Cosmological Backreaction

In the last few weeks a disagreement has surfaced at the arXiv. The disagreement concerns whether backreaction is important in cosmology.

To summarise my take on the whole thing, it seems to me that the two sides of this disagreement are, to a large extent, talking past each other. I don't doubt that there is genuine disagreement where definitions overlap, but, at least to my present understanding, much of the disagreement actually just lies in what should be considered "backreaction". There seems to be a secondary, though related, disagreement concerning whether one should start with observations and use them to methodically construct a model of the universe, or instead start with a model of the universe and then see whether it fits the data. The side that favours first constructing the model would say that a model without any backreaction is entirely self-consistent and fits the data well enough not to be concerned. To the other side this still doesn't prove that backreaction must be negligible.

But OK, what is cosmological backreaction?

Backreaction itself is quite a common term in physical sciences.

In a surprising proportion of calculations about nature we would normally analyse some sort of interesting object, existing within some external system, but in a scenario where the behaviour of the object has no measurable influence on the overall system. Then, calculating predictions essentially amounts to two independent steps: firstly, calculating what the background system is doing, and then calculating how the interesting object will react to that.

However, this type of scenario isn't always accurate. When it isn't, the background system could be described as "backreacting" to the object's behaviour.

Mysterious news stories about supervoids

Early last week a news story broke about a supervoid. The supervoid was claimed to be a number of things, from an explanation for "the cold spot", to the biggest "structure" yet found in the universe, to just "mysterious".

Whether it is a structure or not entirely depends on how you define structure, so I won't discuss whether it is or isn't a structure. However, if you do allow it to be a structure, it isn't the biggest structure yet found. It's hard to do a like for like comparison with other "superstructures". However, there are regions of the universe where the density of observable matter is smaller, for a wider range, so by any definition I can think of, this structure has been beaten.

The cold spot is a region in the cosmic microwave background (CMB) that has a temperature profile that is somewhat unexpected (due to a combination of a cold central spot and a hot ring around it). Whether this void could be the explanation of the cold spot has been explained in this paper and this blog post by Sesh. It can't, not without a significant deviation from General Relativity (and a sufficiently big deviation that it would be very strange that these deviations haven't been seen elsewhere). It's worth stressing right now that it isn't the coldness of the cold spot that is itself anomalous. This is a subtle point so just about anyone who says "the cold spot is too cold" can be forgiven for the mistake, but in reality the cold spot isn't too cold. In fact it has more or less exactly the coldness expected of the coldest spot in the CMB. What isn't expected is that there will be a hot ring around such a cold spot. Actually, it's worth stressing further that it isn't even the hot ring that is, by itself, anomalous. Such a hot ring is also quite likely in the CMB. The anomalousness of the cold spot is caused by the fact that both of these features are present, right next to each other. I explained this curiosity in this blog entry, but it is worth repeating.

I want to address now quickly the claim that this supervoid is mysterious. The quantitative source for the claim that the void is mysterious comes from the claim in the paper about the void that it is "at least a \(3.3 \sigma\) fluctuation" and that "\(p=0.007\) ... characterizing the cosmic rarity of the supervoid". However (and this is the crucial point) what these numbers quantify is the probability that something as extreme as this void could exist at a random point of the universe (or, more precisely, a random point within the part of the universe seen by a particular observational survey). What these numbers do not quantify is the probability that the whole survey could have seen something this extreme. These are two separate statistical things and the relevant one for claiming mysteriousness is the second one. I'll try to estimate this probability.

I don't have any reason to doubt the numbers they quote for the probability that this void could exist at a random line of sight in the survey. If I use the quoted radius, density contrast and redshift of the void I also calculate it to be a \(\sim 3\sigma\) fluctuation in the matter field. This can be done first by calculating the root-mean-square of the density (contrast) field of the universe when it is smoothed over a particular radius. This quantity, "\(\sigma_R\)", is commonly used in large scale structure. Then, the ratio of the density (contrast) of the obtained void and the \(\sigma_R\) value for the radius of the void gives you \(\sim 3.5\) so I trust that the more sophisticated analyses in the paper are correct, or at least aren't obtaining wildly wrong answers. If one assumes (probably validly) that the large scale density field of the universe has a Gaussian distribution this can be translated into a probability that the observed fluctuation could occur at any random position in the universe.

So, the crucial question that now needs to be asked before calling this supervoid mysterious is whether the survey used to find it saw enough of the universe to witness this rare an event. The size of the void in the sky is approximately \(10\) degrees (as quoted in their abstract). This means it has an area of approximately \(100\) square degrees on the sky. The void was found using data from the WISE and 2MASS all-sky surveys. However the whole sky isn't usable for robust analysis due to foregrounds, the galaxy, etc. Thankfully for our goal, the authors of the supervoid paper also wrote a paper about the catalogue of galaxies they used to find the supervoid and in the abstract of that paper they estimate that their catalogue covers 21,200 square degrees of the sky.

What does this mean when we pull it all together? Well, the catalogue used to find the 100 square degree thing, covered 21,200 square degrees of the sky. Therefore, there were \(\sim 21200/100 \simeq 200\) independent \(100\) square degree patches of the sky seen by the survey. Using their own probability for this void existing at any particular line of sight of \(p=0.007\) this gives a very approximate estimate of the expected number of under-dense regions of the universe at least as extreme as the "mysterious" supervoid. The answer is \(N \sim 200*0.007 = 1.4\).

So, not only is the supervoid not actually mysterious, it is in fact more or less exactly in line with naive expectations!

Twitter: @just_shaun

The Cold Spot is not particularly cold

(and it probably isn't explained by a supervoid; although it is still anomalous)

In the cosmic microwave background (CMB) there is a thing that cosmologists call "The Cold Spot". However, I'm going to try to argue that its name is perhaps a little, well, wrong. This is because it isn't actually very cold. Although, it is definitely notably spotty.

That's the cold spot. It even has its own Wikipedia page (which really does need updated).

Why care about a cold spot?

This spot has become a thing to cosmologists because it appears to be somewhat anomalous. What this means is that a spot just like this has a very low probability of occurring in a universe where the standard cosmological model is correct. Just how anomalous it is and how interesting we should find it is a subject for debate and not something I'll go into much today. There are a number of anomalies in the CMB, but there is also a lot of statistical information in the CMB, so freak events are expected to occur if you look at the data in enough different ways. This means that the anomalies could be honest-to-God signs of wonderful new physical effects, or they could just be statistical flukes. Determining which is true is very difficult because of how hard it is to quantify how many ways in which the entire cosmology community have examined their data.

However, if the anomalies are signs of new physics, then we should expect two things to happen. Firstly, some candidate for the new physics should come up, which can create the observed effect and produce all of the much greater number of other measurements that fit the standard cosmological model well. If this happens, then we would look for additional ways in which the universe described by this new model differs from the standard one, and look for those effects. Secondly, as we take more data, we would expect the unlikeliness of the anomaly to increase. that is, it should become more and more anomalous.

In this entry, I'm not going to be making any judgement on whether the cold spot is a statistical fluke or evidence of new physics. What I want to do is explain why, although it still is anomalous, and is definitely a spot, the cold spot isn't very cold. Then, briefly, I'll explain why, if it is evidence of new physics, that new physics isn't a supervoid.

So, what is the cold spot, and why is it anomalous?

How does one measure the mass of a neutrino, using cosmology?

I'm going to tell you how, soon, humanity might measure the masses of neutrinos just by observing past events in the universe. I like this topic because it is one of the few situations in fundamental physics where a measurement of the greater universe might detect something about fundamental particles and/or their interactions, before we manage to measure it in a lab. Another example is the existence of dark matter; however the mass of dark matter will almost certainly be first measured in a lab. Perhaps with neutrinos it will go in the other direction?

What is a neutrino?

I guess that before telling you how to measure a neutrino's mass, it might be pertinent to tell you what a neutrino is and how we can know it has mass before we've measured that mass. Well...

When an atomic nucleus decays, the decay products we see are other nuclei, electrons and/or positrons. These visible products always carry less energy and momentum than the amount that the initial nucleus had. This suggests strongly that some unknown other particle is also being created in the decay and that we just can't see it. This hypothetical particle was dubbed the neutrino and when theories were developed for the force responsible for nuclear decays, the neutrino became an important part of them. And, eventually, neutrinos were detected directly. It took a while because neutrinos interact incredibly weakly, which means you need either a lot of neutrinos or a lot of transparent stuff for the neutrino to interact with (or both) before you will see them.

Initially, it was assumed that neutrinos are massless. They don't need to be massless, but for a long time there was no evidence that they did have mass, so the simplest assumption was that they didn't. There are three types of neutrinos: those emitted in interactions with electrons, those emitted in interactions with muons and those emitted in interactions with tau particles. If neutrinos were massless, then a neutrino emitted as an electron neutrino would always remain an electron neutrino. Similarly, a muon neutrino would always remain a muon neutrino. However, if neutrinos do have mass, then a neutrino emitted in an interaction with an electron will actually travel as a superposition of an electron neutrino, muon neutrino and tau neutrino. The net result being that this neutrino could be detected as a different type of neutrino. Therefore, a smoking gun thing to look for when determining whether neutrinos have mass is this characteristic signal whereby one type of neutrino appears to oscillate into another type of neutrino.

This effect was then seen and seen and seen again. Neutrinos appear to have mass. From the perspective of particle physics this is a bit weird. Neutrinos must have really small masses and it is unclear why these masses are so small. Unfortunately, this mechanism of neutrino oscillations doesn't directly give the masses of the neutrinos. Although, it can be used to measure the differences of the masses of the neutrinos, thus setting lower bounds on the possible masses of the neutrinos.

What has this got to do with cosmology?

The universe as seen by Planck - Days Three and Four II

[Continued from yesterday...]

In the first piece of this post I covered the implications of Planck for the paradigm of inflation. This piece covers the rest.

The anomalies

This is what the CMB would look like in an unphysical Bianchi universe. A worry for our physicality is that this unphysical Bianchi universe seems to fit the data better than a physical \(\Lambda\)CDM universe.

It would be impossible to provide an overview of this conference without mentioning the features and anomalies that Planck has chosen to draw significant attention to. I have a bunch of notes that I've written down that I might one day turn into a new blog post, but I'm not going to delve into them now.

These features and anomalies are clearly going to become a contentious issue in cosmology for the next few years. In fact, the words believer, atheist and agnostic were even being used by speakers during talks regarding whether the anomalies are real or statistical effects. Each time someone declared themselves an anomaly atheist or anomaly agnostic, someone in the audience inevitably spoke up and passionately defended the significance of the questioned anomaly.

The list of potential anomalies is long. There is the cold spot, the anomalously low quadrupole, the hemispherical asymmetry, the statistical difference between the odd and even multipoles at large scales, there is the dipole modulation, there is the general lack of power at large scales, there is the feature in the temperature power spectrum at small scales, the fact that the universe seems to be in an unphysical Bianchi model and there is the "axis of evil" (to name a few).

Pick your side. Atheist, believer or agnostic. The great anomaly wars of cosmology are about to begin (another inevitable consequence of an observational, rather than experimental science, I suppose - i.e. there is only a finite quantity of information available to us, so for some observables we can't just do the experiment again to check who is right).

What should we make of Planck vs SPT and Planck vs the local universe?

The universe as seen by Planck - Day Two

The cosmic microwave background (CMB) is the best probe we've yet found to study the early universe. The CMB's temperature is very nearly uniform. However this temperature does have very small anisotropies that can be used to study sound waves that existed in the primordial universe. The Planck satellite (an ESA funded experiment) has mapped these temperature anisotropies over the entire sky with the best resolution to date. Last month, Planck released its data and it immediately became the new benchmark for the testing of cosmological models and the measurement of cosmological parameters.

This week ESA is hosting the first conference since Planck released its data. The conference is at ESTEC in the Dutch town of Noordwijk. I am attending this conference and will be doing my best to write updates about what was discussed during the week.You can read my introductory post where I give my motivation for doing this, here.

The CMB is not just useful for studying the primordial universe. As soon as the CMB forms, everywhere in the universe, it travels freely, in every direction, at the speed of light. This means that, in every direction, the CMB we measure here on Earth today has travelled to us from a point billions of light years away. In principle, this makes the CMB not just a really good probe of the state of the universe where and when it was emitted, but also of everything it passed on its way to us.

This secondary use for the CMB turns out to be very useful and many of the highlights from Planck relate to the way in which the CMB interacts on its way to us. The existence of matter in the universe affects the CMB gravitationally. This causes the CMB to bend towards regions of over-density and away from regions of under-density. It also causes the CMB's temperature to shift as it falls into and out of over and under-dense regions. This first effect is known as lensing and one of Planck's most impressive results is a map of the locations of matter in the universe through this lensing effect. The second effect is known as the Sachs-Wolfe effect, something I've written about in some detail.

There is a third way that the CMB is significantly affected by the intervening universe. Within clusters of galaxies there is a lot of hot gas. If the CMB passes through a cluster it can scatter off electrons in this hot gas. The effect of this scattering on the CMB is known as the Sunyaev-Zeldovich (SZ) effect. Therefore, we should be able to use the CMB to detect the lines of sight along which the most massive clusters lie.

We can. And Planck has.

Planck rumours will soon become Planck results

On Thursday, the Planck satellite will be revealing its first cosmological results. In terms of fundamental physics, this will be the biggest event since the Higgs discovery last year. In the cosmology community it is the biggest event for the best part of a decade (possibly in both directions of time). If you don't follow cosmology too closely, you might wonder why this particular experiment might generate so much excitement. After all, aren't there all sorts of experiments, all of the time?

If so, I hope you've come to the right place.

The sky as seen by Planck in 2010. Only, they hadn't removed the foregrounds yet. There's a whole Milky Way galaxy in the way. Why must they make us wait so long?

If you're unaware, Planck is a satellite put in space by the European Space Agency to measure the cosmic microwave background (CMB). The CMB is an incredibly useful source of cosmological information. The impending release of Planck's results on Thursday is big news because Planck has measured the CMB with better resolution than any other experiment that can see the whole sky. Planck might have discovered evidence of interesting new physics, such as extra neutrinos or additional types of dark matter. It might even reveal some effects relating to how physics works at energies we could never probe on Earth. But even if it hasn't discovered anything dramatically new, the precision with which Planck has measured the parameters of the standard cosmological model will immediately make it the new benchmark.

There have been surprisingly few rumours leaked to the rest of the cosmology community about what to expect on Thursday. This has resulted in the most pervasive rumour being that they have simply not found anything worth leaking. Whatever the reality, on Thursday rumours will become results.

What has Planck actually done that is so interesting?

The ISW Mystery IV: Where does the evidence lead?

Where does the evidence lead? (Photograph: H Armstrong Roberts/Corbis)

In my last three major posts (I, II and III) I've been talking you through a mystery: the integrated Sachs-Wolfe mystery. This post will be able to be read on its own, but it you will appreciate it much more if you have also read them. In today's post I will be playing detective, examining the evidence, looking for leads and weighing up the various possible solutions to the mystery. Like any good mystery there are hints as to what the resolution might be, but like any good mystery story some of these hints might turn out to be just be red herrings, so we need to be careful.

At the beginning of my most recent post in this series I warned you that it would be my most technical post to date, but encouraged you to stick with it. With this post, the situation is the opposite. That post contained the details of the actual measurement that was made, which is necessarily going to be somewhat dry and technical. This post, however, speculates about what might have caused the effect. As you'll soon see, solving the mystery potentially requires modifications to our understanding of fundamental physics or the initial conditions of the universe. All very exciting stuff, so congratulations for making it to this point.

An overview of the case:

Before embarking on the detective work, let me recap the first three posts in this series. In the first post, I introduced what the integrated Sachs-Wolfe effect is. It is the very subtle heating and cooling of light as it passes through over and under dense regions of the universe. In the second post I explained that this effect is so small that it almost certainly will never be observed directly. The only hope we have to observe it is to look for statistical correlations between the temperature of light on the sky and the density of the matter that the light travelled through to reach us. Only the cosmic microwave background (CMB) is uniform enough that such a statistical correlation could ever be observed. In the last instalment, I told you of a particular measurement that intended to detect this ISW effect by looking at extreme over and under densities in the universe. The measurement appeared to be a success because it did measure a correlation. The only problem, and the source of the mystery, is that the size of the correlation is far too big to be from the ISW effect.

Something in those structures is heating/cooling the CMB, but what?

The ISW mystery III: How did the CMB get so hot?

An example map of what the ISW effect would look like on the sky if we could observe it directly (arxiv:1003.0974)

This is probably my most technical post to date. I don't want my contributions to this blog to be (all the time) popularised, ready to consume, pieces of quirky science. I want you to know what we, the cosmologists, are thinking and wondering about each day, beyond just vague explanations about accelerated expansion, dark energy and dark matter. I want you to understand how we're trying to explore the mysteries of cosmology. What are we measuring, how are we measuring it and what are we hoping it will tell us? Doing this has to be a two-way process. I invest time writing, doing my best to make things like the Integrated Sachs-Wolfe effect understandable and you invest time and concentration trying to understand.

The benefit for you of doing this is great. You will become engaged in the science in real time. When the mystery I'm about to reveal finally gets solved you will already be there waiting, expecting. You will be able to bask in the wonder of the discovery during the moments of discovery. Hence, it will also be your discovery.

You will only get this though, if you concentrate and think and read this post through. So, if you don't get it the first time, think about it and read it again. And, if you are left confused by anything, ask!

Recap of earlier posts

I'm going to describe in this post why there is an “ISW mystery”. I described in this post that the integrated Sachs-Wolfe (ISW) effect is the subtle heating and cooling of light as it passes through over and under-dense regions/structures in the universe. For most of the universe's history this effect was effectively non-existent. Any energy gained by light falling into a structure in the universe was perfectly balanced by the energy lost by the light climbing out of the structure. However, late in the universe's history something starts pushing the universe apart and as a result there is a net energy change. The gravitational well is smaller when the light leaves the structure than when it goes in.

Then, in this post, I explained that the ISW effect is incredibly small. This makes observing it very difficult. We can't observe it directly by looking at light from galaxies, quasars, supernovae, stars, etc. because we don't know the temperature of the light's source well enough. In fact, there is only one source of light that we do know well enough to use it to detect the ISW effect. This is the cosmic microwave background (CMB), which I introduce here. Unfortunately, even the tiny fluctuations in the temperature of the CMB are of the same size as the expected ISW temperature shifts. So, we still can't observe the ISW effect directly. What we can do though, is observe it on average. We know that the ISW effect occurs as light travels through over and under-dense regions in space. So what we can do is look for over and under-densities and ask whether the CMB is hotter on average when it has passed through an over-density and colder on average when it has passed through an under-density. How to find structures in space and what I mean by on average is covered in the post you are about to read...

The ISW mystery II: Trying to see the invisible

[Note: I'm travelling at the moment and haven't had time to write as substantial a post this time around as I'd hoped. We're all new to this blogging business, so next time I'm travelling for this long I'll plan further ahead and have the post ready in advance, or something. Anyway, enough excuses from me... I'll be back in Helsinki in a few weeks and will hopefully then be able to write something more substantial...]

In my last post I introduced something known as the integrated Sachs-Wolfe (ISW) effect. You'll probably get more out of today's post if you've read that one. However, I've tried to make today's post as self-contained as possible, so don't fret if you're new to the blog or have forgotten things over the last six weeks.

Put most simply, the ISW effect is the very subtle heating and cooling of light as it travels through structures in the universe. In the standard model for the universe's history this ISW effect grows with time and is most significant when dark energy starts to dominate the universe late in its history. The effect occurs because the energy gained or lost by light as it climbs into or falls out of structures becomes smaller with time. Therefore light receives an overall change in energy when it travels through these structures.

Unfortunately, the ISW effect is tiny. It will happen to any light travelling anywhere through the universe, but it is really, really tiny. This means that, for almost every light source in the universe (galaxies, stars, supernovae, etc), we just don't know the initial light source well enough to be able to tell if it has changed by the tiny amount we expect from the ISW effect. But, there is one source for which we have a very clear, very precise prediction. This is the cosmic microwave background, or CMB (note: I introduced the CMB in this post). As regular readers of the blog might be starting to appreciate, the CMB is more or less every cosmologist's favourite data source.

Unfortunately even the CMB has tiny fluctuations in it. These arise because the source of the CMB, a plasma of hydrogen that once permeated the entire universe, was not uniform (I explained the shape of the fluctuations in the CMB in an earlier post). And, most unfortunately, even these tiny fluctuations, fluctuations so small that Nobel prizes were awarded for their detection, are bigger approximately the same size as [Edit: 16/3/2012] the predicted size of the ISW effect. I have to admit that I find this irony amusing. The ISW effect is so small that one of the most significant measurements humanity has ever made is just annoying noise in the quest to detect it.

Alas! So it seems that we can't even see the ISW effect in the CMB?

Not quite...

The ISW mystery I: Introduction

Looks nice Roger, but what are the industrial applications?

Making science a spectator sport

A huge part of the motivation for us starting this blog, if not the main motivation was to present new research as it is being done. In other words, to present the view of new research from the very trenches where the discoveries are made. I still intend (at some point in that mythical, utopian, land called later) to write a more thorough “motivation for the blog” post; however, the main motivation for presenting new research now, rather than waiting for Brian Cox to make a documentary about it, is this: it allows everyone in society to feel involved in scientific research. The hope is that science will then go beyond being just what those guys with beards in white coats do that we, everyone else, don't understand and instead becomes something that society as a whole gets behind and becomes fascinated by and talks about excitedly during their lunch-break.

You might think this is over-ambitious (though possibly not if you're reading this blog). But, meh, I think you are wrong. The public response to scientific discoveries/announcements last year like this and this tells me that people do care and are immensely fascinated by what scientists do. If society is not talking about science at the water-cooler it is because we, the scientists, are not collectively trying hard enough to involve society in science. There are numerous hard working and successful exceptions of course. The fact that they are exceptions is the problem.

Some scientists reading this might wonder why we even want society talking about science at the water-cooler. Mightn't science become corrupted by such base chatter? Think about this again the next time you are applying for some grant money and have to bend over backwards trying to come up with possible industrial applications for your work. Especially when later that evening you could watch a sportsman get paid millions for doing what he or she chooses to do. I doubt Nike have ever asked Roger Federer to come up with potential industrial applications for his backhand. Sportsmen are paid simply because people like watching them play and think they are cool. But people also want to keep track of scientific progress and they definitely also think it is cool. This latent popularity isn't a bad thing and it isn't being utilised enough by science.

In this sense this blog, and others like it, could be described as attempts by scientists to start making science a spectator sport. Hopefully we'll get better with time.

So, with that unnecessarily long introduction out of the way, let me finally (from the perspective of both this post and the blog itself) start telling you about some of my own research...