Tag Archives: acceleration

Cosmology with the Square Kilometre Array

A large fraction of my time over the last 18 months has been spent working out parts of the cosmology science case for the Square Kilometre Array, a gigantic new radio telescope that will be built (mostly) across South Africa and Australia over the coming decade. It’s been in the works since the early 90’s and – after surviving the compulsory planning, political wrangling, and cost-cutting phases that all Big Science projects are subjected to – will soon be moving to the stage where metal is actually put into the ground. (Well, soon-ish – the first phase of construction is due for completion in 2023.)

Infographic: SKA will have 8x the sensitivity of LOFAR.

A detailed science case for the SKA was developed around a decade ago, but of course a lot has changed since then. There was a conference in Sicily around this time last year where preliminary updates on all sorts of scientific possibilities were presented, which were then fleshed out into more detailed chapters for the conference proceedings. While a lot of the chapters were put on arXiv in January, it’s good to see that all of them have now been published (online, for free). This is, effectively, the new SKA science book, and it’s interesting to see how it’s grown since its first incarnation.

My contribution has mostly been the stuff on using surveys of neutral hydrogen (HI) to constrain cosmological parameters. I think it’s fair to say that most cosmologists haven’t paid too much attention to the SKA in recent years, apart from those working on the Epoch of Reionisation. This is presumably because it all seemed a bit futuristic; the headline “billion galaxy” spectroscopic redshift survey – one of the original motivations for the SKA – requires Phase 2 of the array, which isn’t due to enter operation until closer to 2030. Other (smaller) large-scale structure experiments will return interesting data long before this.

Artist's impression of the SKA1-MID dish array.

We’ve recently realised that we can do a lot of competitive cosmology with Phase 1 though, using a couple of different survey methods. One option is to perform a continuum survey [pdf], which can be used to detect extremely large numbers of galaxies, albeit without the ability to measure their redshifts. HI spectroscopic galaxy surveys rely on detecting the redshifted 21cm line in the frequency spectrum of a galaxy, which requires narrow frequency channels (and thus high sensitivity/long integration times). This is time consuming, and Phase 1 of the SKA simply isn’t sensitive enough to detect a large enough number of galaxies in this way in a reasonable amount of time.

Radio galaxy spectra also exhibit a broad, relatively smooth continuum, however, which can be integrated over a wide frequency range, thus enabling the array to see many more (and fainter) galaxies for a given survey time. Redshift information can’t be extracted, as there are no features in the spectra whose shift can be measured, meaning that one essentially sees a 2D map of the galaxies, instead of the full 3D distribution. This loss of information is felt acutely for some purposes – precise constraints on the equation of state of dark energy, w(z), can’t be achieved, for example. But other questions – like whether the matter distribution violates statistical isotropy [pdf], or whether the initial conditions of the Universe were non-Gaussiancan be answered using this technique. The performance of SKA1 in these domains will be highly competitive.

Another option is to perform an intensity mapping survey. This gets around the sensitivity issue by detecting the integrated HI emission from many galaxies over a comparatively large patch of the sky. Redshift information is retained – the redshifted 21cm line is still the cause of the emission – but angular resolution is sacrificed, so that individual galaxies cannot be detected. The resulting maps are of the large-scale matter distribution as traced by the HI distribution. Since the large-scale information is what cosmologists are usually looking for (for example, the baryon acoustic scale, which is used to measure cosmological distances, is something like 10,000 times the size of an individual galaxy), the loss of small angular scales is not so severe, and so this technique can be used to precisely measure quantities like w(z). We explored the relative performance of intensity mapping surveys in a paper last year, and found that, while not quite as good as its spectroscopic galaxy survey contemporaries like Euclid, SKA1 will still be able to put strong (and useful!) constraints on dark energy and other cosmological parameters. This is contingent on solving a number of sticky problems to do with foreground contamination and instrumental effects, however.

The comoving volumes and redshift ranges covered by various future surveys.

The thing I’m probably most excited about is the possibility of measuring the matter distribution on extremely large-scales, though. This will let us study perturbation modes of order the cosmological horizon at relatively late times (redshifts below ~3), where a bunch of neat relativistic effects kick in. These can be used to test fundamental physics in exciting new ways – we can get new handles on inflation, dark energy, and the nature of gravity using them. With collaborators, I recently put out two papers on this topic – one more general forecast paper, where we look at the detectability of these effects with various survey techniques, and another where we tried to figure out how these effects would change if the theory of gravity was something other than General Relativity. To see these modes, you need an extremely large survey, over a wide redshift range and survey area – and this is just what the SKA will be able to provide, in Phase 1 as well as Phase 2. While it turns out that a photometric galaxy survey with LSST (also a prospect for ~2030) will give the best constraints on the parameters we considered, an intensity mapping survey with SKA1 isn’t far behind, and can happen much sooner.

Cool stuff, no?

What does “acceleration” mean in cosmology?

When astronomers look at distant Type-Ia supernovae, they find them to be dimmer than expected. The most popular interpretation of this result is that it’s caused by the expansion of the Universe getting faster – accelerating – and so the supernovae are further away than we first thought. This conclusion is only valid if you assume that the cosmos is filled with homogeneously-distributed matter. In practise, we know that that’s not the way things are (we see galaxy clusters surrounded by large voids; certainly not homogeneous). But, if you can smooth over all of the lumps and bumps on sufficiently large scales, you should get a homogeneous model out. The model that describes this situation is called a Friedmann-Lemaitre-Robertson-Walker (FLRW) model, and when you fit that to the supernova data, you find that about 70% of the energy density of the Universe has to be made up of some sort of mysterious “dark energy“. This is weird. We don’t know what it is.

Much of what we do in cosmology rests on assuming that this smoothing procedure is valid, but actually, we aren’t quite sure that it is yet*. It might be the case that the Universe isn’t homogeneous on large scales, for example, or that the smoothing procedure introduces corrections into the equations for the FLRW model (so-called “backreaction” effects). So, to find out whether the smoothing procedure is sensible or not, people look at inhomogeneous models of the Universe. By necessity, these are gross simplifications; working with inhomogeneous general relativistic models is hard, and you tend only to be able to solve the relevant equations for simple models with lots of symmetry. The real Universe isn’t so symmetric.

3D-averaged distance modulus curves in a Spherical Collapse model.

Once you move away from the simplicity of the homogeneous FLRW models, lots of things change. In particular, the choice of model strongly affects how you interpret your observations. Over the past few weeks (OK, months…), we’ve been looking at the way acceleration is defined in inhomogeneous spacetimes, to see how conclusions about the existence of dark energy are affected by throwing inhomogeneity into the mix.

We pick out four possible definitions of acceleration as being particularly relevant to current ideas on the origin of the apparent accelerating expansion:

  1. The local acceleration of the expansion of a spatial volume, governed by the Raychoudhuri equation;
  2. The acceleration inferred by an observer fitting an FLRW distance-redshift relation to the low-z part of their observed Hubble diagram;
  3. The acceleration inferred by reconstructing only the Hubble diagram locally (i.e. exactly at z=0), as described by Kristian and Sachs;
  4. The acceleration of the effective scale factor of volumes that have been spatially averaged according to the Buchert scalar averaging procedure.

For an exactly homogeneous and isotropic FLRW model, all of these definitions converge to give the same measure of acceleration. In the general case, however, they can all be quite different, to the point where some of them can show strong acceleration, whilst others are decelerating. This is shown in the plot above, for a “spherical collapse” model. This is an inhomogeneous model made up of a bunch of disconnected FLRW regions with different expansion rates and densities. For definitions (2) and (4), we see acceleration, but for (1) and (3) we see deceleration. Yikes. The upshot is that using supernovae might not be the best idea if you want to find out if the apparent acceleration is caused by a cosmological constant or not. It also has some interesting things to say about the relationship between what we actually observe, and what happens when you work with a smoothed-out model (the “fitting problem”).

We’re close to releasing a paper on this, so I’ll have more on it soon.

* When I say “we”, I actually mean “a small subset of the cosmology community”. I think it’s fair to say that many cosmologists feel that the issue is settled, or are not even aware of it. My personal feeling is that it’s not settled, and there’s still much work to be done before it is. But hey, everyone thinks that their own area of research is important, right?