Redshift is the diagonal radial coordinate. It's the same as conformal time, effectively. But this is a log scale. So all the cosmology that we do is typically done within redshift of a few, thanks to the JWST, we can look out up to about 10.
or 20. And if you go further, you get to the point where the universe becomes dense enough, because it's getting smaller as you go out. So remember, because of the spherical geometry, as we look out, the universe is getting bigger and bigger, but after you cross the equator, it's getting smaller and smaller.
And that is how we can reconcile the fact that the universe was small and dense in the past with what we see out in the sky. This is non-Euclidean geometry.
And by the time we get to a red shoot of a thousand, when the scale factor here was a thousand times smaller than today, the universe has got 1,000 times hotter and hot enough to ionize hydrogen, and therefore, after that, it's filled with the plasma, and light cannot come directly through there, it just random walks.
After leaving the initial singularity, but by the time it gets here, it is free to come to us.
And you can also see interesting things from this figure, such as the two photons whose light goes just about intersect each other in the past singularity, are separated by about a degree on the sky. So if I look at the microwave background, I should expect to see fluctuations.
On the scale of a degree, because that's the maximum size that can be causally connected by astrophysical processes. Anything beyond that would have to be an initial condition.
Now, I've spent long enough on that plot, but it's important to kind of get that picture down. Otherwise, the rest is harder to make sense of.
Now, we have to, with this metric construct the usual objects in Einstein theory, the Riemann tensor, the scalar curvature, etc. All that's on the left hand side, and we can relate that to the energy momentum tensor through Newton's constant.
It's passing the UID. Now, the interesting thing is this that.
This keeps happening. Sorry, I think I need to move the pointer here, right?
Yes. No. Yes. So these new and new run from 1 to 4.
So you might think there are 16 equations, but in fact, the energy momentum tensor, all the tensors are symmetric because, for example, the distance between me and u is the same as the distance from U to me. So there are only 10 independent equations.
But thanks to the simplification afforded by this metric, the collapse into just one equation, which is called the Friedman-Lemeth equation, and that relates the rate of change of the scale factor with time, which is called the Hubble parameter, in terms of the energy density of matter.
The curvature of spatial sections, and something called lambda, which I'll come to you in a sec.
So given this equation, I can relate it to the Hubble parameter at the present day and parametrize these in terms of the fractional contributions made to the critical density here in by matter, by curvature, and by lambda. So I define these 3 fractional contributions, omega matter.
Omega K, omega lambda, and physically, if I divide through by it squared, I get a sum rule.
These three components sum up to one. And that is the essence of the standard cosmological model. It's this very simple sum rule with only three terms. Why? Because of the assumed homogeneity and isotropy, which means there are no other terms.
Now, what is this lambda? Well, there is a term on the left-hand side of the equation, which is allowed because then general relativity, there is local coordinate invariance, and to reflect that, you're allowed to add any term arbitrary number.
Multiplying the metric to the left-hand side. However. Bit later in the 1930s, when it was realized that this energy momentum tensor, which was being used to describe non-rativistic particles, dust.
That it actually… that dust, those particles, are actually excitations of quantum fields. And quantum fields of zero point energy.
And it turns out that that zero point energy, because of the requirements of Lorenz invariance, it has… the vacuum has to be the same as seen by any observer.
It has also the same property as this cosmological constant on the left. It multiplies the metric. So now you have two terms, one from the geometry and one from the energy momentum tensor, and they add up together to give what I have called here capital lambda.
To distinguish it from the geometric lambda on the left-hand side. And it is that capital lambda that enters the Friedman equation in terms of this omega lambda, which is lambda over 3 times h naught squared. H0 is the rate of expansion today.
And at this point, you should start… already start thinking about what this would entail when you start making observations, but I'll come to that in the next slide.
I should say that this editorial momentum tensor, the vacuum energy, it has to be, as I said, the same to every observer, and therefore its pressure has to be the negative of the energy density, because the energy momentum tensor has to be diagonal.
And what that means is that if I look at the second equation, the second equation is a simplification of what's called Rajodhiri's equation. The gravitating amount of matter in the universe is not just rho, but it is rho plus 3p because p is.
pressure. It's kinetic energy which also gravitates in Einstein theory. And if P is minus of rho, then you can see this whole thing is going to be negative, and that collaborates with this minus sign out here to make the acceleration of the scale factor positive.
So you'd expect that in any universe with the lambda or vacuum energy, you would get acceleration.
And lo and behold, that's exactly what was found some years later. This was, as I like to say, an accident waiting to happen, because that is the structure of the model in which you're going to interpret data, and it already contains in it all the necessary ingredients to give us non-zero value of lambda.
So we have data from the cosmic microwave background from type 1a supernovae and from features in the correlation function of galaxy clustering, such as these little waves that you can see which are called baryon acoustic oscillations. They are exactly the analog.
of the oscillations that you see in the microwave background 9th power spectrum, which are most prominent on a scale of one degree, as I pointed out earlier, and which… well, you can see the spots with your eye here. And this tells us the position of the spot.
Is of this features is proportional to square root of omega K, so it tells us that omega clay is close to 0 from the microwave background.
The type 1a supernovae give us the difference between omega matter and omega lambda, this combination of these 2 quantities. And all these other measurements, like the baryon traction in clusters, BAO, etc. They tell us that omega matter is something like 0.3.
So now, if I put all these things together, then I have that omega lambda is one minus omega matter minus omega K is about 0.7. And if you remember what the definition of omega lambda was lambda over 3 h naught squared. This means that lambda has a value.
Set by the present-day Hubble parameter square. Because I'm using the sum rule to derive it.
So it is neither fundamental nor a constant, but it is what determines lambda as I have defined it in this framework.
And this is usually shown on this so-called banana plots with omega lambda here, omega matter here. The condition that omega K is 0 is just the diagonal line that says the 2 add up to one. And the supernova constraint is orthogonal to it.
And then you have the constraint from this matter, and they all coincide nicely at this point, and therefore you say that that is the standard model.
Except that… From a fundamental point of view, this is having to buy the assertion that the universe is today dominated by a lambda of order H0 square. H naught is 10 to the 28 centimeters. So in energy units it's 10 to the minus 42 Ge.
Not a scale that you have encountered in any fundamental theory. And… The value of the energy density that is assigned to this is actually this lambda over 8 pi g. We write it in Planck units to get it as a energy scale to the fourth power. And that turns out to be 10 to the minus 12 GED.
Or 10 to the minus 3 electron volts, which is not coincidentally the temperature of the microwave background. Okay, this was all kind of put in by hands on the back. But people often look at it and wonder how come you got such interesting number. It's actually just the geometric mean.
on the plant scale, which is 10 to the 19 GeV, and H0, which is 10 to the minus 42g, right? These are the only fundamental scales in the problem. There are no other scales.
So, you have to now accept that we are seeing a fundamental vacuum energy at a ridiculously small scale, nothing to do with any fundamental theory. And those of us who are concerned about this then do wonder.
Are we inferring this simply because this is the only scale in the problem? It can't take on any other value.
And H naught is, of course, imprinted on every observation we make, because it sets the distance ladder. It enters into every cosmological data.
Now… Some people at this point might be thinking to themselves, haven't I heard talks by lots of prominent people saying that the microwave background, the precision data from Planck has established this model beyond doubt?
Well, here is the plant data. These are the fluctuations mapped by plant, and indeed you get a nice fit to the fluctuations, and from that they extract various parameters which are listed in this table from the Planck paper. So you have the baryon density, which is the ratio of this to the bottom here. You have the cold dark matter density, which is the ratio of subsequent peaks.
You have the optical depth to last scattering, you have the, you know, lots of other parameters. But my point is.
I want you to show me where is the entry for lambda in this table.
There is no entry for lambda, because lambda is not actually measured by the Cmd. Lambda at the time of Cmd decoupling was the redshift was a thousand, so the matter density was 1,000 cubed greater, but lambda was the same. So it was.
10 to the minus 9. It was a completely negligible effect on the baryonic acoustic oscillations that we see. Now.
We inferred lambda from the CMB by making measurements of omega matter and omega curvature. We don't actually measure it directly.
Uh, for the cognition here, there are… it is in principle possible to direct a very faint effect. So these fluctuations are of order 60 microk. The microwave background temperature is 2.7 degrees K.
There is a very small correlation between the CMB and large-scale structure at the level of 0.5 micro K, which is caused by lambda. But that has not yet been detected.
Now, very quickly, I'll remind you of what the expectation for lambda is in the standard model, just so that one can see how odd it is to infer it from possibility. So of course, we all know and love the standard model, and we are now.
not so ambitious as to say that it is everything there is. We accept it could be an effective field theory, valid up to some scale, capital M, which is at least as high as 10TV, since you haven't found anything new at the let's see so far.
And we know all about the gauge fields, we know about how the fermions couple to the Higgs field. We are in the process of trying to measure the Higgs potential at the LHC and so on. And of course, we know that we can accommodate new physics into the standard model.
Uh, like barrier number violation, or electron number violation, etc, by adding other terms which are damned by powers of this cutoff, at which the new physics arises, so they can be naturally small, they'll decouple.
However, what people don't talk about much, because they're embarrassing, are two terms that you can add to the standard model Lagrangian, which are dimension less than 4.
And one of these is the notorious Higgs quadratic mass hierarchy problem, which is that the Hays, if it is fundamental, will cover to everything in the vacuum, including in particular, the top quark, which is actually heavier, and its mass correction from.
do stack coupling. diverges quadratically as the cutoff.
So this is embarrassing because it's 125 GeV, and it ought to be a lot heavier if M is higher.
Now, the way we attempt to solve that, as you all know, is either to argue that there is a whole set of super partner particles whose corrections should be of opposite sign, and they would cancel that one and leave all the logarithmic correction.
Just as happens with the electron, whose divergence is canceled by the positron, and you have only a log correction log of M, which is small enough that it's under control.
But that possibility has not unfortunately, been realized yet, as far as you know, the other option is to make the Higgs composite just like a pion, and then there is no quadratic gravigence. But that also has not been so far seen in the data.
So, the first term here that I'm going to focus on in this talk is even more embarrassing, because that is the scale of the quantum fluctuations in the standard model.
Now, to be precise, we can't actually calculate vacuum energy, can only calculate differences in quantum field theory, not the absolute value. But the absolute value does couple to gravity.
And order of magnitude, its case should be of order n to the fourth, and what that means is that the expectation for this thing, however conservative you are, is at least 60 orders of magnitude higher than what the astronomers are telling us the vacuum energy is.
And what this means is that when the universe cools down from a high temperature, when you get down to a TV scale, at that point, the thermal energy is gone. The only thing that is left is vacuum energy, and if it really did gravitate, it should have sent the universe off into.
expansion forever, inflation, or if the sign of this thing is negative, it will recollapse. Actually, in Qfgt. We can't even calculate the sign.
So if you read an astronomy textbooks that this is the biggest mistake in theoretical physics, or something has some distinguished colleagues have called it, it's complete nonsense because we can't calculate it. So you can't predict it. But nevertheless, it is an embarrassment.
is a serious embarrassment, so when Pauli realized it and Zeldovich back in the 30s, Paoli actually said in the Handbook of Physics, which I have looked up now, that, uh.
But I think it's gone again. Just one second. Oh, yes.
probably writes in the Handbook of physics. As is obvious from experience, the 0 point energy does not produce any gravitational field. He was, of course, at the time talking just about electromagnetism, but it holds will bells on when by the time you get up to other gauge fields.
So this is not supposed to happen in general relativity. So we don't understand why this vacuum energy should not couple to gravity. But that's the statement is as given here. If it gravitated, we would not be here talking about it.
And yet, because we brush that problem under the carpet, because nobody has found a solution to this problem.
And because it doesn't affect anything you do in the lab, so, you know, it's reasonable that we should forget about it and get on with doing what we can do.
But that problem was still there, and it was waiting for the astronomers to come along years later and find lambda in their data, and then interpret it as vacuum energy, and then start this whole business of the standard cosmological model without ever solving the original cosmological constant problem.
So I think I have said enough to indicate where I stand on this. I cannot believe that Lambda can be of order H0 square, and I think it must be an artifact.
So, how do you proceed? Oh, I should mention, then, you know, many of you like doing precision experiments, that people would expect some change in the theory of gravity at the spatial scale that corresponds to that energy scale of dark energy.
Which turns out to be about 100 microns. And people have been doing very elaborate Cavendish balance style experiment.
To try and see… If there's a departure from Newtonian gravity, you can, for example, parametrize it by some kind of like coupling with some coefficient and the range. And here is the coefficient versus the range. And this is the scale where you would expect to see something happening.
But the coupling has already been limited to being below a tenth. I think this is a few years ago. It has really gone down more by now. Basically, there is no indication for any change in the theory of gravity, as you might expect.
If that dark energy is something to do with gravity.
All right. This, by the way, also applies to lots of mechanisms that have been suggested. Thousands of papers have been written suggesting that gravity is somehow screened by matter, and so on, so on. No evidence for any of that.
So why do we still believe in the Lambda Cdm model?
Because it gives a nice description of the formation of large-scale structure in the universe, starting with those fluctuations that we saw imprinted on the CNB, which we ascribe to some prior period of inflation. Although I should mention that Edward Harrison, who I referred to earlier.
was at this lab. Harrison and Zeldovich have a spectrum named after them, because they said, in order to create structure as we see it, we must have equal power in the fluctuations, in equal logarithmic intervals of wave number.
And that Harrison-Zelovich spectrum predates inflation by 30 years. The reason why inflation became popular is because it naturally provides such a spectrum of fluctuations from a ruling scalar fee. But inflation is subject to the same cosmological constant problem that I have been.
moaning about for the last 15 minutes. So, you know, all this is basically make it up as you go along, because it all fits. But we'll have to yet determine if it is… any of it is correct.
But given those fluctuations, they can grow under gravity to create the structure today.
It just needs one new ingredient. You need about five times as much dark matter as ordinary matter, because otherwise the range in redshift from here to here is just thousand. The fluctuations grow proportional to the redshift, so they can only grow by a factor of 1000.
And they would not be strong enough to match what is seen on the sky. So you need them to start growing before the universe had become transparent. And for that, you need some matter to support that growth, which doesn't interact with radiation.
So, if you allow me 6 times as much dark matter as there is baryonic matter, and some mechanism that has created a Harrison-Zellowitz spectrum of fluctuations, then I can describe the present universe. But that's not bad going. So you just need to.
new ingredients. Now… at least from this point of view, we have accepted that we have some working model of how structure formed, and that the universe is inhomogeneous, and sure enough, if you map the universe, we are at the center of this picture. It is very homogeneous. This is a plot.
Of the distribution of visible galaxies around us, we can't, of course, see the dark matter. And what is plotted here is the peculiar velocity. So, there is a velocity proportional to distance, which is the Hubble expansion, but then you also have, because of the homogeneity.
You have local velocities, which had nothing to do with Hubble expansion. For example, Andrometa is not even going away from us, it's falling towards us. It has a blue shift, not a red shift. And that's because we are bound together in a dance that will end in 5 billion years.
These fine lines are measures of the velocity which is plotted here, and this is also important, I should remark that all measurements are typically made in velocity space in redshift space, to transform to physical space, you need to know.
the scale, which is the Hubble parameter. If you go out further, this is about 200 megaparsecs. Megaparsec is million parsecs. A parsec is 3.3 light years. If you go out to something like 700 megaparsec, that is the biggest survey done. The Sloan Digital Sky Survey, and you see that web of galaxies you saw in the simulation.
All that fits. But this raises various questions. Are we justified in approximating this universe as homogeneous? Are we justified in assuming that we are at a typical point? Does it not matter if I'm in a dense region or an empty region? Surely my past light cone on which my observations are coming will be quite different.
In the two cases. Does it not matter what direction I'm looking at? Because you can see just from this picture, there's clearly a gross violation of isotropy.
Now we have to make measurements in order to test these ideas, because these questions are not asked in the literature. Now we are flowing towards this super cluster called Shapley, and the idea is that that's because there's some big lump of matter that is pulling us.
If that is the case, then our velocity should drop off as roughly 1 over r as we average over larger and larger volumes, and it should basically go too close to zero when we get to the scale of homogeneity, which in the standard model is around a couple of hundred megaparsecs.
Shapley is at about 160 megapascals. So is our peculiar velocity falling off as 1 by R?
Well, we do know that we have a particular velocity because when you look at the cosmic microwave background, we see this yin and yang sort of figure, which is what you expect if you are an inertial observer moving through an isotropic radiation path.
at some velocity, this temperature difference is about a millike. So that means your velocity is also of order 10 to the minus 3 of C. And in fact, this was predicted by Stewart and Sharma, because they knew that we have a peculiar velocity.
And it was indeed found. And Peebles and Wilkinson gave that formula for how the temperature should vary on the sky, which is today special relativity exercise for undergraduates.
But in fact, we are not moving at just 370 kilometers per second, which this indicates we are actually moving at twice that speed. But as it happens, we are all… because we are moving backwards in the galaxy, we are also orbiting around the center in the opposite direction to this red spot.
Therefore, half of that velocity is canceled out. So real motion is 620 kilometers per second, which is shared by the local group of galaxies, including Andromeda, as it shows here. And we are all moving towards what was called the Great Attractor.
So the game is to find the great attractor which I'll give you the spoiler alert has never been found and nevertheless, we persist in.
Analyzing old data according to this model, in which you should converse to the frame in which the micro background is isotropic by averaging on scales larger than about 100 over 8 megaparsec. All distances are… have this H inverse.
Because that is a quantity that determines the physical scale related to the redshift scale.
So, do we, in fact, converge to the CMB frame by doing averaging? Well, here is a plot of all the data accumulated in the last 40 years, showing the bug flow, our local velocity as a function of the averaging radius.
So there are some technical details you have to say, whether you are averaging on a top hat or a Gaussian, etc. Never mind. The point is that this purple line is the expectation from the standard model, and these are the data.
So locally, things seem to be nicely consistent. But as you go further out, the C. 11 was actually our work using type 1 and Subandra V. It seems to be getting discrete at least the, you know, 1 sigma level.
The uncertainties are large, because these… data points to determine the distance of these objects. You can't rely on the redshift. You have to have a direct measure of the distance. And that's very rare, very hard to combine cosmology.
You have to use some empirical relation. There's one called the Tully Fisher, which is a correlation between the rate at which a spiral galaxy is spinning and its absolute brightness. And there is a similar thing for elliptical galaxies between the velocity dispersion of the brightness called the fundamental plane.
you use those indicators, they're only good to about 15-20% to get these, so there are actually large horizontal error bars also on these things, which is why people haven't been taking this seriously until quite recently, two sets of, uh.
authors have now measured this bulk flow, especially from the cosmic flows for survey. The picture I showed you was cosmic flows 3. The latest survey they find that the bulk flow, if anything, is now definitely not falling.
It is, if anything rise. And the remark that they make in the paper is that this is in tension with the standard model at something like, I don't know, 4.56 sigma, something like that, right?
So this is nevertheless, while interesting, not definitive, not just because of the sigmas, but because of the systematic uncertainties that people know are associated with this distance measures.
Uh, by the way, I should quickly say, although I'm running out of time rapidly, that if we are in a bug flow which is indicated here in this yellow region, and you calculate what an observer embedded in the buffalo will see when they look at.
data from distant objects, then according to Christoph Sagas, who is a relativist in Thessaloniki, if you… the blood flow is converging.
Then you will have a correction term to the deceleration parameter, which is the rate of change of the Hubble parameter, which is of opposite side to the first one, and can cancel it out if that bulk flow is strong enough. And what that means is that even if the universe is globally decelerating.
You might locally think of it as exhilaration. Now, when I met Christos, I heard his talk, and I said, can you calculate that term? And he said, well, you'll have to tell me the VTCD and share of the local bulk flu, and I said, no, no one has measured that, but surely it will be in the direction that we are moving.
And he says, yes. So I said, in that case, the acceleration, if it is a artifact of this, should be only in the direction you are moving. And he said, Yes. I said, we can look for that in the data, and we did. We took a catalog of 740 supernovae all analyzed using the same.
Light curve template, etc. And we do a tailored expansion of the luminosity distance, the brightness of the supernovae, in terms of the Hubble parameter and the next quantity is the deceleration parameter, which is defined thus.
with the minus sign, because it was expected to be decelerating, but it turned out that the deceleration parameter is actually negative. It's wanting it to be positive. But what we see here is that it's actually very slightly negative.
But the dipole, if I allow that term to have a monopole term and a dipole term, the dipole is 50 times bigger than the monopole. It's basically a dipole.
There is a tiny monopole term consistent with 0 at 1.4 sigma.
So, in fact, Christos was right. The acceleration is in the direction that we are moving.
It is not in isotropic as it should be if it was due to lambda.
Now, this was, of course, highly contested because it obviously directly disproves the existence of lambda. And we thought, as a matter of interest, you'd go back and look at the supernovae that the two teams that got the Nobel Prize for the discovery of phosphine acceleration.
looked at. Interestingly, they looked at only about 50 or 60 each, and most of them are in the direction of our bulk group. They did not have telescopes at the time with which to look at the other part of the sky.
And then one of them complained that we had looked at a old catalog. The 740 was from 2014. Actually, he was the author of the catalog, but never mind. Now we have a new catalogue of.
price that number, and then you can see the redshift distribution here, and we see the same pattern. We see a strong dipole which is decaying away on a length scale of a few hundred megapascals. So that is exactly how we'd expect a bulk flow to behave.
And everything seems to fit with the idea that we have local anisotropic acceleration only up to a few hundred megaparsecs beyond that point, we don't really know, because there is no data, but there's data soon coming from the Rubin telescope.
So now let me, in the remaining 8 min, 10 min, get on to my actual topic, which is the isotropy of the universe. Now, this is a picture from people's textbook, which says this picture shows the radio sources mapped from.
Green Bank with Virginia, and it shows that the university is isotropic.
So for a long time, I wondered what that, you know, you see this little streak here? I wondered what that was. That's actually our galaxy, because there are radio sources in our galaxy.
And these blank regions are the bits you can't see from West Virginia.
Now, the statement that this shows the isotropy of the universe cannot be correct because if the microwave background is showing a distinct dipole anisotropy, then so should this.
Why can't we see it? Because there are only 30,000 sources here.
You want to look for the effect of one part in 10 to the 3. You need at least a million sources. And that was lacking in the old days. But the reason why we are so sure we should see it is because it is an effect called aberration.
which was actually discovered a couple of 100 years before the theory of special relativity by Bradley, who was the civilian chair of astronomy at Oxford, and he, in fact, discovered it and gave a formula for it, which is the special relativistic formula, long before special relativity.
What he observed was that a star is displaced on the sky in the direction of our motion, and in fact, this tells you the ratio of the velocity of the, uh, our motion relative to that of light, because Bradley correctly deduced this was due to the finite speed of light.
And he estimated the speed of light to within one person.
You know, amazing going in 1728, right? Now, this therefore is for real. You can't avoid this aberration effect. But of course, for individual sources, you have to worry about what you are seeing. So, for example, in the power law spectrum.
you're sampling a different part of the spectrum as a moving observer, and if the number distribution of sources is falling off as a power law on top of, according to the flux, then you have to take this into account as well. So you're looking, maybe I should show a picture.
If I have a picture here of isotropically distributed sources, and if I'm moving in that direction towards the red point, then I should see the sources bunched up around there, leaving a hole in this direction, because the sources which have been below my flux threshold in the flux limited survey will be boosted above it.
And reverse in the backward direction, right? And this was calculated by George Ellis and John Baldwin. John Baldwin was the head of the Mallard Space Radio Astronomy Lab at Cavendish. They were about to undertake the.
Cavendish Survey of radio sources, and George Ellis is a radivist from South Africa.
And they pointed out that V over C cos theta, which you saw for the CMB, has to be multiplied by a small factor, which adds up to about 5. It boosts the signal by a factor of 5, according to these indices, alpha and x, which are the.
Paul Lo indices of these objects. So, this is Alison Baldwin's original paper.
written, as you see at the Orthodox Academy of Crete. I don't know if any of you have been there, it's a lovely place right on the beach. So I can just imagine Ellison Baldwin chatting about this at 2 in the morning over a glass of regen or two, and saying, you know, we have found a.
Consistency tests of the FLRW metric, because if the.
Microwave background and the number counts, the dipoles, that is, were to be in serious disagreement, then one would have to abandon the standard FLRW universe models if the radio sources are indeed cosmologically distant and the interpretation of the CMBS primordial is true.
So let me go a bit quickly, because I don't want to keep you beyond. I know we are all waiting for lunch. So we got data from this catalog created by a satellite called Wise, a infrared satellite.
which orbited for many years. In fact, it shut down only a couple of months ago, finally. And it surveyed the sky in four bands, all that few micron wavelengths, and if you do multiple bands, then you can do a color-color plot and isolate quasars.
From other kinds of stuff that you don't want. And of course, you can then examine them individually as to what the spectra is with some other instrument. Wise itself doesn't have spectroscopy. And by doing so, we created a catalog.
of about 1.5 million quasars. You have to make sure that they are complete down to some flux limit. So these checks were done. You have to also check that there are no systematics associated with the orbit or the scanning pattern. And in fact, we found.
A 1% drift in the number counts with the angle which is usually involved in these things called the ecliptic, because we are orbiting in the ecliptic, so you tend to see.
Anything associated with that. So you correct for all those things, and we create a map of the sky which has got about 1.4 million quasars, and we are lucky to get these, because our first author, Nathan Seacrest, he's at the Naval Observatory in Washington.
And he sits on the committee that actually maintains the reference frame for satellite navigation, for which they use quasars. So they are really meticulous speed. They have to be.
And my other collaborators are Mohammad Ramiz, who is at the Tata Institute in Bombay. Sebastian Von House, who's a postdoc in Oxford, and Roya Moai. She is a relativist and cosmologist at the Institute of Astrophysics in Paris.
So our lucky break was that these quasars, some of them had their redshifts measured by the Sloan Digital Sky Survey, and that told us that they are indeed a cosmological distances. The mean redshift, as you see, is more than one.
And when we smooth this map, we see the expected dipole pattern, right? And we see the hotspot and the cold spot. And now we can create mock skies by sampling from the distribution of spectral indices and flux indices for these.
And I should say that Wilbur was kind enough to help us on our first paper, uh, keep us honest when we did this. So we generated 10 million mock skies and asked, what is the expected diver you should see? And that is that hill here.
And, uh, what we find is that the direction of this dipole is consistent with the direction of the CMB dipole to within the uncertainty, but its magnitude is way out. Out of the 10 million simulations, only five made it up to the point that we observed.
So the p-value is transparently five times 10 to the minus 7, which is 4.9 sigma for a one-sided Gaussian. We did a frequentist analysis because that's what I like. It's transparent, it's simple. There's no hand waving going on. But of course, we have now created the Bayesian estimator like everybody else.
I should point out that this dipole is also seen in the catalog of radio sources from the very large array, the NVSS catalog, and that has got left after you mask out the galaxy, etc, then there are less sources. So but the.
Directions are consistent, and the velocity is consistent. And in fact, since these two catalogs, the NVSS catalog and the WISE catalog, are totally independent. I should say that NVSS is looking at radio sources which are basically the jets of plasma being ejected from the central black hole and creating huge radio lobes.
Whereas Wise is looking at the central engine, which is shouted by accretion disk, and that heats up and emits infrared. And that is what we see in the Y satellite.
So although they're both powered by black holes, the surveys are independent and pick out different objects. In fact, there were 50 objects in common in the two catalogs. We, of course, removed them. And then we have two independent measurements, and we can combine them.
And we get more than 5 sigma. Other people have checked our results. They find even stronger significance in the Bayesian analysis. And now, very recently, there's a PRL by people from Billefield.
And they have over five sigma from radio data alone. So it seems to be that this is being confirmed independently using radio sources which are mapped from the ground and satellites, which, of course, do it from the sky.
And which, therefore, a very different systematics. They're seeing the same result. So at least we are pretty confident that it's for real.
Okay, I'll skip this for lack of time. This is because some people started saying, why are you using special data? You should use general relativity. And the bottom line is, if you use general relativity, then we get back the Ellis Baldwin formula plus a correction, which turns out to be about.
10 to the minus 4. So, you know, Ellis and Baldwin were quite right.
And there is no issue with, I mean, the fact that it's a three-dimensional universe is not relevant because what you are seeing projected onto the sky contains all that information about the evolution and so on. So that's one way to look at it.
So this is the bottom line. We now have this anomalous dipole in at least 3 different samples. It is consistent in direction with the Cmb dipole, but not consistent in the amplitude. We have, of course, done various systematic checks to see that the dipole is stable with the magnitude cut.
The direction does drift, but not the magnitude. And very recently, this is a paper about to come out in monthly notices. We have constructed the angular power spectrum of this catalog, and at small scales, it matches what you expect for structure formation in CDN, as you one might expect.
So we can then extrapolate that to L of 2 and read off what sort of a dipole might there be on the sky from clustering, which is something which is often invoked to try and account for our observation. But you can see for yourself.
That this is what you expect from lambda Cdm, and this is what we are measuring, and there is quite a bit of clear water in between the 2.
And in fact, there is no other large-scale power. Other people had found large-scale power because they didn't clean up the map enough, but it is essentially like the CMB.
So what has the community said about this? Well, I thought I would quote Jim Peebles, who is the kind of dawn of our field, and he says this anomaly is as well established as the Hubble parameter as the Hubble tension.
Yet the literature on it is much smaller than the hundreds of papers about the Hubble tension. I expect the difference is an inevitable consequence of the way we behave. I have no idea what he means by this.
However, the the problem is the following that this is not something that you can just tweak a model and write a, you know, toss of a theory paper about.
It does mean going back to square one. And so although there has been a fair bit of interest from the theory community, it is fair to say we have neither they nor we have any alternative to put in the place of the standard cosmological model.
And for that reason, it has been largely ignored, and I thank you for having the patience to listen to the evidence, which is just come out of the fact that this model was constructed back in 1922 by Alexander Friedman.
And he didn't have any data. In 2022, we didn't even know that we lived in a galaxy. We didn't even know about the Hubble expansion.
Now that we have data, we should be doing this cross-checks. And yet, the most recent sets of data, for example, from the dark energy spectroscopic Instrument, DAISI, which is run by Berkeley out of satellite telescope at Kit Peak.
They analyze all their data, assuming FLRW. The Dark Energy Survey that has just finished its five or six year mission does the same. Everybody continues to assume something for which now we have five sigma evidence demonstrating that it is not the case.
More interestingly, the inferred acceleration is also in the same direction, and therefore cannot be due to lambda.
This is more serious, because it means that we can't assume the fundamental metric that is used for space time. And departing from this situation of symmetry is asking for trouble, because Einstein's equations are very hard to solve.
And you proliferate the number of parameters if you go away from this situation, and the data has not been there until today to address with such a more complicated model.
But now the data is coming. There is the legacy survey of space and time about to start on the Rubin telescope in which there is strong UK involvement. There is nuclear satellite up in space. The successor to WISE called CRX, which you probably haven't heard so much about.
was launched by Caltech last April. It's already done a survey of the sky, and that maps the sky in the same bands, or more or less, as Vice. So, very soon, not 10 years from now, 2 years from now, we'll know whether any of this is true.
Now, that data will represent a data challenge. So now you're talking about petabytes of data, and maybe to construct a cosmological model. Now we can go trendy and like everybody else is doing, start using machine learning.
To try to… To interrogate that data in order to construct the cosmological model directly from the data, rather than make a philosophical assumption and then test it.
So I think I will end there. If any of you want to know more about the philosophy behind this approach to cosmology, I did write a popular level talk, popular meaning it does have equations, but it's not technical, which you are very welcome to look at.
It's online and it's free. Thank you.
Sorry for going over time. Question from room. Yeah, Bob?
Fantastic talk, actually, and opens up many questions. I remember you talking in the past about type one supernova not being the same everywhere. Is that is that correct? Or is there something?
Yes, that is still true. So, what is done is that.
There are standardizable candles. So, basically, the intrinsic magnitude vary by a factor of 10. This has been known all along.
It was found that once you had CCD cameras to scan the sky, you could actually, when a supernova went off, you could go back and look at how much light you are getting from that direction two weeks earlier.
Right? So you could actually construct the whole rice track. And then it was realized that the width of the light curve, so it rises and then falls, right? The width correlates with the absolute magnitude.
So, this is called the Phillips relation. And using this, you can then reduce the scatter from a factor of 10 to less than a factor of 2, and then they can be used as standard candles.
But of course, people keep finding other things that this absolute magnitude might correlate with, you know, might it correlate with the mass of the host galaxy? Might it correlate with some other property with the supernova is in it? So these are open questions. These are all empirical.
correlations. There's no theory behind them. And. Basically, the J-Link catalog I showed you was done by taking four different surveys and analyzing all the supernovae with the same so-called spectral, uh.
salt. Salt stand for spectral adaptive light curve. That's it. Sol 2.
So now we are on to solve 3, and no doubt we'll go on to solve 4. But basically, that's how it is done.
Any questions from the room? Yeah.
So you probably know that the Ruben telescope had quite some ups and downs in terms of the 3.2 gigapixel spoke later on and finally got it right in shape. I haven't actually heard. Is it… is it now operating by doing the survey regularly? No, the… it's about to… the survey is going to about to begin, but I believe… you know, first light has been obtained and get, like, 10 events a day about how it's all going to be, and so on. So hopefully it will be on… but I believe it had to be scaled down, as you said, the original plan.
The thing is that, uh… If I may say so, it seemed to me that the telescope was built by particle physicists, and the data pipelined by particle physicists, but the people who use it would be astronomers. Yes. And…
Oh. It would be important to ensure that the data analysis is done in a blinded way.
And not using the kind of circular logic that has been employed so far in cosmological analysis. And this might be somewhat hard to do.
But yes, this is Slack had quite some problems with negotiating. That's right, yes. It didn't start at working each other. Sure, exactly. But LSST UK has got almost every astronomy department in the UK involved.
And we are also… we have also joined it, because there's been a lot of service work done by the UK, so that, you know, people who haven't done actually anything for the tennis group like me, we can also join.
But we'll be able to therefore have access to the data.
for any questions from Zoom, please. Raise your hands.
Hi, this is a really incredible and informative talk. I mean, I don't have a great understanding of cosmology, but.
Would we expect this security meeting to be reflected in when you try to study like bias and direction of neutrinos that we receive as well? Because from what I understand, we've measured like biases in direction with respect to the sun.
But would we also get a higher collection of neutrinos in the direction where we have the higher density as well.
So to date, the total number of cosmic neutrinos we have detected is in the tens.
That's not… like I said, you need like a billion events to look for this kind of one party in a thousand or few pots in a thousand and isotropy. So a long way from doing that. But of course, for example, an ice cube, you do look for correlation of neutrinos with large scale structure.
Even that so far has not been proved definitively. But you're right that eventually any… anything that is generated cosmologically, at sufficiently large distances, should show the same anisotropy. Now, this is simply a consequence of our local motion.
So therefore, it imprints itself on everything, on the whole sky.
If we find, however, that the imprint is not the same in two different traces, right? That means that our fundamental assumption in which we expect the two to be the same, namely this assumption of isotropin homogeneity, something has to get there.
Unfortunately, it does not tell us what has to give. What is the weak point? That we can only determine by doing further observation. So, for example, with Ruben and also with Spherex.
We'll have spectroscopic data, so this million objects will be able to actually measure the spectra and redshifts, and then we can do tomogram. So we can actually detect shells of objects and trace out this dipole from locally out to wherever it's coming from.
And hopefully that will then tell us something about the origin of this. So right now, there's a fair bit of speculation, but no hard data.
And I expect that, as I said, to happen within the next few years.
which is just as well, because I can't wait 30. But this is so, for example, there are a lot of activity among the gravitational wave community as to what they might be able to see once they have, you know, millions of.
Standard silence, which is the Blackwood merges. But that's going to take a while.
The good news is that there is already data in the pipeline, and more data coming in the next 2-3 years, which is very relevant to.
you know, checking, falsifying if necessary, what you have found.
Thank you. Let's take a question from Zoom. Stefan, please unmute and go ahead.
Can you hear me?
Um, so you mentioned the Hubble tension.
Yes.
There's lots of attention on that. How does this interact with the Hubble tension? Could it explain it? Does it change it?
Uh, yeah, I had a comment on a previous slide that when we looked at the Pantheon plus catalog of supernovae, we found that there is also an anisotropy in the Hubble parameter.
Uh, so that is to be expected in this universe. You don't expect the Hubble parameter to be the same, expansion rate to be the same in every direction.
And therefore, the Hubble tension as it is posed is supposed to be a discrepancy between something called H0, which is an isotropic quantity reduced from the microwave background.
And that measured in the local universe today. Now, the deductions on the microwave background is fine, because once you subtract this dipole, the remaining fluctuations are 1.4 in 100,000. The CMD is pretty isotropic.
But today, the universe is not isotropic, and therefore, if somebody claims to measure H0, I would have to ask them what direction you are measuring it in, because it's a bit like saying, you know, what's the radius of the earth?
Uh, that question presupposes that the Earth is a sphere, but the Earth is not a sphere. It's actually a geoid. It's got ups and downs. And, you know, these go up to 100, 200 kilometers. So you cannot measure the.
Radius of the Earth to within one person, because the Earth is not a sphere to that accuracy. So, think of the contours of the Hubble expansion similarly, and we need to map out those irregularities before we can answer the question as to whether there is a Hubble tension.
We certainly found evidence for anisotropy at a level higher than the claimed precision of the measurement by the Schus collaboration.
just to follow up, if Cmp is not the right thing for the late universe, then what is the the Cnp and matter where in thermal contact right before they decor. So you naturally expect them to have the.
shared the same reference frame today. If we are finding that the two don't match.
Then you have to find some way to distinguish photons from matter.
Now, that is hard to do because under gravity, things fall at the same rate.
So in particular, any calculations which is so-called adatic, which fluctuates in matter and radiation together, is not going to cut it.
You could imagine that there is something called an isocurvature fluctuation, which is one in which, as it says, the curvature remains constant, but matter and radiation fluctuate opposite.
Thereby keeping the curvature the same. And in fact.
Jim Gunn, who's an astronomer at Princeton, he had suggested quite some years ago in the 90s, that there could be a giant Iso curvature perturbation on the scale of the present horizon of the universe.
which can affect, you know, create such a distribution.
Um, that is possible. But then it seems to require some fine tuning, because if the Cb dipole is due to our motion.
And then something else is creating the matter dipole, why should the two be aligned?
Now, it's true, they're not perfectly aligned. They are aligned to within 2030 degrees. So, you know, there is a few percent chance of getting that alignment by chance.
But not a satisfactory thing. You'd want some more, you know.
sort of better reason for why this discrepancy is arising.
As I said, all these questions currently cannot be answered. They need more data. But most importantly, they need people other than our small group to work on it, right? Because if we really have to go back to square one, that is going to take a lot more.
Then just pointing out that there's something wrong in Denmark.
Okay, so then we have the questions, then please let's thank our speaker.
Sorry, there was value over time. I think I need to… close this thing.
on top of it and see what they can do? Yes, indeed. One can, in fact.
Construct your new list with one axis. This direction, and sort of expand around that. And people have tried doing that, but then you ask whether that access should come from, right? Why is there a particular access? Oh, sorry, there are lots of messages in the chat. Yeah, I mean, I was checking them on, so it's okay. But do you have a record of them? Yeah, okay, then if you would say.
Sorry, are you joining us for lunch? Yes, please. Okay.
Will this be visible on the software? Yes, we have a recording, we'll upload it, and then you go. Okay, good.
Hi, nice. How are you? I'm good, yeah.
Well, this keeps you busy.
just like go to your business.
It's like a standard model.
Unless he wants to scale.
Yes. Those, like, the current standing model. Otherwise, otherwise.
And that's actually consistent with the observations we have. I remember this observation is also observation.
It's as cool as it is. We are already at the point where there is really attractive, as we said to the 17th. Yeah. I don't think we did something.
Do you have any last one?
Yeah. And from that. Well, there's and so I thought I don't necessarily.
I think you are right. So, yeah, so, uh…
How's it going? It's so cold, it's freezing. Isn't it?
Crazy. I thought my forehead was going to fall off walking over. I was in Finland in January. I didn't feel anyone there.
I wish I brought my bobble hat now. Oh, here we are.
That's okay. Um. I think Charlie's been in to switch it on, but he's not there, and he's the kind of person… I mean, we do need him.
We also want to do a sound test on a webinar as well, so I was just, like, debating whether I try that, but he's… Again, we need him more.
All right. I brought some flowers over. I bought a bunch of flowers. They're for you to keep or smash, upkeep.
The rest of the flowers are in the kitchen in some water. We can use them for a day, but if you… He's trying.
The whole point of this run through is so that he can see what camera angles he needs for what bits. Yes. So that we can make sure that people online.
You can see as well. Right, in which case, I want to get some screens, so we can set up a proper area.
It's not going to be safe if we don't have our full section.
So… When it comes to the area itself.
Do we want to have a separate table altogether? Or could we just do it on a table like this? We could do it on the table like that, and then the whole point is to have cameras, so it'll be on here as well, so you could do some things.
Over here, and you can do some things… over here. So depending on where people are sitting, they're either watching it.
Yes. Okay, cool. And for technology, for the… lecture itself. We want to have the mobile microphone, so we can, like, walk around and interacting with the lapel mics.
He has already provided said clicker. I is the best thing.
He helps the job inside. Okay.
Cool. All right. I need screens, so I might have to dart back to my lab to put those up. I mean.
don't necessarily… I mean, you could, because obviously there's no audience here at the moment, so you can just… I assume their perspective, you can see through them. Yeah, the perspective you can see through them, but I was sad.
say welcome. How big are they? Well, you're going to struggle to see that?
Well, that's okay because that's what the cameras are for because we're getting far away because we make sure our camera and we can see aspects for that sort of angle.
Y'all. Right. Might just do this.
Test. Why are you not letting me select Zoom?
In progress. No meetings.