Monday, January 16, 2012

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...

I will explain this research through a series of posts (unknown now in number). These posts will be about a mystery. Something that in the title to this post I have called the ISW mystery. At the moment, nobody knows the answer to the ISW mystery. It is a new mystery. It first became apparent as recently as 2008 and although the problem is better understood now than then it still remains a mystery. My contributions towards solving the ISW mystery started last year.

It is highly possible that by the time I'm finished with this series of posts it won't be a mystery anymore (maybe my collaborators and I will have solved it, maybe we'll get scooped). In any case, this is it, the frontier of research. I don't know the final destination of this any better than you do!

Your humble writer, standing on the metaphorical edge of human
knowledge, more than a little terrified about what lies beyond.

The CMB's journey (or a different type of mineral in the quarry)

In a previous post I introduced the great and (for a little while longer) plentiful quarry of cosmological information known as the Cosmic Microwave Background (CMB). Then, in another previous post, I began to explain what the tiny fluctuations in the CMB's temperature can tell us about the early universe.

What I have only vaguely alluded to so far is the 13.7 billion year journey taken by the CMB's light between its creation and its detection. There is a habit of cosmologists to view this journey as uninteresting and anything that happens during it as a nuisance. This is partially well-motivated. The CMB, when formed, was an almost perfect image of the state of the early universe. Anything that happened to it afterwards will have corrupted what could otherwise have been an ideal photograph. However, it is ultimately foolish because in these secondary effects there is much that we can determine about the evolving universe. The CMB is the one thing we can currently measure in the universe that is literally everywhere. At every single cosmological event since it was formed the CMB was there, watching. So, if we are clever enough, and the CMB interacted somehow with an event, we can use the CMB to learn things about it. We may even learn things about events that would otherwise be completely impossible to actually see.

In other words these secondary effects aren't nuisances, they're just a different type of mineral in the amazing CMB quarry.

I am going to be writing in this series of posts about the effects of gravity on the CMB. This is because it appears that certain gravitational effects on the CMB from enormously large structures in the universe are much, much, larger than we expect (i.e. the ISW mystery). Why this anomaly exists, nobody yet knows. It could be that it is an indication that some sort of adaptation is needed to general relativity, which gives us the laws of gravity. It could be that the sizes of the largest structures in the universe are much bigger than we expect. This would indicate that the initial fluctuations of the universe do not follow the distribution that our simplest models predict (and that work everywhere else). Either of these results would have huge implications for our knowledge of fundamental physics.

Alternatively, this anomaly could be evidence that some seemingly obvious assumptions being made in cosmological calculations are wrong. There are even candidates for what these assumptions might be. This might sound like the most likely possible explanation (and also the least interesting). However, it is actually the most messy potential explanation of them all. These assumptions are widespread in our cosmological calculations and, mostly, they seem to work very well. Any proof that they are wrong (and they may be wrong) would have dramatic consequences to our understanding of the evolution of the universe. This in turn could have dramatic consequences for the interpretations we've made about fundamental physics based on that understanding.

Or, finally, the anomalously large signal could be a statistical fluke. The chances of this are less than 1 in 1000, so very unlikely, but not impossibly unlikely. Chance may just be playing a cruel trick on us – it is possible!

Whatever the explanation for this anomaly is, it will have to change the anomalous calculation in such a way as to remove the discrepancy without ruining all the other predictions that the standard cosmological model got right elsewhere in the universe. This is no simple task and each of the possibilities I listed above, except for the statistical fluke, comes with baggage concerning other measurable quantities. Really, this just makes this anomaly (and any others) all that much more intriguing. Is it really telling us that something is wrong with our understanding of the fundamental aspects of the universe? And if so... what?

How does gravity affect the CMB?

There is structure in the universe. All through the CMB's journey towards detection there have been regions of space that are slightly more dense and regions that are slightly less dense. Gravitationally, all (ordinary) matter will pull other things towards it. As I've explained before, this means that the more dense regions of space will pull things towards them slightly more than the less dense regions.

Light, and thus the CMB, are no exceptions to this pulling. As the CMB has travelled the universe it has been receiving subtle net pulls towards over dense regions that pull slightly more than the rest of the universe and subtle net pushes away from under dense regions that pull slightly less. This subtle pushing and pulling on light as it travels past structure is known as gravitational lensing. Lensing is responsible for small deviations to what would otherwise be a straight path for the light in the CMB.

Extremely dense objects, such as galaxy clusters, can actually lens some light travelling past them so strongly that they act just like an optical lens would on Earth, producing (for example) multiple images of something behind them. However, objects dense enough to act like such a strong lens are rare and small in size. What is more common is known as weak lensing. Weak lensing merely distorts an image behind the lensing object. But it can be seen and measured and can be used to obtain information about the lensing object and the light source being lensed. Both of these types of lensing are important sources of knowledge in cosmology. However it isn't only lensing that affects the CMB gravitationally and it isn't lensing that I will be discussing in these posts (not for a while at least).

Some pretty intense gravitational lensing going on around a galaxy.
(The blue horseshoe is a galaxy lensed by the red galaxy at the centre of the image)

When matter is pulled by other matter it doesn't just change path it can also speed up or slow down. This speeding up or slowing down results in changes in the energy of the matter being pulled. Unlike matter, light can't change its speed. That is constant. But it can change energy, and does (remember that different energy light has a different wavelength/frequency/colour). When light falls towards an attractive region of higher density, it gains energy. When it climbs out of such a region it loses energy. Conversely, when it climbs into a net repulsive region of lower density it loses energy and when it falls out of such a region it gains energy. For the CMB, any gain or loss in energy corresponds directly to a gain or loss in temperature. With luck (for me) this won't be new to readers of this blog because it is also this phenomenon that (partially) generates the initial fluctuations in the CMB temperature as it climbs (or falls) out of the density fluctuations it was formed in (as I explained earlier).

Therefore, as the CMB travels through the universe it is constantly climbing in and out of gravitational wells and hills, gaining and losing energy as it goes. The miracle is... very nearly, none of this matters. To understand why, first consider the CMB's light travelling through a perfectly stationary universe. Even in this hypothetical world there would still be gravitational wells and hills, but none of this would matter. The reason is that no matter how deep into a well any part of the CMB fell, or how high up a hill it got, we know it must come back out of the structure if we are to detect it at Earth! Therefore, if we are following the CMB from origin to detection, if we want to know the net change in its temperature/energy we don't need to know anything about what path it took to get here. All we need to know is how far up or down a well or hill it was when created and how far up or down a hill we are here. Turning that around, if we can measure the temperature fluctuations of the CMB here at Earth, then we are directly measuring the density perturbations where the CMB was formed 13.7 billion years ago.

But wait, the universe is not stationary. In fact, in the real universe, the density perturbations are actually always growing with time.

Surely this means that the gravitational wells and hills are growing too?

In fact, it doesn't and here is why...

The universe is also expanding!

Because the universe is expanding, even though (everywhere) the fluctuations in density are growing, they are also getting further apart (almost everywhere). The energy gained or lost by light (or anything else) as it travels past any matter in the universe depends both on how much mass the matter has and how close the light gets to the matter. In our expanding universe with ever growing structures these effects almost completely cancel out.

Two things conspire to stop them cancelling perfectly. These are dark energy and (writing a bit loosely) gravitational instability. Dark energy stops the effects cancelling by providing a push that increases the expansion rate of the universe. This means that structures in the universe move apart at a faster rate than the rate at which they gain more mass. This causes the gravitational wells and hills to shrink late in the universe's history when dark energy starts to work its magic. Gravitational instability causes structures to start to form more quickly, (probably) without also causing the universe to expand faster. This causes the gravitational wells and hills to grow late in the universe's history. Any parts of the CMB that are caught in a well or hill while the well or hill changes size will experience a net shift in temperature. This is simple to see. If a well was deeper when light fell into it than when the light climbed out of it, then there will be a net increase in the light's energy/temperature from traversing the well. If the well was shallower, there will be a net decrease in the light's energy/temperature. The converse holds for hills.

This net temperature shift in the CMB is called the integrated Sachs-Wolfe (ISW) effect. This name comes from the Sachs-Wolfe effect which is applied to the simple gain and loss of energy as light falls in and out of gravitational wells (that name came about in the obvious manner). It is this ISW effect that seems to have been measured and appears to be much larger than expected.

How it has (probably) been measured and how we know how big the signal should be will come in later posts... (now continued here)

Twitter: @just_shaun


  1. I find it interesting that you say 'at Earth' rather than 'on Earth', which would be the usual convention. I suppose that if you're always considering the Earth in the wider context of the Universe then 'at' would be more appropriate.

    I'm disappointed you chose Federer over Kásás or Kiss!

  2. Hah, yes I made a conscious decision about that. I did originally write "on Earth". The reason why I changed actually has nothing to do with the universe in a wider context. Two of the CMB detectors (COBE and WMAP) have been space based satellites (with a third, Planck, still to report) and many have been balloon based. So quite literally, "on Earth" just didn't feel right to me.

    For the second point... I blame the Australian Open.

  3. Trying to understand ISW as it pertains to law of conservation of energy - if light exits a gravity well with a different energy to when it went in, how do we account for the difference? Is it drawn from or deposited with the massive body responsible for the gravitational field? What form does this energy take? In a different context, I guess I'm asking if a photon can minutely affect the kinetic energy of a planet!

  4. Hi inductible, thanks for the comment.

    Firstly, yes a photon definitely does minutely affect the kinetic energy of a planet. In general relativity it is energy that causes gravitational forces, not mass. Mass of course does also gravitate, but only because it carries energy. So, because any photon carries energy it also pushes and pulls anything else that is affected by gravity.

    But more surprisingly, in general relativity, energy is not actually conserved. Or, at least, the energy of all the matter and radiation in the universe is not conserved. This is somewhat obvious when you realise that dark energy is a field of constant energy *density*, no matter what volume it is put in. So, even when the universe doubles in volume, the *density* of dark energy remains the same, which means that as the universe expands the total energy in the dark energy field is constantly increasing. This post at the Cosmic Variance blog explains the issue of energy conservation in general relativity quite well.

    The point is that, even though the photon is exchanging energy with the matter as it falls in and out of the gravitational wells, the fact that there is a net gain or loss of energy in the photon doesn't necessarily require that there is a net loss or gain of energy in the matter to compensate. It is precisely the uncompensated decay in the gravitational potential of the matter that allows for there to be a net effect on the photon.

    I hope that helps. If it isn't clear, feel free to ask for clarification. And you should definitely read through the link to Cosmic Variance that I provided.