## From Phase Walks to Undergraduate Research

Posted in Education, The Universe and Stuff with tags , , , , , on September 28, 2018 by telescoper

This week I put together a couple of brief descriptions for possible research projects for final-year undergraduate and/or Masters students in the Department of Theoretical Physics at Maynooth University, and I was reminded of the value of projects like this when I found this paper on the arXiv:

In fact the Phase Walk Analysis’ developed here is based on an original idea I had for an undergraduate summer research project when I was at Nottingham University and have mentioned before on this blog. The student who did the project with me was Andrew Stannard (who is now at King’s College, London) and the work led to a paper that was published in a refereed journal in 2005 and has now been cited 21 times by various authors including the Planck Team.

Although Andrew is now working in a completely different area (Condensed Matter Physics), I like to think this taste of research was of at least some assistance in developing his career. Above all, though, it relates to something I read in the Times Higher by astronomer, Nobel Prize winner, and Vice-Chancellor of the Australian National University, namely that the idea that many politicians seem to have of separating teaching from research in universities is at best misguided and at worst threatens the very idea of a university.

## The Simons Observatory: Science Goals and Forecasts

Posted in The Universe and Stuff with tags , , on August 27, 2018 by telescoper

I haven’t been involved in this project, but several of my former colleagues at Cardiff have beenm and still are, so I know how much work has gone into this (especially by the amazing Erminia Calabrese), so I am happy to share this impressive work here. This long (54 pages) paper, which appeared on the arXiv last week, describes the latest step forward in ground-based cosmology using the cosmic microwave background. It shows just how rapid the onward march of instrumental technology continues to be.

The Simons Observatory Site, in Chile

It is likely that the Simons Observatory (based on a single 6m dish) will form part of the next generation CMB experiment known currently as CMB-S4.

The Simons Observatory (SO) is a new cosmic microwave background experiment being built on Cerro Toco in Chile, due to begin observations in the early 2020s. We describe the scientific goals of the experiment, motivate the design, and forecast its performance. SO will measure the temperature and polarization anisotropy of the cosmic microwave background in six frequency bands: 27, 39, 93, 145, 225 and 280 GHz. The initial configuration of SO will have three small-aperture 0.5-m telescopes (SATs) and one large-aperture 6-m telescope (LAT), with a total of 60,000 cryogenic bolometers. Our key science goals are to characterize the primordial perturbations, measure the number of relativistic species and the mass of neutrinos, test for deviations from a cosmological constant, improve our understanding of galaxy evolution, and constrain the duration of reionization. The SATs will target the largest angular scales observable from Chile, mapping ~10% of the sky to a white noise level of 2 μK-arcmin in combined 93 and 145 GHz bands, to measure the primordial tensor-to-scalar ratio, r, at a target level of σ(r)=0.003. The LAT will map ~40% of the sky at arcminute angular resolution to an expected white noise level of 6 μK-arcmin in combined 93 and 145 GHz bands, overlapping with the majority of the LSST sky region and partially with DESI. With up to an order of magnitude lower polarization noise than maps from the Planck satellite, the high-resolution sky maps will constrain cosmological parameters derived from the damping tail, gravitational lensing of the microwave background, the primordial bispectrum, and the thermal and kinematic Sunyaev-Zel’dovich effects, and will aid in delensing the large-angle polarization signal to measure the tensor-to-scalar ratio. The survey will also provide a legacy catalog of 16,000 galaxy clusters and more than 20,000 extragalactic sources.

## Nature After Planck…

Posted in Maynooth, The Universe and Stuff with tags , , , , , , on July 24, 2018 by telescoper

After last week’s short update about the last tranche of papers from the European Space Agency’s Planck Mission it’s time for another short update about a piece in Nature (by David Castelvecchi) that explains how researchers are moving to smaller projects studying different aspects of the cosmic microwave background.

In the spirit of gratuitous self-promotion I should also mention that there’s a little quote from me in that piece. My comment was hardly profound, but at least it gets Maynooth University a name check…

Much of Davide’s piece echoes discussions that were going on at the meeting I attended in India  last October, but things have moved on quite a bit since then at least as far as space experiments are concerned. In particular, the proposed Japanese mission Litebird has been shortlisted for consideration, though we will have to wait until next year (2019) at the earliest to see if it will be selected. An Indian mission, CMB-Bharat, has also emerged as a contender.

While the end of Planck closes one chapter on CMB research, several others will open. These are likely to focus on polarization, gravitational lensing and on cosmic reionization rather than refining the basic cosmological parameters still further.

## Planck’s Last Papers

Posted in The Universe and Stuff with tags , , , , on July 17, 2018 by telescoper

Well, they’ve been a little while coming but just today I heard that the final set of a dozen papers from the European Space Agency’s Planck mission are now available. You can find the latest ones, along with the all the others, here.

This final Legacy’ set of papers is sure to be a vital resource for many years to come and I can hear in my mind’s ear the sound of cosmologists all around the globe scurrying to download them!

I’m not sure when I’ll get time to read these papers, so if anyone finds any interesting nuggets therein please feel free to comment below!

## Remembering Clover

Posted in Biographical, Science Politics, The Universe and Stuff with tags , , , , , , , on April 10, 2018 by telescoper

I was tidying up some papers in my desk yesterday and came across a clipping dated April 9th 2009, i.e. exactly nine years ago to the day. Amazed by this coincidence, I resolved to post it on here but was unable to work out how to use the new-fangled scanner in the Data Innovation Institute office so had to wait until I could get expert assistance this morning:

Sorry it’s a bit crumpled, but I guess that demonstrates the authenticity of its provenance.

The full story, as it appeared in the print edition of the Western Mail, can also be found online here. By the way it’s me on the stepladder, pretending to know something about astronomical instrumentation.

I wrote at some length about the background to the cancellation of the Clover experiment here. In a nutshell, however, Clover involved the Universities of Cardiff, Oxford, Cambridge and Manchester and was designed to detect the primordial B-mode signal from its vantage point in Chile. The chance to get involved in a high-profile cosmological experiment was one of the reasons I moved to Cardiff from Nottingham almost a decade ago, and I was looking forward to seeing the data arriving for analysis. Although I’m primarily a theorist, I have some experience in advanced statistical methods that might have been useful in analysing the output. It would have been fun blogging about it too.

Unfortunately, however, none of that happened. Because of its budget crisis, and despite the fact that it had already spent a large amount (£4.5M) on Clover, the Science and Technology Facilities Council (STFC) decided to withdraw the funding needed to complete it (£2.5M) and cancel the experiment. I was very disappointed, but that’s nothing compared to Paolo (shown in the picture) who lost his job as a result of the decision and took his considerable skills and knowledge abroad.

We will never know for sure, but if Clover had gone ahead it might well have detected the same signal found five years later by BICEP2, which was announced in 2014. Working at three different frequencies (95, 150 and 225GHz) Clover would have had a better capability than BICEP2 in distinguishing the primordial signal from contamination from Galactic dust emission (which, as we now know, is the dominant contribution to the BICEP2 result; see thread here), although that still wouldn’t have been easy because of sensitivity issues. As it turned out, the BICEP2 signal turned out to be a false alarm so, looking on the bright side, perhaps at least the members of the Clover team avoided making fools of themselves on TV!

P.S. Note also that I moved to Cardiff in mid-2007, so I had not spent 5 years working on the Clover project by the time it was cancelled as discussed in the newspaper article, but many of my Cardiff colleagues had.

## WMAP wins the 2018 Breakthrough Prize for Fundamental Physics

Posted in The Universe and Stuff with tags , , , , on December 4, 2017 by telescoper

It’s very nice on a gloomy Monday morning to be able to share some exciting news and to congratulate so many friends and colleagues, for last night the 2018 Breakthrough Prize for Fundamental Physics was awarded to the team who worked on the Wilkinson Microwave Anisotropy Probe (WMAP). The citation reads:

For detailed maps of the early universe that greatly improved our knowledge of the evolution of the cosmos and the fluctuations that seeded the formation of galaxies.

The award, which is for the sizeable sum of \$3 Million, will be shared among the 27 members of the WMAP team whose names I list here in full (team leaders are in italics):

Chris Barnes; Rachel Bean; Charles Bennett; Olivier Doré; Joanna Dunkley,;Benjamin M. Gold; Michael Greason; Mark Halpern; Robert Hill, Gary F. Hinshaw, Norman Jarosik, Alan Kogut, Eiichiro Komatsu, David Larson, Michele Limon, Stephan S. Meyer, Michael R. Nolta, Nils Odegard, Lyman Page, Hiranya V. Peiris, Kendrick Smith, David N. Spergel, Greg S. Tucker, Licia Verde, Janet L. Weiland, Edward Wollack, and Edward L. (Ned) Wright.

I know quite a few of these people personally, including Hiranya, Licia, Eiichiro, Joanna, Olivier and Ned, so it’s a special pleasure to congratulate them – and the other members of the team – on this well-deserved award.

Don’t spend all the money in the same shop!

## What the Power Spectrum misses

Posted in The Universe and Stuff with tags , , , , , , , on August 2, 2017 by telescoper

Just taking a short break from work I chatted over coffee to one of the students here at the Niels Bohr Institute about various things to do with the analysis of signals in the Fourier domain (as you do). That discussion reminded me of this rather old post (from 2009) which I thought might be worth a second airing (after a bit of editing). The discussion is all based on past cosmological data (from WMAP) rather than the most recent (from Planck), but that doesn’t change anything qualitatively. So here you are.

The picture above shows the all-sky map of fluctuations in the temperature of the cosmic microwave background across the sky as revealed by the Wilkinson Microwave Anisotropy Probe, known to its friends as WMAP.

I spent many long hours fiddling with the data coming from the WMAP experiment, partly because I’ve never quite got over the fact that such wonderful data actually exists. When I started my doctorate in 1985 the whole field of CMB analysis was so much pie in the sky, as no experiments had yet been performed with the sensitivity to reveal the structures we now see. This is because they are very faint and easily buried in noise. The fluctuations in temperature from pixel to pixel across the sky are of order one part in a hundred thousand of the mean temperature (i.e. about 30 microKelvin on a background temperature of about 3 Kelvin). That’s smoother than the surface of a billiard ball. That’s why it took such a long time to make the map shown above, and why it is such a triumphant piece of science.

I blogged a while ago about the idea that the structure we see in this map was produced by sound waves reverberating around the early Universe. The techniques cosmologists use to analyse this sound are similar to those used in branches of acoustics except that we only see things in projection on the celestial sphere which requires a bit of special consideration.

One of the things that sticks in my brain from my undergraduate years is being told that `if you don’t know what you’re doing as a physicist you should start by making a Fourier transform of everything. This approach breaks down the phenomenon being studied into a set of  plane waves with different wavelengths corresponding to analysing the different tones present in a complicated sound.

It’s often very good advice to do such a decomposition for one-dimensional time series or fluctuation fields in three-dimensional Cartesian space, even you do know what you’re doing, but it doesn’t work with a sphere because plane waves don’t fit properly on a curved surface. Fortunately, however, there is a tried-and-tested alternative involving spherical harmonics rather than plane waves.

Spherical harmonics are quite complicated beasts mathematically but they have pretty similar properties to Fourier harmonics in many respects. In particular they are represented as complex numbers having real and imaginary parts or, equivalently, an amplitude and a phase (usually called the argument by mathematicians),

$Z=X+iY = R \exp(i\phi)$

This latter representation is the most useful one for CMB fluctuations because the simplest versions of inflationary theory predict that the phases φ of each of the spherical harmonic modes should be randomly distributed. What this really means is that there is no information content in their distribution so that the harmonic modes are in a state of maximum statistical disorder or entropy. This property also guarantees that the distribution of fluctuations over the sky should have a Gaussian distribution.

If you accept that the fluctuations are Gaussian then only the amplitudes of the spherical harmonic coefficients are useful. Indeed, their statistical properties can be specified entirely by the variance of these amplitudes as a function of mode frequency. This pre-eminently important function is called the power-spectrum of the fluctuations, and it is shown here for the WMAP data:

Although the units on the axes are a bit strange it doesn”t require too much imagination to interpret this in terms of a sound spectrum. There is a characteristic tone (at the position of the big peak) plus a couple of overtones (the bumps at higher frequencies). However these features are not sharp so the overall sound is not at all musical.

If the Gaussian assumption is correct then the power-spectrum contains all the useful statistical information to be gleaned from the CMB sky, which is why so much emphasis has been placed on extracting it accurately from the data.

Conversely, though, the power spectrum is completely insensitive to any information in the distribution of spherical harmonic phases. If something beyond the standard model made the Universe non-Gaussian it would affect the phases of the harmonic modes in a way that would make them non-random.

However,I will now show you how important phase information could actually be, if only we could find a good way of exploiting it. Let’s start with a map of the Earth, with the colour representing height of the surface above mean sea level:

You can see the major mountain ranges (Andes, Himalayas) quite clearly as red in this picture and note how high Antarctica is…that’s one of the reasons so much astronomy is done there.

Now, using the same colour scale we have the WMAP data again (in Galactic coordinates).

The virture of this representation of the map is that it shows how smooth the microwave sky is compared to the surface of the Earth. Note also that you can see a bit of crud in the plane of the Milky Way that serves as a reminder of the difficulty of cleaning the foregrounds out.

Clearly these two maps have completely different power spectra. The Earth is dominated by large features made from long-wavelength modes whereas the CMB sky has relatively more small-scale fuzz.

Now I’m going to play with these maps in the following rather peculiar way. First, I make a spherical harmonic transform of each of them. This gives me two sets of complex numbers, one for the Earth and one for WMAP. Following the usual fashion, I think of these as two sets of amplitudes and two sets of phases. Note that the spherical harmonic transformation preserves all the information in the sky maps, it’s just a different representation.

Now what I do is swap the amplitudes and phases for the two maps. First, I take the amplitudes of WMAP and put them with the phases for the Earth. That gives me the spherical harmonic representation of a new data set which I can reveal by doing an inverse spherical transform:

This map has exactly the same amplitudes for each mode as the WMAP data and therefore possesses an identical power spectrum to that shown above. Clearly, though, this particular CMB sky is not compatible with the standard cosmological model! Notice that all the strongly localised features such as coastlines appear by virtue of information contained in the phases but absent from the power-spectrum.

To understand this think how sharp features appear in a Fourier transform. A sharp spike at a specific location actually produces a broad spectrum of Fourier modes with different frequencies. These modes have to add in coherently at the location of the spike and cancel out everywhere else, so their phases are strongly correlated. A sea of white noise also has a flat power spectrum but has random phases. The key difference between these two configurations is not revealed by their spectra but by their phases.

Fortunately there is nothing quite as wacky as a picture of the Earth in the real data, but it makes the point that there are more things in Heaven and Earth than can be described in terms of the power spectrum!

Finally, perhaps in your mind’s eye you might consider what it might look lie to do the reverse experiment: recombine the phases of WMAP with the amplitudes of the Earth.

If the WMAP data are actually Gaussian, then this map is a sort of random-phase realisation of the Earth’s power spectrum. Alternatively you can see that it is the result of running a kind of weird low-pass filter over the WMAP fluctuations. The only striking things it reveals are (i) a big blue hole associated with foreground contamination, (ii) a suspicious excess of red in the galactic plane owing to the same problem, and (iiI) a strong North-South asymmetry arising from the presence of Antarctica.

There’s no great scientific result here, just a proof that spherical harmonic phases are potentially interesting because of the information they contain about strongly localised features

PS. These pictures were made by a former PhD student of mine, Patrick Dineen, who has since quit astrophysics  to work in the financial sector for Winton Capital, which has over the years recruited a number of astronomy and cosmology graduates and also sponsors a Royal Astronomical Society prize. That shows that the skills and knowledge obtained in the seemingly obscure field of cosmological data analysis have applications elsewhere!