Archive for Cosmic Microwave Background

Cosmology and the Born-Again Bayesians!

Posted in Bad Statistics, Biographical, The Universe and Stuff with tags , , , , on May 10, 2021 by telescoper

The other day, via Twitter, I came across an interesting blog post about the relatively recent resurgence of Bayesian reasoning in science. That piece had triggered a discussion about why cosmologists seem to be largely Bayesian in outlook, so I thought I’d share a few thoughts about that. You can find a lot of posts about various aspects of Bayesian reasoning on this blog, e.g. here.

When I was an undergraduate student I didn’t think very much about statistics at all, so when I started my DPhil studies I realized I had a great deal to learn. However, at least to start with, I mainly used frequentist methods. Looking back I think that’s probably because I was working on cosmic microwave background statistics and we didn’t really have any data back in 1985. Or actually we had data, but no firm detections. I was therefore taking models and calculating things in what I would call the forward direction, indicated by the up arrow. What I was trying to do was find statistical descriptors that looked likely to be able to discriminate between different models but I didn’t have the data.

Once measurements started to become available the inverse-reasoning part of the diagram indicated by the downward arrow came to the fore. It was only then that it started to become necessary to make firm statements about which models were favoured by the data and which weren’t. That is what Bayesian methods do best, especially when you have to combine different data sets.

By the early 1990s I was pretty much a confirmed Bayesian – as were quite a few fellow theorists -but I noticed that most observational cosmologists I knew were confirmed frequentists. I put that down to the fact that they preferred to think in “measurement space” rather than “theory space”, the latter requiring the inductive step furnished by Bayesian reasoning indicated by the downward arrow. As cosmology has evolved the separation between theorists and observers in some areas – especially CMB studies – has all but vanished and there’s a huge activity at the interface between theory and measurement.

But my first exposure to Bayesian reasoning came long before that change. I wasn’t aware of its usefulness until 1987, when I returned to Cambridge for a conference called The Post-Recombination Universe organized by Nick Kaiser and Anthony Lasenby. There was an interesting discussion in one session about how to properly state the upper limit on CMB fluctuations arising from a particular experiment, which had been given incorrectly in a paper using a frequentist argument. During the discussion, Nick described Anthony as a “Born-again Bayesian”, a phrase that stuck in my memory though I’m still not sure whether or not it was meant as an insult.

It may be the case for many people that a relatively simple example convinces them of the superiority of a particular method or approach. I had previously found statistical methods – especially frequentist hypothesis-testing – muddled and confusing, but once I’d figured out what Bayesian reasoning was I found it logically compelling. It’s not always easy to do a Bayesian analysis for reasons discussed in the paper to which I linked above, but it least you have a clear idea in your mind what question it is that you are trying to answer!

Anyway, it was only later that I became aware that there were many researchers who had been at Cambridge while I was there as a student who knew all about Bayesian methods: people such as Steve Gull, John Skilling, Mike Hobson, Anthony Lasenby and, of course, one Anthony Garrett. It was only later in my career that I actually got to talk to any of them about any of it!

So I think the resurgence of Bayesian ideas in cosmology owes a very great deal to the Cambridge group which had the expertise necessary to exploit the wave of high quality data that started to come in during the 1990s and the availability of the computing resources needed to handle it.

But looking a bit further back I think there’s an important Cambridge (but not cosmological) figure that preceded them, Sir Harold Jeffreys whose book The Theory of Probability was first published in 1939. I think that book began to turn the tide, and it still makes for interesting reading.

P.S. I have to say I’ve come across more than one scientist who has argued that you can’t apply statistical reasoning in cosmology because there is only one Universe and you can’t use probability theory for unique events. That erroneous point of view has led to many otherwise sensible people embracing the idea of a multiverse, but that’s the subject for another rant.

Cosmology Talks: Eiichiro Komatsu & Yuto Minami on Parity Violation in the Cosmic Microwave Background

Posted in Cardiff, Maynooth, The Universe and Stuff with tags , , , , , , , , on December 2, 2020 by telescoper

It’s time I shared another one of those interesting cosmology talks on the Youtube channel curated by Shaun Hotchkiss. This channel features technical talks rather than popular expositions so it won’t be everyone’s cup of tea but for those seriously interested in cosmology at a research level they should prove interesting.

In this video, Eiichiro Komatsu and Yuto Minami talk about their recent work, first devising a way to extract a parity violating signature in the cosmic microwave background, as manifested by a form of birefringence. If the universe is birefringent then E-mode polarization would change into B-mode as electromagnetic radiation travels through space, so there would be a non-zero correlation between the two measured modes. They  try to measure this correlation using the Planck 2018 data, getting  a 2.4 sigma `hint’ of a result.

A problem with the measurement is that systematic errors, such as imperfectly calibrated detector angles,  could mimic the signal. Yuto and Eiichiro’s  idea was to measure the detector angle by looking at the E-B correlation in the foregrounds, where light hasn’t travelled far enough to be affected by any potential birefringence in the universe. They argue that this allows them to distinguish between the two types of measured E-B correlation. However, this is only the case if there is no intrinsic correlation between the E-mode and B-mode polarization in the foregrounds, which may not be the case, but which they are testing. The method can be applied to any of the plethora of CMB experiments currently underway so there will probably be more results soon that may shed further light on this issue.

Incidentally this reminds me of Cardiff days when work was going on about the same affect using the Quad instrument. I wasn’t involved with Quad but I do remember having interesting chats about the theory behind the measurement or upper limit as it was (which is reported here). Looking at the paper I realize that paper involved researchers from the Department of Experimental Physics at Maynooth University.

P. S. The paper that accompanies this talk can be found here.

Debating the Cosmological Principle

Posted in The Universe and Stuff with tags , , , , on November 5, 2020 by telescoper

Whether you need something to distract you from world events or are just interested in the subject I thought I’d share something cosmological today.

You may recall that I recently posted about a paper by Subir Sarkar and collaborators.  Here is the abstract and author list:

In that post I mentioned that Subir would be taking part in an online debate about this issue. Well, although I wasn’t able to watch it live there is a recording of it which is available here:

It’s rather long, but there are many interesting things in it…

A Test of the Cosmological Principle using Quasars

Posted in The Universe and Stuff with tags , , , , on October 8, 2020 by telescoper

I’m not getting much time these days to even think about cosmology but Subir Sarkar drew my attention to an intriguing paper by his team so I thought I’d share it here. Here is the abstract and author list:

I find this an intriguing result because I’ve often wondered about the dipole anisotropy of the cosmic microwave background might not be exclusively kinematic in origin and whether they might also be a primordial contribution. The dipole (180°) variation corresponds to a ΔT/T of order 10-3, which a hundred times larger than the variation on any other angular scale. This is what it looks like:

This is usually interpreted as being due to the motion of the observer through a frame in which the cosmic microwave background is completely isotropic. A simple calculation then gives the speed of this motion using ΔT/T ≈ v/c. This motion is assumed to be generated by gravitational interaction with local density fluctuations rather than being due to anything truly cosmological (i.e. of primordial origin).

The features in the cosmic microwave background temperature pattern on smaller angular scales (the quadrupole, octopole, etc…) , which have ΔT/T of order 10-5 are different in that they are dominated by primordial density fluctuations. There should be a primordial dipole at some level, but the fact that these other harmonic modes have such low amplitudes and the assumption that the primordial dipole should be of the same order, combined with the fact that the CMB dipole does indeed roughly line up with the dipole expected to be generated by local inhomogeneities, has led to the widespread belief that this intrinsic dipole is negligible. This analysis suggests that it might not be.

What the authors have done is study the anisotropy of a large sample of quasars (going out to redshifts of order three) finding the dipole to be larger than that of the CMB. Note however that the sample does not cover the whole sky because of a mask to remove regions wherein AGN are hard to observe:

As well as the mask there are other possible systematics that might be at play, which I am sure will be interrogated when the paper is peer-reviewed which, as far as I know, is not yet the case.

P.S. I might just quibble a little bit about the last sentence of the abstract. We know that the Universe violates the cosmological principle even in the standard model: with scale-invariant perturbations there is no scale at which the Universe is completely homogeneous. The question is really how much and in what way it is violated. We seem to be happy with 10-5 but not with 10-3

Update: On 23rd October Subir will be giving a talk about this an participating in a debate. For more details, see here.

Primordial Figures

Posted in Biographical, The Universe and Stuff with tags , , , , on August 28, 2020 by telescoper

I was rummaging around looking for some things related to a paper I’m struggling to finish before term starts and I found some vintage diagrams. They brought back a lot of memories of working on the textbook I wrote with Francesco Lucchin way back in the 1990s. In particular I remember how long it took to make these figures, when nowadays it would take a few minutes. In fact I’m thinking of setting this as a Computational Physics project for next year. These are not full computations either, just a simple fluid-based approach.

The curves show the evolution of fluctuations in both matter δm and radiation δr on a particular scale (i.e. a Fourier mode of given wavelength) defined as δm=δρmm, etc.  The x-axis shows the cosmic scale factor, which represents the expansion of the Universe and in both cases the universe is flat, i.e. it has a critical density. The first graph shows a universe with only baryonic matter:

Notice the strongly coupled oscillations in matter and radiation until a scale factor of around 10-3, corresponding to a redshift of a thousand or so, which is when matter and radiation decouple. The y-axis is logarithmic so the downward spikes represent zero points.

It is these oscillations which are responsible for the bumps and wiggles in the spectrum of the cosmic microwave background spectrum, as different Fourier modes arrive at the last scattering surface at a different phase of its oscillation. Of course going from the Figure above to the CMB fluctuation spectrum (see below) involves more calculations, and there is now a well-established machinery for doing these with full physical descriptions, but I think the above diagram makes the physical origin of these features clear.

The CMB power spectrum from Planck

The second diagram shows what happens if you add a third component called `X’ in the Figure below which we take to be cold non-baryonic matter. Because  this stuff doesn’t interact directly with radiation (while baryons do) it doesn’t participate in the oscillations but the density perturbations just carry on growing:

Notice too that at late times (i.e. after the baryonic matter and radiation have decoupled) the baryonic component grows much more quickly than in the first Figure. This is because, when released from the effect of the photon background, baryons start to feel the gravitational pull of the dark matter perturbations.

There’s nothing new in this of course – these Figures are thirty years old and similar were produced even earlier than that – but I still think pictures like these are pedagogically useful,

 

Cosmology Talks – Deanna Hooper on CMB spectral distortions

Posted in The Universe and Stuff with tags , , , , on May 26, 2020 by telescoper

Here is another one of those Cosmology Talks curated on YouTube by Shaun Hotchkiss. This one was published over a month ago, but I missed it at the time.

In the talk, Deanna Hooper tells us about what we could learn from future measurements of the spectral distortions in the CMB, as well as how spectral distortions complement current and future measurements of CMB anisotropies. I’m particularly interested in this as I wrote a paper on it with John Barrow almost thirty years 30 ago and it’s fascinating to see how far the field has moved on from the theoretical point of view. Our paper was motivated by limits on spectral distortions imposed by the FIRAS instrument on COBE, and there hasn’t been anywhere near as much observational progress since then.

The paper that accompanies this talk can be found here.

Cosmology Talks: Omar Darwish on Lensing Maps

Posted in The Universe and Stuff with tags , , , , , on April 17, 2020 by telescoper

If you are missing your regular seminar experience because of the Coronavirus lockdown, Shaun Hotchkiss has set up a YouTube channel just for you!

The channel features technical talks rather than popular expositions so it won’t be everyone’s cup of tea but for those seriously interested in cosmology at a research level they should prove interesting.

Here’s another example from that series in which Omar Darwish talks about CMB Lensing Maps and specifically about an extremely impressive example thereof which he made using data from the Atacama Cosmology Telescope.

More Cosmic Tension?

Posted in The Universe and Stuff with tags , , , , , , , , , on November 12, 2019 by telescoper

Quite a lot of fuss was being made in cosmological circles while I was away last week concerning a paper that had just been published in Nature Astronomy by Eleonora Di Valentino, Alessandro Melchiorri and Joe Silk that claims evidence from the Planck Cosmic Microwave background and other data that the Universe might be closed (or at least have positive spatial curvature) in contrast to the standard cosmological model in which the spatial geometry is Euclidean. Nature Astronomy is behind a paywall but the paper is available for free on the arXiv here. The abstract reads:

The recent Planck Legacy 2018 release has confirmed the presence of an enhanced lensing amplitude in CMB power spectra compared to that predicted in the standard ΛCDM model. A closed universe can provide a physical explanation for this effect, with the Planck CMB spectra now preferring a positive curvature at more than 99% C.L. Here we further investigate the evidence for a closed universe from Planck, showing that positive curvature naturally explains the anomalous lensing amplitude and demonstrating that it also removes a well-known tension within the Planck data set concerning the values of cosmological parameters derived at different angular scales. We show that since the Planck power spectra prefer a closed universe, discordances higher than generally estimated arise for most of the local cosmological observables, including BAO. The assumption of a flat universe could, therefore, mask a cosmological crisis where disparate observed properties of the Universe appear to be mutually inconsistent. Future measurements are needed to clarify whether the observed discordances are due to undetected systematics, or to new physics, or simply are a statistical fluctuation.

I think the important point to take from this study is that estimates of cosmological parameters obtained from Planck are relatively indirect, in that they involve the simultaneous determination of several parameters some of which are almost degenerate. For example, the `anomalous’ lensing amplitude discussed in this paper is degenerate with the curvature so that changing one could mimic the effect on observables of changing the other; see Figure 2 in the paper.

It’s worth mentioning another (and, in my opinion, better argued) paper on a similar topic by Will Handley of Cambridge which is on the arXiv here. The abstract of this one reads:

The curvature parameter tension between Planck 2018, cosmic microwave background lensing, and baryon acoustic oscillation data is measured using the suspiciousness statistic to be 2.5 to 3σ. Conclusions regarding the spatial curvature of the universe which stem from the combination of these data should therefore be viewed with suspicion. Without CMB lensing or BAO, Planck 2018 has a moderate preference for closed universes, with Bayesian betting odds of over 50:1 against a flat universe, and over 2000:1 against an open universe.

Figure 1 makes a rather neat point that the combination of Planck and Baryon Acoustic Oscillations does not separately give consistent values for the Hubble constant and the curvature and neither does the combination of Planck and direct Hubble constant estimates:

I don’t know what the resolution of these tensions is, but I think it is a bit dangerous to dismiss them simply as statistical flukes. They might be that, of course, but they also might not be. By shrugging one’s shoulders and ignoring such indications one might miss something very fundamental. On the other hand, in my opinion, there is nothing here that definitely points the finger at spatial curvature either: it is possible that there is something else missing from the standard model that, if included, would resolve these tensions. But what is the missing link?

Answers on a postcard, or through the comments box.

A Nobel Prize for Jim Peebles!

Posted in The Universe and Stuff with tags , , , , , , on October 8, 2019 by telescoper

I’ve just dashed back in excitement to the office from two hours of mandatory Financial Report Training to write a quick post before my 12 o’clock lecture on Astrophysics & Cosmology because of the news about the award of the 2019 Nobel Prize for Physics.

My recent post was half right in the sense that half this year’s prize goes to Michel Mayor and Didier Queloz for the discovery of an extrasolar planet. I don’t know either of them personally, but heartiest congratulations to both!

My heart lept with joy, however, to see the other half of the prize go to Jim Peebles (above) for his work on theoretical cosmology. Much of the reason for that is that I’ve had the great honour and pleasure to meet Jim many times over the years. He is not only a truly great scientist but also a extremely nice man whose kindness and generosity is universally recognized. He’s not known as `Gentleman Jim’ for nothing!

The other reason for the excitement is that I was completely taken by surprise by the announcement. I had feared that his chance of winning a Nobel Prize had passed – I argued at the time that Jim should have been awarded a share of the 2006 Nobel Prize because without his amazing pioneering theoretical work the importance of the cosmic microwave background for cosmology and the large-scale structure of the Universe would not have been established so rapidly. As an author of the first paper to provide a theoretical interpretation of the signal detected by Penzias and Wilson, Jim was there right at the start of the modern era of cosmology and his subsequent work constructed the foundations of the theory of structure formation through gravitational instability. I was sad that he didn’t get a share in 2006 for this work, but am absolutely delighted that this has been rectified now!

This was one of the first cosmology books I ever bought. It’s an amazing piece of work that has been essential reading for cosmologists for almost 40 years!

Congratulations to Jim!

Now let me think about what to say to my students about this!

A Bayesian Look at Cosmic Anomalies

Posted in Cosmic Anomalies with tags , , , on March 3, 2019 by telescoper

I’ve posted a few times on this blog about Cosmic Anomalies, by which I mean apparent departures from the predictions of the standard cosmological model. From time to time I also talk about this subject at seminars and conferences.

There’s an interesting new paper on this topic on the arXiv now by Shaikh et al., with the following abstract:

You can click on the image to make it larger. You can also find the PDF version of the full paper here.

I find this Bayesian analysis of two of the apparent anomalies (low amplitude in the power spectrum at large angular scales and hemispherical power asymmetry) may be different manifestations of the same underlying phenomenon, which would make them easier to account for without invoking new physics. Rather than being two independent statistical flukes these measurements might both be the result of one, which would be more likely to occur in the standard model. This analysis however suggests that this might not be the case after all, and these are two different things after all. This presupposes, however, that the model chosen to describe the asymmetries is appropriate. Anyway, this paper is well worth a read if you’re into Bayesian model testing (which you should be)…

This also gives me the excuse to post the following poll, which has been running for several years (even longer than Brexit):