## The Zel’dovich Universe – Day 2 Summary

Posted in History, The Universe and Stuff with tags , , , on June 25, 2014 by telescoper

Day Two of this enjoyable meeting involved more talks about the cosmic web of large-scale structure of the Universe. I’m not going to attempt to summarize the whole day, but will just mention a couple of things that made me reflect a bit. Unfortunately that means I won’t be able to do more than merely mention some of the other fascinating things that came up, as phase-space flip-flops and one-dimensional Origami.

One was a very nice review by John Peacock in which he showed that a version of Moore’s law applies to galaxy redshift surveys; since the first measurement of the redshift of an extragalactic object by Slipher in 1912, the number of redshifts has doubled every 2-3 years ago. This exponential growth has been driven by improvements in technology, from photographic plates to electronic detectors and from single-object spectroscopy to multiplex technology and so on. At this rate by 2050 or so we should have redshifts for most galaxies in the observable Universe. Progress in cosmography has been remarkable indeed.

The term “Cosmic Web” may be a bit of a misnomer in fact, as a consensus may be emerging that in some sense it is more like a honeycomb. Thanks to a miracle of 3D printing, here is an example of what the large-scale structure of the Universe seems to look like:

One of the issues that emerged from the mix of theoretical and observational talks concerned the scale of cosmic homogeneity. Our standard cosmological model is based on the Cosmological Principle, which asserts that the Universe is, in a broad-brush sense, homogeneous (is the same in every place) and isotropic (looks the same in all directions). But the question that has troubled cosmologists for many years is what is meant by large scales? How broad does the broad brush have to be? A couple of presentations discussed the possibly worrying evidence for the presence of a local void, a large underdensity on scale of about 200 MPc which may influence our interpretation of cosmological results.

I blogged some time ago about that the idea that the Universe might have structure on all scales, as would be the case if it were described in terms of a fractal set characterized by a fractal dimension $D$. In a fractal set, the mean number of neighbours of a given galaxy within a spherical volume of radius $R$ is proportional to $R^D$. If galaxies are distributed uniformly (homogeneously) then $D = 3$, as the number of neighbours simply depends on the volume of the sphere, i.e. as $R^3$, and the average number-density of galaxies. A value of $D < 3$ indicates that the galaxies do not fill space in a homogeneous fashion: $D = 1$, for example, would indicate that galaxies were distributed in roughly linear structures (filaments); the mass of material distributed along a filament enclosed within a sphere grows linear with the radius of the sphere, i.e. as $R^1$, not as its volume; galaxies distributed in sheets would have $D=2$, and so on.

We know that $D \simeq 1.2$ on small scales (in cosmological terms, still several Megaparsecs), but the evidence for a turnover to $D=3$ has not been so strong, at least not until recently. It’s just just that measuring $D$ from a survey is actually rather tricky, but also that when we cosmologists adopt the Cosmological Principle we apply it not to the distribution of galaxies in space, but to space itself. We assume that space is homogeneous so that its geometry can be described by the Friedmann-Lemaitre-Robertson-Walker metric.

According to Einstein’s theory of general relativity, clumps in the matter distribution would cause distortions in the metric which are roughly related to fluctuations in the Newtonian gravitational potential $\delta\Phi$ by $\delta\Phi/c^2 \sim \left(\lambda/ct \right)^{2} \left(\delta \rho/\rho\right)$, give or take a factor of a few, so that a large fluctuation in the density of matter wouldn’t necessarily cause a large fluctuation of the metric unless it were on a scale $\lambda$ reasonably large relative to the cosmological horizon $\sim ct$. Galaxies correspond to a large $\delta \rho/\rho \sim 10^6$ but don’t violate the Cosmological Principle because they are too small in scale $\lambda$ to perturb the background metric significantly.

The discussion of a fractal universe is one I’m overdue to return to. In my previous post I left the story as it stood about 15 years ago, and there have been numerous developments since then, not all of them consistent with each other. I will do a full “Part 2” to that post eventually, but in the mean time I’ll just comment that current large surveys, such as those derived from the Sloan Digital Sky Survey, do seem to be consistent with a Universe that possesses the property of large-scale homogeneity. If that conclusion survives the next generation of even larger galaxy redshift surveys then it will come as an immense relief to cosmologists.

The reason for that is that the equations of general relativity are very hard to solve in cases where there isn’t a lot of symmetry; there are just too many equations to solve for a general solution to be obtained. If the cosmological principle applies, however, the equations simplify enormously (both in number and form) and we can get results we can work with on the back of an envelope. Small fluctuations about the smooth background solution can be handled (approximately but robustly) using a technique called perturbation theory. If the fluctuations are large, however, these methods don’t work. What we need to do instead is construct exact inhomogeneous model, and that is very very hard. It’s of course a different question as to why the Universe is so smooth on large scales, but as a working cosmologist the real importance of it being that way is that it makes our job so much easier than it would otherwise be.

PS. If anyone reading this either at the conference or elsewhere has any questions or issues they would like me to raise during the summary talk on Saturday please don’t hesitate to leave a comment below or via Twitter using the hashtag #IAU308.

## The Power Spectrum and the Cosmic Web

Posted in Bad Statistics, The Universe and Stuff with tags , , , , , , on June 24, 2014 by telescoper

One of the things that makes this conference different from most cosmology meetings is that it is focussing on the large-scale structure of the Universe in itself as a topic rather a source of statistical information about, e.g. cosmological parameters. This means that we’ve been hearing about a set of statistical methods that is somewhat different from those usually used in the field (which are primarily based on second-order quantities).

One of the challenges cosmologists face is how to quantify the patterns we see in galaxy redshift surveys. In the relatively recent past the small size of the available data sets meant that only relatively crude descriptors could be used; anything sophisticated would be rendered useless by noise. For that reason, statistical analysis of galaxy clustering tended to be limited to the measurement of autocorrelation functions, usually constructed in Fourier space in the form of power spectra; you can find a nice review here.

Because it is so robust and contains a great deal of important information, the power spectrum has become ubiquitous in cosmology. But I think it’s important to realise its limitations.

Take a look at these two N-body computer simulations of large-scale structure:

The one on the left is a proper simulation of the “cosmic web” which is at least qualitatively realistic, in that in contains filaments, clusters and voids pretty much like what is observed in galaxy surveys.

To make the picture on the right I first  took the Fourier transform of the original  simulation. This approach follows the best advice I ever got from my thesis supervisor: “if you can’t think of anything else to do, try Fourier-transforming everything.”

Anyway each Fourier mode is complex and can therefore be characterized by an amplitude and a phase (the modulus and argument of the complex quantity). What I did next was to randomly reshuffle all the phases while leaving the amplitudes alone. I then performed the inverse Fourier transform to construct the image shown on the right.

What this procedure does is to produce a new image which has exactly the same power spectrum as the first. You might be surprised by how little the pattern on the right resembles that on the left, given that they share this property; the distribution on the right is much fuzzier. In fact, the sharply delineated features  are produced by mode-mode correlations and are therefore not well described by the power spectrum, which involves only the amplitude of each separate mode. In effect, the power spectrum is insensitive to the part of the Fourier description of the pattern that is responsible for delineating the cosmic web.

If you’re confused by this, consider the Fourier transforms of (a) white noise and (b) a Dirac delta-function. Both produce flat power-spectra, but they look very different in real space because in (b) all the Fourier modes are correlated in such away that they are in phase at the one location where the pattern is not zero; everywhere else they interfere destructively. In (a) the phases are distributed randomly.

The moral of this is that there is much more to the pattern of galaxy clustering than meets the power spectrum…

## The Zel’dovich Universe – Day 1 Summary

Posted in Biographical, History, The Universe and Stuff with tags , on June 24, 2014 by telescoper

I’m up possibly bright but definitely early to get ready for day two of IAU Symposium No. 308 The Zel’dovich Universe. The weather was a bit iffy yesterday, with showers throughout the day, but that didn’t matter much in practice as I was indoors most of the day attending the talks. I have to deliver the conference summary on Saturday afternoon so I feel I should make an effort to attend as much as I can in order to help me pretend that I didn’t write my concluding talk in advance of the conference.

Day One began with some reflections on the work and personality of the great Zel’dovich by two of his former students, Sergei Shandarin and Varun Sahni, both of whom I’ve worked with in the past.
Zel’dovich (left) was born on March 8th 1914. To us cosmologists Zel’dovich is best known for his work on the large-scale structure of the Universe, but he only started to work on that subject relatively late in his career during the 1960s. He in fact began his life in research as a physical chemist and arguably his greatest contribution to science was that he developed the first completely physically based theory of flame propagation (together with Frank-Kamenetskii). No doubt he also used insights gained from this work, together with his studies of detonation and shock waves, in the Soviet nuclear bomb programme in which he was a central figure, and which no doubt led to the chestful of medals he’s wearing in the photograph. In fact he was awarded the title of  Hero of Socialist Labour no less than three times.

My own connection with Zel’dovich is primarily through his scientific descendants, principally his former student Sergei Shandarin, who has a faculty position at the University of Kansas, but his work has had a very strong influence on my scientific career. For example, I visited Kansas back in 1992 and worked on a project with Sergei and Adrian Melott which led to a paper published in 1993, the abstract of which makes it clear the debt it owed to the work of Ze’dovich.

The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel’dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is ‘enhanced’ by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel’dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

The Zel’dovich Approximation referred to in this abstract is based on an extremely simple idea but which, as we showed in the above paper, turns out to be extremely accurate at reproducing the morphology of the “cosmic web” of large-scale structure.

Zel’dovich passed away in 1987. I was a graduate student at that time and had never had the opportunity to meet him. If I had done so I’m sure I would have found him fascinating and intimidating in equal measure, as I admired his work enormously as did everyone I knew in the field of cosmology. Anyway, a couple of years after his death a review paper written by himself and Sergei Shandarin was published, along with the note:

The Russian version of this review was finished in the summer of 1987. By the tragic death of Ya. B.Zeldovich on December 2, 1987, about four-fifths of the paper had been translated into English. Professor Zeldovich would have been 75 years old on March 8, 1989 and was vivid and creative until his last day. The theory of the structure of the universe was one of his favorite subjects, to which he made many note-worthy contributions over the last 20 years.

As one does if one is vain I looked down the reference list to see if any of my papers were cited. I’d only published one paper before Zel’dovich died so my hopes weren’t high. As it happens, though, my very first paper (Coles 1986) was there in the list. That’s still the proudest moment of my life!

We then went into a Dick Bond Special, with a talk entitled: From Superweb Simplicity to Complex Intermittency in the Cosmic Web. The following pic will give you a flavour:

It’s all very straightforward, really. Um…

The rest of the day consisted of a number of talks about the Cosmic Web of large-scale structure using techniques inspired by the work of Zel’dovich, particularly the Zel’dovich approximation which I’ve mentioned already. There were many fascinating talks but I had to single out Johan Hidding of Groningen for the best use of graphics. Here’s a video of his from Youtube as an example:

Well, I must get going for the start of Day Two. The first session starts at 9am (7am UK time) and the day ends at 19.30. Conferences like this are hard work!

PS. If anyone reading this either at the conference or elsewhere has any questions or issues they would like me to raise during the summary talk on Saturday please don’t hesitate to leave a comment below or via Twitter using the hashtag #IAU308.

## Synesis, Metonymy and the FIFA World Cup

Posted in Football with tags , , , , , , on June 23, 2014 by telescoper

I was asleep during last night’s dramatic World Cup game between Portugal and USA which ended in a 2-2 draw thanks to an equaliser in injury time from Portugal. That’s why I found out about the result from Twitter when I woke up this morning. I was struck by the fact that virtually all comments from Americans talked about their team in the singular (e.g. “USA has drawn against Portugal”) whereas on this side of the Atlantic we almost always refer to a team in the plural (e.g. “England have lost against everyone”).

Strictly speaking, the singular form is correct (as was Nelson with his “England expects..” message at Trafalgar) but that doesn’t mean that British English is necessarily wrong. This is an example of a figure of speech called a metonymic shift, whereby a thing or concept is referred to not by its own name but by the name of something associated with it. An example is found in the phrase “to boil a kettle”: obviously it is not the kettle that gets boiled, but the water within it, but this isn’t an error as such, merely a grammatical device. Metonymic shifts also take place when we refer to the Government as “Westminster” or the film-making industry as “Hollywood”.

When we come to the “England lose” verses “England loses” debate, the noun “England” can be taken to mean “The England team” (singular) but in British English the metonymic shift takes this to mean a collection of individual players (plural), i.e. the meaning is transferred from the “England team” to the “England players”. The use of a verb indicating a singular subject constitutes “formal agreement” with “team” whereas the plural form would be “notional agreement”.

I know that this usage is regarded as incorrect by American colleagues I have discussed it with, to the extent that it actually grates on them a bit. But I think “the team are fighting amongst themselves” is a better construction than any I can think of that includes formal rather than notional agreement. Moreover this kind of construction is correct in languages with more precise grammatical rules than English. The Greek term synesis refers to a grammatical alteration in which a word takes the gender or number not of the word with which it should regularly agree, but of some other word implied by that word, a device much used in both Greek and Roman poetry and also in rhetoric. The distinction between “the Government is united” and “the Government are divided” offers a particularly interesting example.

However, having done my best to stick up for “England” as a plural, I can’t help thinking that if they ever learn how to play like a team than as a collection of individuals they might not be so strongly associated with the verb “to lose”…

## Welcome Reception

Posted in Biographical, The Universe and Stuff with tags , on June 22, 2014 by telescoper

So I made it to Talinn, where it is fairly cold and rainy, for the IAU Symposium No 308 on the Zel’dovich Universe . Here is the description of the conference from the website

It will be 100 years since the birth of Yakov Zeldovich, whose seminal work paved the way towards a theoretical understanding of the complex weblike patterns that have been observed in our Universe.

Impressive progress of observational studies, of modelling and simulations and of analytical work has led to revolutionary new insights into the structure and emergence of the Cosmic Web. With the coming years marked by major observational developments – in terms of large new telescopes, instruments and corresponding versatile surveys – and with the continuing growth of computational resources, the window will be opened towards understanding the dynamics and observing the evolution of cosmic structure.

The symposium will focus on the subject of the structure, constituents, properties, dynamics and analysis of the cosmic web in the large-scale cosmic matter and galaxy distribution. The symposium will synthesize the insights obtained from many different observational and theoretical studies and set out the lines for the major upcoming scientific programs that will not only extend our view over a far larger fraction of the visible Universe but also allow the systematic investigation of the evolution of cosmic structure.

I’m looking forward to the meeting, which starts properly tomorrow morning but it was nice to have a reception event this evening to welcome those of us who made it to Estonia in time. Thp ere was plenty of wine on offer, and I had the chance to meet up with quite a few people I haven’t seen for ages:

First impressions of Estonia are that the word for “Taxi” is “Tacso” and the word for “Big Bang” is also slightly different:

Other than that the natives seem friendly and my hotel, though inexpensive, is positively luxurious. The crucial challenge, however, is the quality of the breakfast, which will have to wait until tomorrow morning!

Posted in The Universe and Stuff with tags , , , , on June 21, 2014 by telescoper

I thought I’d give you a sneak preview of something soon to feature at the forthcoming Royal Society Summer Science Exhibition. With input from particle physicists from the Department of Physics & Astronomy at the University of Sussex, the inestimable Dorothy Lamb has designed a “Knit your own Neutralino” pack, which contains a knitting pattern and embellishments (wool not included), that can be used to construct a plushie representing the lightest neutralino, χ01, a candidate for the dark matter that pervades the Universe.

Here are some examples, as produced by Dorothy herself:

Here are some more elaborate variations, representing (I think) different types of chargino.

Whatever they are, they’re a lot of fun and in my opinion more than a little bit camp!

I think we should introduce knitting as part of the “transferable skills” element of our physics courses. If we did, Dorothy would definitely graduate with first class honours!

## Music for the Solstice

Posted in Music with tags , on June 21, 2014 by telescoper

Well, in case you didn’t realize, the summer solstice (when the Sun reaches its most northerly point in the sky) occurred at 11.51 BST today. I guess that means it’s all downhill from here. Anyway, this gives me some sort of excuse for me posting a piece of music I’ve loved ever since I was a young child for its energy and wit. It’s the Overture to a Midsummer Night’s Dream, which was written by Felix Mendelssohn when he was just 17 years old, and even so it’s his Opus 21. This performance is by the Leipzig Genwandhausorchester conducted by Kurt Mazur. Enjoy!