## Cosmic Clumpiness Conundra

Posted in The Universe and Stuff with tags , , , , , , , , , , , , , , on June 22, 2011 by telescoper

Well there’s a coincidence. I was just thinking of doing a post about cosmological homogeneity, spurred on by a discussion at the workshop I attended in Copenhagen a couple of weeks ago, when suddenly I’m presented with a topical hook to hang it on.

New Scientist has just carried a report about a paper by Shaun Thomas and colleagues from University College London the abstract of which reads

We observe a large excess of power in the statistical clustering of luminous red galaxies in the photometric SDSS galaxy sample called MegaZ DR7. This is seen over the lowest multipoles in the angular power spectra Cℓ in four equally spaced redshift bins between $0.4 \leq z \leq 0.65$. However, it is most prominent in the highest redshift band at $z\sim 4\sigma$ and it emerges at an effective scale $k \sim 0.01 h{\rm Mpc}^{-1}$. Given that MegaZ DR7 is the largest cosmic volume galaxy survey to date ($3.3({\rm Gpc} h^{-1})^3$) this implies an anomaly on the largest physical scales probed by galaxies. Alternatively, this signature could be a consequence of it appearing at the most systematically susceptible redshift. There are several explanations for this excess power that range from systematics to new physics. We test the survey, data, and excess power, as well as possible origins.

To paraphrase, it means that the distribution of galaxies in the survey they study is clumpier than expected on very large scales. In fact the level of fluctuation is about a factor two higher than expected on the basis of the standard cosmological model. This shows that either there’s something wrong with the standard cosmological model or there’s something wrong with the survey. Being a skeptic at heart, I’d bet on the latter if I had to put my money somewhere, because this survey involves photometric determinations of redshifts rather than the more accurate and reliable spectroscopic variety. I won’t be getting too excited about this result unless and until it is confirmed with a full spectroscopic survey. But that’s not to say it isn’t an interesting result.

For one thing it keeps alive a debate about whether, and at what scale, the Universe is homogeneous. The standard cosmological model is based on the Cosmological Principle, which asserts that the Universe is, in a broad-brush sense, homogeneous (is the same in every place) and isotropic (looks the same in all directions). But the question that has troubled cosmologists for many years is what is meant by large scales? How broad does the broad brush have to be?

At our meeting a few weeks ago, Subir Sarkar from Oxford pointed out that the evidence for cosmological homogeneity isn’t as compelling as most people assume. I blogged some time ago about an alternative idea, that the Universe might have structure on all scales, as would be the case if it were described in terms of a fractal set characterized by a fractal dimension $D$. In a fractal set, the mean number of neighbours of a given galaxy within a spherical volume of radius $R$ is proportional to $R^D$. If galaxies are distributed uniformly (homogeneously) then $D = 3$, as the number of neighbours simply depends on the volume of the sphere, i.e. as $R^3$, and the average number-density of galaxies. A value of $D < 3$ indicates that the galaxies do not fill space in a homogeneous fashion: $D = 1$, for example, would indicate that galaxies were distributed in roughly linear structures (filaments); the mass of material distributed along a filament enclosed within a sphere grows linear with the radius of the sphere, i.e. as $R^1$, not as its volume; galaxies distributed in sheets would have $D=2$, and so on.

The discussion of a fractal universe is one I’m overdue to return to. In my previous post  I left the story as it stood about 15 years ago, and there have been numerous developments since then. I will do a “Part 2” to that post before long, but I’m waiting for some results I’ve heard about informally, but which aren’t yet published, before filling in the more recent developments.

We know that $D \simeq 1.2$ on small scales (in cosmological terms, still several Megaparsecs), but the evidence for a turnover to $D=3$ is not so strong. The point is, however, at what scale would we say that homogeneity is reached. Not when $D=3$ exactly, because there will always be statistical fluctuations; see below. What scale, then?  Where $D=2.9$? $D=2.99$?

What I’m trying to say is that much of the discussion of this issue involves the phrase “scale of homogeneity” when that is a poorly defined concept. There is no such thing as “the scale of homogeneity”, just a whole host of quantities that vary with scale in a way that may or may not approach the value expected in a homogeneous universe.

It’s even more complicated than that, actually. When we cosmologists adopt the Cosmological Principle we apply it not to the distribution of galaxies in space, but to space itself. We assume that space is homogeneous so that its geometry can be described by the Friedmann-Lemaitre-Robertson-Walker metric.

According to Einstein’s  theory of general relativity, clumps in the matter distribution would cause distortions in the metric which are roughly related to fluctuations in the Newtonian gravitational potential $\delta\Phi$ by $\delta\Phi/c^2 \sim \left(\lambda/ct \right)^{2} \left(\delta \rho/\rho\right)$, give or take a factor of a few, so that a large fluctuation in the density of matter wouldn’t necessarily cause a large fluctuation of the metric unless it were on a scale $\lambda$ reasonably large relative to the cosmological horizon $\sim ct$. Galaxies correspond to a large $\delta \rho/\rho \sim 10^6$ but don’t violate the Cosmological Principle because they are too small to perturb the background metric significantly. Even the big clumps found by the UCL team only correspond to a small variation in the metric. The issue with these, therefore, is not so much that they threaten the applicability of the Cosmological Principle, but that they seem to suggest structure might have grown in a different way to that usually supposed.

The problem is that we can’t measure the gravitational potential on these scales directly so our tests are indirect. Counting galaxies is relatively crude because we don’t even know how well galaxies trace the underlying mass distribution.

An alternative way of doing this is to use not the positions of galaxies, but their velocities (usually called peculiar motions). These deviations from a pure Hubble flow are caused by lumps of matter pulling on the galaxies; the more lumpy the Universe is, the larger the velocities are and the larger the lumps are the more coherent the flow becomes. On small scales galaxies whizz around at speeds of hundreds of kilometres per second relative to each other, but averaged over larger and larger volumes the bulk flow should get smaller and smaller, eventually coming to zero in a frame in which the Universe is exactly homogeneous and isotropic.

Roughly speaking the bulk flow $v$ should relate to the metric fluctuation as approximately $\delta \Phi/c^2 \sim \left(\lambda/ct \right) \left(v/c\right)$.

It has been claimed that some observations suggest the existence of a dark flow which, if true, would challenge the reliability of the standard cosmological framework, but these results are controversial and are yet to be independently confirmed.

But suppose you could measure the net flow of matter in spheres of increasing size. At what scale would you claim homogeneity is reached? Not when the flow is exactly zero, as there will always be fluctuations, but exactly how small?

The same goes for all the other possible criteria we have for judging cosmological homogeneity. We are free to choose the point where we say the level of inhomogeneity is sufficiently small to be satisfactory.

In fact, the standard cosmology (or at least the simplest version of it) has the peculiar property that it doesn’t ever reach homogeneity anyway! If the spectrum of primordial perturbations is scale-free, as is usually supposed, then the metric fluctuations don’t vary with scale at all. In fact, they’re fixed at a level of $\delta \Phi/c^2 \sim 10^{-5}$.

The fluctuations are small, so the FLRW metric is pretty accurate, but don’t get smaller with increasing scale, so there is no point when it’s exactly true. So lets have no more of “the scale of homogeneity” as if that were a meaningful phrase. Let’s keep the discussion to the behaviour of suitably defined measurable quantities and how they vary with scale. You know, like real scientists do.

## Dark Horizons

Posted in Cosmic Anomalies, The Universe and Stuff with tags , , , , , , on March 21, 2010 by telescoper

Last Tuesday night I gave a public lecture as part of  Cardiff University’s contribution to National Science and Engineering Week. I had an audience of about a hundred people, although more than half were students from the School of Physics & Astronomy rather than members of the public. I’d had a very full day already by the time it began (at 7pm) and I don’t mind admitting I was pretty exhausted even before I started the talk. I’m offering that as an excuse for struggling to get going, although I think I got better as I got into it. Anyway, I trotted out the usual stuff about the  Cosmic Web and it seemed to go down fairly well, although I don’t know about that because I wasn’t really paying attention.

At the end of the lecture, as usual, there was a bit of time for questions and no shortage of hands went up. One referred to something called Dark Flow which, I’ve just noticed, has actually got its own wikipedia page. It was also the subject of a recent Horizon documentary on BBC called Is Everything we Know about the Universe Wrong? I have to say I thought the programme was truly terrible, but that’s par for the course for Horizon these days I’m afraid. It used to be quite an interesting and informative series, but now it’s full of pointless special effects, portentous and sensationalising narration, and is repetitive to the point of torture. In this case also, it also portrayed a very distorted view of its subject matter.

The Dark Flow is indeed quite interesting, but of all the things that might threaten the foundations of the Big Bang theory this is definitely not it. I certainly have never lost any sleep worrying about it. If it’s real and not just the result of a systematic error in the data – and that’s a very big “if” – then the worst it would do would be to tell us that the Universe was a bit more complicated than our standard model. The same is true of the other cosmic anomalies I discuss from time to time on here.

But we know our standard model leaves many questions unanswered and, as a matter of fact, many questions unasked. The fact that Nature may present us with a few surprises doesn’t mean the whole framework is wrong. It could be wrong, of course. In fact I’d be very surprised if our standard view of cosmology survives the next few decades without major revision. A healthy dose of skepticism is good for cosmology. To some extent, therefore, it’s good to have oddities like the Dark Flow out in the open.

However, that shouldn’t divert our attention from the fact that the Big Bang model isn’t just an arbitrary hypothesis with no justification. It’s the result of almost a century of  vigorous interplay between theory and observation, using an old-fashioned thing called the scientific method. That’s probably too dull for the producers of  Horizon, who would rather portray it as a kind of battle of wills between individuals competing for the title of next Einstein.

Anyway, just to emphasize the fact that I think questioning the Big Bang model is a good thing to do, here is a list of fundamental questions that should trouble modern cosmologists. Most of them are fundamental,  and we do not have answers to them.

Is General Relativity right?

Virtually everything in the standard model depends on the validity of Einstein’s general theory of relativity (or theory of general relativity…). In a sense we already know that the answer to this question is “no”.

At sufficiently high energies (near the Planck scale) we expect classical relativity to be replaced by a quantum theory of gravity. For this reason, a great deal of interest is being directed at cosmological models inspired by superstring theory. These models require the existence of extra dimensions beyond the four we are used to dealing with. This is not in itself a new idea, as it dates back to the work of Kaluza and Klein in the 1920s, but in older versions of the idea the extra dimensions were assumed to be wrapped up so small as to be invisible. In “braneworld models”, the extra dimensions can be large but we are confined to a four-dimensional subset of them (a “brane”). In one version of this idea, dubbed the Ekpyrotic Universe, the origin of our observable universe lies in the collision between two branes in a higher-dimensional “bulk”. Other models are less dramatic, but do result in the modification of the Friedmann equations at early times.

It is not just in the early Universe that departures from general relativity are possible. In fact there are many different alternative theories on the market. Some are based on modifications of Newton’s gravitational mechanics, such as MOND, modifications of Einstein’s theory, such as the Brans-Dicke theory, as well as those theories involving extra dimensions, such as braneworld theory, and so on

There remain very few independent tests of the validity of Einstein’s theory, particularly in the limit of strong gravitational fields. There is very little independent evidence that the curvature of space time on cosmological scales is related to the energy density of matter. The chain of reasoning leading to the cosmic concordance model depends entirely this assumption. Throw it away and we have very little to go on.

What is the Dark Energy?

In the standard cosmology, about 75% of the energy density of the Universe is in a form we do not understand. Because we’re in the dark about it, we call it Dark Energy. The question here is twofold. One part is whether the dark energy is of the form of an evolving scalar field, such as quintessence, or whether it really is constant as in Einstein’s original version. This may be answered by planned observational studies, but both of these are at the mercy of funding decisions. The second part is to whether dark energy can be understood in terms of fundamental theory, i.e. in understanding why “empty space” contains this vacuum energy.  I think it is safe to say we are still very far from knowing how vacuum energy on a cosmological scale arises from fundamental physics. It’s just a free parameter.

What is the Dark Matter?

Around 25% of the mass in the Universe is thought to be in the form of dark matter, but we don’t know what form it takes. We do have some information about this, because the nature of the dark matter determines how it tends to clump together under the action of gravity. Current understanding of how galaxies form, by condensing out of the primordial explosion, suggests the dark matter particles should be relatively massive. This means that they should move relatively slowly and can consequently be described as “cold”. As far as gravity is concerned, one cold particle is much the same as another so there is no prospect for learning about the nature of cold dark matter (CDM) particles through astronomical means unless they decay into radiation or some other identifiable particles. Experimental attempts to detect the dark matter directly are pushing back the limits of technology, but it would have to be a long shot for them to succeed when we have so little idea of what we are looking for.

Did Inflation really happen?

The success of concordance cosmology is largely founded on the appearance of “Doppler peaks” in the fluctuation spectrum of the cosmic microwave background (CMB). These arise from acoustic oscillations in the primordial plasma that have particular statistical properties consistent owing to their origin as quantum fluctuations in the scalar field driving a short-lived period of rapid expansion called inflation. This is strong circumstantial evidence in favour of inflation, but perhaps not strong enough to obtain a conviction. The smoking gun for inflation is probably the existence of a stochastic gravitational wave background. The identification and extraction of this may be possible using future polarisation-sensitive CMB studies even before direct experimental probes of sufficient sensitivity become available. As far as I am concerned, the jury will be out for a considerable time.

Despite these gaps and uncertainties, the ability of the standard framework to account for such a diversity of challenging phenomena provides strong motivation for assigning it a higher probability than its competitors. Part of this  is that no other theory has been developed to the point where we know what predictions it can make. Some of the alternative  ideas  I discussed above are new, and consequently we do not really understand them well enough to know what they say about observable situations. Others have adjustable parameters so one tends to disfavour them on grounds of Ockham’s razor unless and until some observation is made that can’t be explained in the standard framework.

Alternative ideas should be always explored. The business of cosmology, however,  is not only in theory creation but also in theory testing. The great virtue of the standard model is that it allows us to make precise predictions about the behaviour of the Universe and plan observations that can test these predictions. One needs a working hypothesis to target the multi-million-pound investment that is needed to carry out such programmes. By assuming this model we can make rational decisions about how to proceed. Without it we would be wasting taxpayers’ money on futile experiments that have very little chance of improving our understanding. Reasoned belief  in a plausible working hypothesis is essential to the advancement of our knowledge.

Cosmologists may appear a bit crazy (especially when they appear on TV), but there is method in their madness. Sometimes.