pretty important. It depends where we look on the sky, of course, and it's not at the moment totally well understood how we can separate out the two signals. So I think from my point of view at least,

right now it's exciting evidence that could suggest parity violation, but we really need better data and hopefully a future will tell us a lot more about that. Okay, so observation number two, this is the one that I've mostly been involved with, and I'll talk mostly from my side. But I'll say there's also parallel work done by Jamit Hu, and Zach Slippian and Bob Kahn over in the US. And this guy is all to do with these four-point functions. And in particular, galaxy four-point functions and has led to this interesting,

surprisingly lopsided claim from the new scientist. So what have we done? In principle, we simply counted up every set of four galaxies in the universe. And for each one have said, is it, does it form a left-handed tetrahedron or does it form a right-handed tetrahedron? And we said, do we have the same number of left-handed and right-handed tetrahed In principle, it's a little bit more technical. We do it as a function of scale, we do it as a function of shape. But in practice, that's really what we're doing. We say, do we have a left and a right-handed asymmetry? And the claim, which has led to some of these articles, is that

we do have an asymmetry. We're finding that the number of left and right-hand isn't the same. But when we square it, this number is considerably bigger than zero. And bigger than anything would expect just from random fluctuations. So I won't go into the big details of the actual how this is computed, but there's been some interesting developments, which I was involved with, one of the Oncore codes in particular, which allows this to be computed pretty robustly. But so, let's give me to the actual interesting bit. What have we done with the data? So we have, in practice, around a million galaxies to play with. These have all been observed by the STSS project, in particular the Boss survey, in the Barian Oscillation spectroscopic survey, I think.

And these measure galaxies kind of like those shown in the white and blue dots here. I think the white dots are really the main ones used in this analysis. And we can condense these into measurements of this parity odd or parity even four point function. So it contains two contributions. This one on the right here is the parity even contribution. So this is what happens if I add together the number of left ones and the number of right tetrahedra. So we would expect there to be a signal here. Gravity should give us some kind of signal.

We found it, back in the paper in 2021. That was exciting. It says gravity, in the parity, even bit, acts the way we think it should. These plots are notoriously difficult to understand. It's a problem because four-point function involves four different galaxies, and it's a tetrahedron, which has six different sides you have to specify. So you have to sort of collapse it all into one axis. This is just a snapshot of some of the data.

But really the interesting thing here is on the left, these points don't really go through zero. and they're not just random fluctuations that's significantly away from zero. And that's telling us that on the left size, which is very small-scale tetrahedra, and sort of about 20 megaparsects, or I guess 60 million light years in size,

we have some interesting gravitational effects. Oliver, can you talk about the computational, you know, input and output? It seems like, you know, a million people may think, oh, you know, that's big, but it's not that. But when you're doing the four-point, you know, higher fun, how many permutations, how many different combinations,

long, what kind of computer are you using? What are some of the details of this calculation? Don't be afraid to nerd out, as I say. Absolutely. Yeah, so I skip that slide, but let me actually talk about it. So it's actually a really computationally intensive procedure. So let's say I have a million galaxies. If I want to compute every possible tetrahedron of a million galaxies, that's a total of a million to the power four objects. So it's 10 to the 24 sets with these objects you see on the left here. And for each one, I have to assemble a tetrahedron, and then basically, look at all the different sides. So it's characterized by the six sides you can see here,

or if you prefer three lengths and three angles. Now, even with the best computers in the world, 10 to the 24 tetrahedron evaluations takes way too long. This would take, I think, of the order of many years, actually, possibly considerably more than that. So it's something that was just totally not possible, which was a little of a shame, because it seemed like a fun problem. But in the end, the actual method we use to evaluate this

uses kind of an interesting trick. I'm trying to sketch in this picture here. So the crucial point of this is that a tetrahedron contains four galaxies, and I can equivalently write it not as four galaxies, but as three pairs of galaxies. So if I tell you the galaxy at the bottom, I hold that one fixed, and then I tell you the distance to the second galaxy,

the third galaxy, and the fourth galaxy, you can go ahead and make up your own tetrahed. And the crucial point is that we can do all these independently. Basically, if I hold the first one fixed, I can then go ahead and count up every single second galaxy, every single third galaxy, and every single fourth galaxy,

and doing those all basically in parallel and all independent. And this is useful because at any point I only ever need to consider a pair of galaxies. And the number of pairs of galaxies is 10 to the 12, which is considerably better than the number of quadruplets, which was of the order of 10 to the 24. So once I got all those pairs of galaxies,

at the end, it's just a problem of assembling them altogether. And you can do this with kind of a bunch of tricks. In practice, what's actually going on here is we're utilizing a bunch of techniques borrowed from chemistry. Actually, everything is expressed in spherical harmonics There's a lot of really fun discrete maths going on. It's actually sort of quantum chemistry is where a lot of these techniques get borrowed from.

But suffice it to say you can do this, kind of recoupling all at the end to get out at tetrahedra. And then the computation actually is viable. So I think for the dataset used in these analyses, computation took, I think it's of the order about, I think it's about 100 computer hours. And this was primarily done on a supercomputer in Princeton and Princeton University. Of course, we have to do this not just for the data, but also for a whole whole. load of simulations. So we had to do it for a thousand simulations as well. So in the end, it's more like 100,000 CPU hours, which is starting to get a little bit more costly, but significantly less than doing this for all the 10 to the 24 galaxies. So I guess 100,000 times

10 to the 12th would be the extra time we'd need. That's probably longer than, it's probably longer than the length of my career, put it that way. So your great grand, great daughter can work on this. Yeah. Absolutely. Yeah. So basically, it's quite a lot of work needed to get statistics, but we're now in the point that we can do them. And with the sort of advanced computing power that we're now getting, things like GPU power, we can actually do this considerably faster. It's things like putting all these calculations on GPU rather than a CPU probably allows this to be sped up by perhaps an order of magnitude. So maybe instead of 100 hours, it's going to be more like 10 hours. And that would be super useful in the future as we have more

and more galaxies. So if we have 10 to the 8 galaxies instead of 10 to the 6, then this 10 to the 12 becomes I guess 10 to the 16, which is 10,000 times harder. So at that point, we really need to throw in all the computational tricks we can, which sort of be working on doing it. Great. So I said a little bit about the parity even four point function, so the stuff we already understand. But what can we say about the parity odd four point function?

So this is just looking at the difference between a left-handed and a right-handed tetrahedra. And I should just say, there are sort of fundamentally good ways of establishing what a left and a right-handed tetrahedron is. It's actually to do with some sort of basic, vectors and the left and the right-handed rule. If you want to be technical about it, you take the distance to the three galaxies, you do a triple product and you see if it's positive, it's right-handed, and if it's negative, it's left-handed. So we can do this in a

fundamentally good way. But this is some of the data. So I'm only showing you a little fraction of it. It's actually about 20 plots like this. Again, they're a little complicated to interpret, but on the left we have small scales and on the right we have large scales. And what you can see is a whole jumble of stuff. Like the sort of bands here are results from simulations. So these simulations don't have any weird parody-violating physics in them, because we didn't put it in, but the data possibly could do. And the data are little points in blue and red here, which are from two different areas of the sky, one in the north, one in the south. So from this plot, you can't really tell if the contributions are zero or in fact one zero. So we're going to need to do

some interesting statistical analyses to try and work this out. And a lot of the statistical challenge is that we have order like a thousand data points. We started off with a million galaxies and then we measured the distribution of tetrahedra in a thousand different bins. And each bin is telling us a different configuration of different side lengths, for example. So it's hard work, about a thousand objects. It's very high dimensional. Each of these different data points is super correlated with each other, which makes our life significantly more difficult,

because we have a lot of, basically, there's different ways you can write down a tetrahedron. You can say one tetrahedron, you can then flip it around to a different shape or different sort of just rotate it, and it looks like a different object. It's got different side lengths. Maybe the first side length is now the second one, etc., because I've rotated it around. But those tetrahedral are the same.

And in practice, this just gives us some complicated correlations in our data that we have to be able to deal with. So kind of the standard approach is to do kai squared analyses. This is what's done a lot in particle physics and cosmology as well. So you basically take your statistic. You try and work out the noise in the statistic as given by its covariance matrix. So this is just saying if I would have totally random fluctuations in my data, how correlated would those fluctuations be? So what sort of signal would I get on average?

What be the square of that signal on average? And I just put them together in a combination that this guy, should be able to be modeled by some basic statistics. So it's kai squared, should follow a kai square distribution. Of course, the devil is a little bit in the detail of this. So one of the complexities is that we need to be able to model this covariance, so the noise fluctuations. And we basically have two ways we can do it.

Firstly, we can do it from theory, so we can scratch ahead and do some pen and paper theory, or black, wood and chalk, whatever your preferred theoretical method is. This has been done. It's a nice paper led by Jarmine Hove doing this last year. However, of course, anything we do analytically comes with assumptions. You have to make assumptions about how the universe behaves on large scales and what terms we put into our theory. The other option is we can do it with simulations.

So we can say we have a lot of kind of good guesses of what the universe might look like. So each of our simulations is a thousand galaxies in the universe, in a position they could be. We've just sort of taken the universe from its earliest moments and evolved it, and at the end popped in some galaxies, and we measure this thing from every single simulation. And we could try and use this to get out the covariance. out the covariance. This has somewhat different assumptions. We don't need to assume that we can understand everything on paper, but we do need to assume that the simulations are accurate enough,

basically saying, do the simulations look like our own universe? There's a second assumption, which is whether this likelihood is actually Gaussian, or whether this kai squared is kai squared distributed. So this basically comes down to how correlated is the data. We generally like to make some nice simplifying assumptions on likelihoods and statistics. This actually might be a scenario when things could possibly break down, because everything's a bit high dimension. So let me now show you the result. So this is the result from one of the papers, John and Hoves version, which is showing you the expected distribution in this black curve here,

and in the orange, what we got from the data. So basically we made this measurement of kai squared from data. We then said, does it match a theoretical expectation? And if it doesn't, it's telling you there's something weird going on with parity in the universe, which would be stretched. So this technically is about 7 sigma. 7 sigma is way past the physicist's 5 sigma. So immediately somebody should be.

getting a noble prize and everything should be great. Unfortunately, things are never quite that easy. So it's useful to think, we think about different ways to process the data. In fact, there was another analysis that was done by me simultaneously, which is actually doing things in a little bit different way. So the previous analysis was doing things by assuming that we understood the covariance and we could model it with our pen and paper theory, a lot of equations. That's really pages of equations, quite a painful calculation, actually.

The second approach was saying, I'm going to base everything on simulations instead. instead. So this makes slightly different assumptions. We assume slightly less about the statistical modeling. However, we do assume the simulations are accurate. And this plot on the right here, I'm showing you the statistic we get from our simulations and what we get from the data, so the red line. So once again, we're seeing that the red line doesn't really fit with the simulations. In fact, it's larger than 2040 out of the 2048 simulations. So tentatively, we have a detection of something at 2.9 Sigma. It's significantly less than 7 sigma, because we made fewer assumptions. But it's a lot of still something interesting. So what are the implications of this? Before I say that, I should

just say, let's, we should dig in a little bit more about the differences between these two approaches. So 7 sigma versus 3 sigma is obviously very different. So the kind of two things that could be causing it is really what I mentioned before. First that I likely it might not be Gaussian. Got a lot of correlations going on. Things are in a lot of high dimensions. Quite difficult to model it. And secondly, maybe our covariance isn't adequate. Now I'm not going to say that one of these approaches is right and the other one is wrong. I think the fact that different approaches get different answers tells us that we have to be very careful, tells us that at least one of them isn't perfect. Now maybe our covariance with

pure theory wasn't accurate, but maybe it's not accurate with simulations either. However, we are still seeing an interesting result. And I want to say a little bit more about what could possibly cause that result. So I said before, we can have something interesting going on in the very early universe, maybe in inflation, or we could have some interesting physics in the super late universe, for example, with modified gravity. So inflation tends to be the easiest scenario, basically because in the In the inflationary period, we really don't have a great idea of what's going on. We know lots about what isn't going a lot going on, but we do know everything's happening,

super high energy, super high temperatures, so effectively we can add as much random new physics as we want, as long as it hasn't already been constrained by something, we can try adding it in and seeing if it can be detected in that data. In the late universe, we have to have some kind of modified gravity, but this modified gravity has to be important on very large scales, because the minimum distance between the galaxies in these analyses I was talking about, was about 20 megaparsecs, or about 60 million light years. And that's actually quite a large distance, given that since the very early universe, our galaxies have moved a bit, but they've only really moved about 20 megaparsecs since inflation,

so about that minimum scale. So some kind of modified gravity would have to have really important effects on very large scales. We don't quite have a great idea of how that would work right now, but of course there's always sort of different ways that you could come up with that could potentially do this, I'm sure more will be explored in the future. So that brings us to inflation. So I'll skip the technical details here because inflationary modeling gets a little bit complicated. But basically, there's a bunch of theorems that says,

with our simplest model of inflation, we wouldn't get anything interesting, violating cosmic parity. However, if we have more interesting inflation, we could do. So, for example, if inflation depends on scale, or basically how evolves in time, or if inflation involves multiple particles. It's like we often like to think about it as just a single particle in the universe, sort of just as the universe happily super expands or single field. If we have other ones with different spins, for example, this could give us something interesting.

Or if even inflation happens in a slightly different way to what we thought about, something called ghost condensates. And of course, there's a bunch of other things. So actually, this is led us thinking with a couple of colleagues down in the Institute for Advanced Study in Princeton, in particular Giovanni Kibas and Misha Ivanov, about whether we can kind of learn something interesting about inflation from this day. Like we've made this tentative detection of something. Could we use this to make a stronger detection of,

a particularly interesting form of new physics. In general, if you're just trying to make a detection of, do we have parity violation? Yes or no. That's quite hard. But if you're trying to make a detection of a specific model, you can in general do much better, basically because you know where to look in your data.

Your model says, maybe large scales are most important, or small scales are most important. So, you basically focus your analyses on those regions. So again, I won't go into details, but two of the, I'll just say briefly, two of the interesting things are exchanging a spin-1 particle during inflation. So this means inflation,

In inflation, I don't just have a scaler. I also have a vector going along. Basically, we've been able to use this data set to do quite a few very interesting analyses, and in particular, try and work out if we can find any evidence for specific models of parity violation in inflation. And right now, the situation wasn't quite as promising as we might have hoped.

Every model we've tested, we don't detect. So I think we tested a total of 18 models so far, and all of them return values consistently zero. So we try and detect the amplitude, like this one shown on the right hand side here. You can see it's something very close to zero, across the zero. So at this point, if the signal is real, it's eluding us. So let me just conclude a little bit with what actually, what my thoughts on what this signal could be are. So it could be something new and exciting in the universe.

And as Mark Kermakowski was saying, if this is true, this would be incredibly exciting. It would tell us that weird new physics in the universe is going on that we don't know and that we haven't already hypothesized. Simple models we have hypothesized don't seem to work. So maybe it's some other model of inflation that we haven't thought about. Some model of late-time physics, some kind of modified gravity, or some other interesting physics happening in a different time that we at this point just haven't thought about. Of course, there are, however, non-cosmological options,

and it's possible that we have errors in how we analyze the data, or errors in how we do the analysis. So I did say a little bit about whether our simulations or our theory is good enough. I think that's something that definitely needs to be explored more in the future. So to me, the kind of status of this right now is, we detect something, detecting something very interesting. And in the future, we're going to get a lot more data. So we're going to have results from the dark energy spectroscopic instrument,

which has been observing millions of galaxies and it's going on right now. So that's going to give us a huge big data set, which we can look for the same thing in and see, do we see it? And hopefully we're going to see it much better because the data sets a lot bigger. And also we can look at other things that aren't galaxies. So for example, the cosmic microwave background is another option. So that's something I've been considering a lot of the moment to say, let's look at the C&B temperature.

If we see the signal there, that would confirm the galaxy signal with a totally different set of assumptions. And really, if we were to see the same thing in both things, this would be great. This will be pretty good evidence that something interesting is in fact going on. So as with ever, as with all things, the time will tell. I'm very excited to see what the future is going to bring. And hopefully we will know pretty soon. Absolutely. Well, this has been really phenomenal, absolutely crystal clear.

You can stop sharing the screen. And I'll have links to that, the presentation. and other work that Oliver works on in the video description below. While you're down there, leave a thumbs up if you'd like to have in a comment, if you'd like to have Oliver back on the channel to discuss his other work, massive uvra, as they say. It's been really delightful following the progress, and I would love to have you back in the near future after you go to Stockholm.

But even before you go to Stockholm, that would be wonderful. So we can talk Oliver Philcox of the Simon Society of Fellows, of Cambridge, of Columbia University. and I hope we can meet up in person. I'll be there probably later this year. And I'd love to meet you in person. Maybe I'll do a part two in person and have even better audio and visual delights. Signing stuff.

Thank you so much for having me. This has been great. And I'll have links to follow you on Twitter and everywhere else. And yeah, let's stay in touch. This has been so delightful. Thank you so much, Oliver. Have a wonderful rest of your day. Bye.

You too. Thanks for listening to this episode of Into the Impossible with host extraordinaire Brian Keating, please leave us a review. Brian loves hearing from you. For a chance to win your very own piece of an exploded star in the form of a meteorite fragment, subscribe to Brian's mailing list at Briankeetting.com. To fully appreciate Oliver Phil Cox's work, see the video of this episode, which includes his detailed slides on Professor Keating's YouTube channel, Dr. Brian Keating, that's DR. Brian Keating. Remember, always be curious.

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