Wednesday, July 1, 2015

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.

Wednesday, April 29, 2015

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

Wednesday, March 25, 2015

The science of three-parent children

2015 has already been a significant year in the field of human medicine as February saw the UK become the first country in the world to legalise the generation of so-called 'three-parent' children. This marks a milestone for preventative genetics and embryology and offers hope to many people around the UK and beyond who would be unable to have healthy children otherwise. The votes to bring this into law were fairly comfortably won by those in favour - 382 vs 128 in the House of Commons (the lower house) and 280 vs 48 in the House of Lords (the upper house) - however there have been a number of vocal opponents to the measure. In this post I hope to explain just what the process involves, and why it is considered necessary by the majority of British MPs.

A cellular energy crisis

Mitochondria, as you may recall from a previous post, are the powerhouses of our cells. They metabolise a range of molecules derived from food at use them to generate energy in the form of another molecule, ATP. You would not last long without them - just try holding your breath for a few minutes, since anaerobic respiration is all a cell without mitochondria would be able to manage. It is not surprising, therefore, that problems with mitochondrial function can be fairly nasty. Mitochondrial diseases are a range of genetic disorders in which the proper role of the mitochondria is disrupted due to mutations in one of the genes responsible for making mitochondrial proteins. These diseases never completely knock out mitochondrial function (since an embryo with such a disease could never survive to full development) but still cause severe symptoms in sufferers. Depending on the exact mutation, these can include blindness, deafness, diabetes, muscle weakness, cardiac problems, and problems with the central nervous system. Prognoses vary from one disorder to the next, but they invariably shorten lifespan, often severely. Sufferers of Leigh's disease, for example, rarely live past 7 years of age, and spend their short lives experiencing muscle weakness, lack of control over movement (particularly of the eyes), vomiting, diarrhea, an inability to swallow, and heart problems, among others. 

Tuesday, February 3, 2015

Combined constraints from BICEP2, Keck, Planck and WMAP on primordial gravitational waves

This week, the joint analysis of BICEP2 (+ BICEP2's successor Keck) and Planck has finally arrived. The result is more or less what was expected, which is that what BICEP2 saw last year in the B-mode polarisation signal of the CMB was not actually primordial gravitational waves (as had originally been hoped and claimed), but was unfortunately actually due to dust in the Milky Way. Such is life. Though we did of course have the best part of a year to come to grips with this reality.

Combined constraint on \(r\) from polarisation and temperature measurements (in blue). Freshly digitised in the spirit of modern cosmology. Gives \(r\lesssim 0.09\) at \(95\%\) confidence.

As a result of subtracting the dust component in BICEP2/Keck's signal (obtained by comparing the measurements from BICEP2/Keck and Planck), the final constraint on the "tensor to scalar ratio" (or \(r\)) from the BICEP2/Keck measurement is that \(r<0.12\) at \(95\%\) confidence. This \(r\) parameter essentially measures the amplitude of a primordial gravitational wave signal, so the net result is that the subtraction of dust takes BICEP2's high significance measurement of non-zero \(r\) and converts it into simply an upper bound.

I've seen some comments on blogs, in media, on Twitter, etc that there is still evidence of some sort of excess signal in BICEP2/Keck over and above the dust, but I can't see any evidence of that in any of their published results. The final likelihood for \(r\) (shown above in black) shows a plot consistent with \(r=0\) at less than \(1-\sigma\) (i.e. \(r=0\) is less than one standard deviation away from the maximum likelihood value). In fact, it would seem that the measurement of the dust that has been obtained by comparing BICEP2/Keck's measurements with Planck's measurements has been so good that the B-mode constraint on \(r\) from BICEP2/Keck is now competitive with (or even slightly better than) the constraint arising from temperature measurements of the CMB. This was always going to happen at some point in the future and it seems that this future has now arrived.

Wednesday, October 22, 2014

Why is Ebola so scary?

Unless you've been living under a reasonably sizable rock for the last few months, it can't have escaped your attention that the world has yet another terror to throw on the mountain of things we should be scared of: Ebola. The ongoing situation in Africa is the largest Ebola outbreak in history and has seen the disease spread beyond Africa for the first time. At the time of writing this, nearly 10,000 people have become infected, almost half of whom have died. This number is growing...rapidly.
Ebola cases and deaths in the 2014 outbreak.
In this post, I will describe what Ebola is, why it is so scary, and what chances we have of defeating it.

What is Ebola?

'Ebola' as a biological term actually refers to a group of five viruses within the Filoviridae family, of which four can cause the disease generally called Ebola, but more specifically known as Ebola virus disease. The recent outbreak has been caused by just one of these viruses, which used to be known as Zaire Ebolavirus, but is now simply 'Ebola virus' given that it is the most common among humans, and Zaire no longer exists! It doesn't look a whole lot like most viruses, it has to be said - with long, tubular filaments waving around rather than the tight, spherical viruses we're used to seeing for 'flu, HIV, and most others.

The Ebola virus.

Friday, September 19, 2014

Comparing Planck's noise and dust to BICEP2

In case anyone reading this doesn't recall, back in March an experiment known as BICEP2 made a detection of something known as B-mode polarisation in the cosmic microwave background (CMB). This was big news, mostly because this B-mode polarisation signal would be a characteristic signal of primordial gravitational waves. The detection of the effects of primordial gravitational waves would itself be a wonderful discovery, but this potential discovery went even further in the wonderfulness because the likely origin of primordial gravitational waves would be a process known as inflation which is postulated to have occurred in the very, very early universe.

The B-mode polarisation in the CMB as seen by BICEP2. Seen here for the first time in blog format without the arrows. Is it dust, or is it ripples in space-time? Don't let Occam's razor decide!

I said at the time, and would stand by this now, that if BICEP2 has detected the effects of primordial gravitational waves, then this would be the greatest discovery of the 21st century.

However, about a month after BICEP2's big announcement a large crack developed in the hope that they had detected the effects of primordial gravitational waves and obtained strong evidence for inflation. The problem is that light scattering of dust in the Milky Way Galaxy can also produce this B-mode polarisation signal. Of course BICEP2 knew this and had estimated the amplitude of such a signal and found it to be much too small to explain their signal. The crack was that it seemed they had potentially under-estimated this signal. Or, more precisely, it was unclear how big the signal actually is. It might be as big as the BICEP2 signal, or it might be smaller.

Either way, the situation a few months ago was that the argument BICEP2 made for why this dust signal should be small was no longer convincing and more evidence was needed to determine whether the signal was due to dust, or primordial stuff.

Tuesday, August 26, 2014

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?