Monday, 31 October 2011

How was the Universe born?

Just a quick note to say that I had an article published in Australasian Science on the birth of the Universe. As you can see, I also got the cover. Unfortunately, you have to pay to subscribe, but I think this appears in many Australian schools. Anyway, here's the abstract

Modern cosmology tells us that the universe as we know it arose 13.7 billion years ago in the fiery birth of the Big Bang, but our understanding of the laws of physics is incomplete and we are currently unable to answer the questions of where the universe actually came from. Cosmologists have many ideas, ranging from the reasonably strange to the extremely outlandish.

Wednesday, 26 October 2011

Gravitational Lensing with Three-Dimensional Ray Tracing

One of the cool things about the universe is that light rays don't travel in straight lines. As they pass through the cosmos, lumps of mass (stars, galaxies, clusters, black holes etc) tug on the path of light rays and so they follow a wiggly path.

It looks something like this

The colours here represent density in the universe, where yellow is high density, purple middling and black low density, and you can see the cosmic web of mass which has come from a computer simulation of structure formation.

The green line is a light path travelling through the universe, and as you can see, it wiggles.

Here's another version of the picture
The result is that view of the distant universe is distorted, and a considerable focus of future telescopes is to measure the amount of distortion that we see. This will allow us to measure a couple of key things, namely the distribution of matter (which is good, because a lot of it is that pesky dark matter that we can't see), and also the underlying cosmology (and so will be a probe of dark energy).

But to understand all of this, we need some theoretical models to compare to the observations. How do we do this? Well, it's not easy to follow light rays and typically people use what's known as the multi-plane approximation. It's easy to visualize - you take your continuous mass distribution and chop it into chunks, and then squash the chunks onto flat planes. Light rays then travel in straight lines between the planes, but as they pass through a plane, they feel the mass in the plane and get deflected.

This looks something like this
which I took from the paper by Hilbert et al.

But the question is, is this a good approximation. People generally shrug and go "I think so".

I'm please to announce that my ex-student, Madhura Killedar, who got her PhD earlier this year and is now a postdoc in Trieste, has just had one of her thesis papers accepted where she tests this, by comparing the multiplane method with a more "correct approach", actually integrating the geodesic equation through the simulations.

The task should not be underestimated, as it took three years of her PhD to do this. There are lots of technical issues which I will not go into here, but involved big simulations, Fourier transforms, multi-dimensional integrals, resolution scales etc etc, So this paper is the first of a series presenting her thesis work. This one got a pretty sweet referees report too :)

I encourage you to have a look. Well done Mud!!

Gravitational Lensing with Three-Dimensional Ray Tracing

High redshift sources suffer from magnification or demagnification due to weak gravitational lensing by large scale structure. One consequence of this is that the distance-redshift relation, in wide use for cosmological tests, suffers lensing-induced scatter which can be quantified by the magnification probability distribution. Predicting this distribution generally requires a method for ray-tracing through cosmological N-body simulations. However, standard methods tend to apply the multiple thin-lens approximation. In an effort to quantify the accuracy of these methods, we develop an innovative code that performs ray-tracing without the use of this approximation. The efficiency and accuracy of this computationally challenging approach can be improved by careful choices of numerical parameters; therefore, the results are analysed for the behaviour of the ray-tracing code in the vicinity of Schwarzschild and Navarro-Frenk-White lenses. Preliminary comparisons are drawn with the multiple lens-plane ray-bundle method in the context of cosmological mass distributions for a source redshift of $z_{s}=0.5$.

Monday, 17 October 2011

A sad C day

I understand a lot of people were moved by the death of Steve Jobs, but IMHO a gianter (if that's a word) person of the computer world also died last week. Sadly, Dennis Ritchie died on the 12th October.
While Steve gave us shiny toys (and yes, I am typing this on a MacBook, and I have an iPad), Ritchie gave us (well, me) some of the vital tools of the trade. With Ken Thompson, he developed the best operating system in the world, namely
Yes, UNIX. When I started my PhD, we used VMS on VAXes, but these were superseded by these beauties -
Sun machines running SunOS, my first experience of UNIX. Soon after, we had the birth of penguin, and we could have real computing in the home with Linux.
In the old days, we were spending a fortune on maintenance contracts for Vaxes and Sun machines, so the prospect of running a free proper operating system on cheap hardware was very appealing (and no, windows of any variety is not a proper operating system - good for games, but not for my research).

People realised that that you can string computers  together to build cheap supercomputers and computational astrophysics forged ahead. Many of the spectacular cosmological simulations were run on such supercomputers.

But if that was not enough, Ritchie give us one more thing, the C programming language. I'm going to moan and gripe like an old man that students today don't know how to code, and perhaps they can get away with Python, but I'm a fan of basic languages, C and fortran, for coding in supercomputer environments (and I'm not going to get all religious on programming language).

However, I started to learn C from Ritchie's own book
While I now realise this is an excellent book, it is not the book to learn C from. Many times I ended up shouting at the book "Why!!! Oh why doesn't it work!!" Ah, the joy of being a research student. Thank you Dennis Ritchie :)

Monday, 10 October 2011

Faster than the speed of light

After a weekend of great rugby (from the Welsh, the English and Australians were rather blah), I have responded to a good question posted over at The Conversation on distances in the Universe. It's a question that gets raised quite a bit and basically put it goes something like
If the Universe began 13.7 billion years ago, when the distance between any pair of points was zero, how can anything be more than 13.7 billion light years away?
The answer is the difference between local motions and global motions. Here's the response I posted

An excellent question, and one which may not make sense to start with. We know from special relativity, nothing can travel faster than light (recent neutrino claims excepted). But in reality, special relativity says that nothing can go faster than the speed of light **locally**, so in a small box, if I try and race an electron and a photon across the box, the photon will win.

With the expanding universe, the question we are asking is a little different. We are asking how fast something is moving "over there", rather than locally. It turns out that, if you crank the handle of general relativity, that something over there can be moving faster than the speed of light here. But anyone in the universe who does the local test on the speed of light, by racing photons and electrons, will always find that the photons will win.
If you think about it, what it means that, relative to the speed of light here, light out there is moving faster than the speed of light.
This is a very important point. It seems that everyone takes the statement from special relativity, namely that you can't travel fast than light, and then tries to apply it into a global picture. But that is not correct.

One key feature of the curved space-time of general relativity is that you map any patch into the flat space-time coordinates of special relativity, where you only need to worry about the physics of special relativity (and gravity vanishes). At this point, all massive objects sit within their future light-cones - which basically means their local motion is less than the speed of light.

But there is no simple way to compare a patch here to a patch there, and talking about how fast something is moving "over there" really does not have a unique answer in relativity. It depends on the coordinates you choose to us (and if something depends on coordinates, it ain't physically observable).

Here's an excellent example (taken from Tamara Davis's website).
The dotted lines are are the motions of objects. In the top one, in "physical" distance, the more distance objects are very "tilted over" and are moving faster than the speed of light locally. But then again, light out there is moving fast than the speed of light locally.

Moving down the pictures, the bottom one is in comoving coordinates, and now distant objects are stationary with respect to us. How fast a distant something is moving with respect to us depends on which coordinates you choose.

It's actually messier than that. I can chose to mix up time and space into new coordinates, and this demonstrates that superluminal verses subluminal motions get even more confusing. But I won't write about it here, but let you have some reading.

Coordinate Confusion in Conformal Cosmology

Geraint F. Lewis, Matthew J. Francis, Luke A. Barnes, J. Berian James
A straight-forward interpretation of standard Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies is that objects move apart due to the expansion of space, and that sufficiently distant galaxies must be receding at velocities exceeding the speed of light. Recently, however, it has been suggested that a simple transformation into conformal coordinates can remove superluminal recession velocities, and hence the concept of the expansion of space should be abandoned. This work demonstrates that such conformal transformations do not eliminate superluminal recession velocities for open or flat matter-only FRLW cosmologies, and all possess superluminal expansion. Hence, the attack on the concept of the expansion of space based on this is poorly founded. This work concludes by emphasizing that the expansion of space is perfectly valid in the general relativistic framework, however, asking the question of whether space really expands is a futile exercise.

Wednesday, 5 October 2011

Accelerated Expansion

The Science Blogosphere is going to be full of comments on the winning of the 2011 Nobel Prize by Perlmutter, Riess and Schmidt, and so I am not going write a lot on this topic, other than to say that I know Brian well and I am very happy for him. The fact Riess is younger than me suggests that I may not be personally on the Nobel Prize trajectory :)

Anyway, I quite like the Nobels. Not the prize itself, as it rewards individuals from what are typically large groups, but guessing who the next winner will be is fun.

This year I was correct, and I have evidence over at Uncertainty Principles, and it looks like I win a prize myself :)