Archive for Cold Dark Matter

What is the Standard Cosmological Model?

Posted in The Universe and Stuff with tags , , , , on May 12, 2021 by telescoper

There’s a nice little paper – a summary of a talk – by Eric Linder on the arXiv here. The abstract is:

Reports of “cosmology in crisis” are in vogue, but as Mark Twain said, “the report of my death was an exaggeration”. We explore what we might actually mean by the standard cosmological model, how tensions – or their apparent resolutions – might arise from too narrow a view, and why looking at the big picture is so essential. This is based on the seminar “All Cosmology, All the Time”.

You can find a PDF here.

The paper discusses not only the question “what is the standard cosmological model?” in a fairly general way but also the more basic question “what is cosmology?” I’d think you’d be surprised how different would be the answers to that question from different cosmologists!

Anyway, I usually say when I give talks that the following are the six main ingredients of the standard model:

  1. General Relativity
  2. The Cosmological Principle
  3. Cold Dark Matter
  4. Cosmological Constant
  5. Primordial (nearly) Gaussian adiabatic fluctuations
  6. Inflation in the very early Universe

There are other ingredients of course, such as baryons and neutrinos but I don’t include them in a model because I feel one should distinguish at some level between the ingredients of a model and the  ingredients of the actual Universe. What I mean by that is that we know baryons exist (though we may not know their cosmic abundance precisely) but we don’t know for sure whether Cold Dark Matter exists.

Note that (1) isn’t really a model because it has no free parameters: it’s only when you add (2) that it comes a FLRW model with e.g. the curvature as a free parameter, and some assumed form of the energy-momentum tensor. The other ingredients have one or more free parameters, e.g. the density of CDM (3) and the value of Λ (4); these can be made more flexible by including, e.g., a dark energy term with equation of state w. Ingredient (5) needs the user to specify an initial power spectrum, which is at least two parameters (amplitude and slope), which may or may not be motivated by (6).

Anyway, the following items in the above list are – to a greater or lesser extent – open to question:

  1. General Relativity
  2. The Cosmological Principle
  3. Cold Dark Matter
  4. Cosmological Constant
  5. Primordial (nearly) Gaussian adiabatic fluctuations
  6. Inflation in the very early Universe

We’d be unwise to question only, e.g., 3 or 4 while ignoring the possibility that we may be wrong about the others!


An Integral Appendix

Posted in Biographical, Cute Problems, The Universe and Stuff with tags , , , , , , on August 7, 2013 by telescoper

After the conference dinner at the Ripples in the Cosmos meeting in Durham I attended recently, a group of us adjourned to the Castle bar for a drink or several. I ended up chatting to one of the locals, Richard Bower, mainly on the subject of beards. I suppose you could call it a chinwag. Only later on did  we get onto the subject of a paper we had both worked on a while ago. It was with some alarm that I later realized that the paper concerned was actually published twenty years ago. Sigh. Where did all that time go?

Anyway, Richard and I both remembered having a great time working on that paper which turned out to be a nice one, although it didn’t exactly set the world on fire in terms of citations. This paper was written before the standard “concordance” (LCDM) cosmology was firmly established and theorists were groping around for ways of reconciling observations of the CMB from the COBE satellite with large-scale structure in the galaxy distribution as well as the properties of individual galaxies. The (then) standard model (CDM with no Lambda) struggled to satisfy the observational constraints, so in typical theorists fashion we tried to think of a way to rescue it. The idea we came up with was “cooperative galaxy formation”, as explained in the abstract:

We consider a model in which galaxy formation occurs at high peaks of the mass density field, as in the standard picture for biased galaxy formation, but is further enhanced by the presence of nearby galaxies. This modification is accomplished by assuming the threshold for galaxy formation to be modulated by large-scale density fluctuations rather than to be spatially invariant. We show that even a weak modulation can produce significant large-scale clustering. In a universe dominated by cold dark matter, a 2 percent – 3 percent modulation on a scale exceeding 10/h Mpc produces enough additional clustering to fit the angular correlation function of the APM galaxy survey. We discuss several astrophysical mechanisms for which there are observational indications that cooperative effects could occur on the scale required.

I have to say that Richard did most of the actual work on this paper, though all four authors did spend a lot of time discussing whether the idea was viable in principle and, if so, how we should implement it mathematically. In the end, my contribution was pretty much limited to the Appendix, which you can click to make it larger if you’re interested.


As is often the case in work of this kind, everything boiled down to evaluating numerically a rather nasty integral. Coincidentally, I’d come across a similar problem in a totally different context a few years previously when I was working on my thesis and therefore just happened to know the neat trick described in the paper.

Two things struck me looking back on this after being reminded of it over that beer. One is that a typical modern laptop is powerful enough to evaluate the original integral without undue difficulty, so if this paper had been written nowadays we wouldn’t have bothered trying anything clever; my Appendix would probably not have been written. The other thing is that I sometimes hear colleagues bemoaning physics students’ lack of mathematical “problem-solving” ability, claiming that if students haven’t seen the problem before they don’t know what to do. The problem with that complaint is that it ignores the fact that many problems are the same as things you’ve solved before, if only you look at them in the right way. Problem solving is never going to be entirely about “pattern-matching” – some imagination and/or initiative is going to required sometimes- but you’d be surprised how many apparently intractable problems can be teased into a form to which standard methods can be applied. Don’t take this advice too far, though. There’s an old saying that goes “To a man who’s only got a hammer, everything looks like a nail”. But the first rule for solving “unseen” problems has to be to check whether you might in fact already have seen them…

What’s the Matter?

Posted in The Universe and Stuff with tags , , , , , on September 19, 2011 by telescoper

I couldn’t resist a quick comment today on a news article to which my attention was drawn at the weekend. The piece concerns the nature of the dark matter that is thought to pervade the Universe. Most cosmologists believe that this is cold, which means that it is made of slow-moving particles (the temperature of  a gas being related to the speed of its constituent particles).  They also believe that it is not the sort of stuff that atoms are made of, i.e. protons, neutrons and electrons. In particular, it isn’t charged and therefore can’t interact with electromagnetic radiation, thus it is not only dark in the sense that it doesn’t shine but also transparent.

Cold Dark Matter (CDM) particles could be very massive, which would make them much more sluggish than lighter ones such as neutrinos (which would be hot dark matter), but there are other, more complicated, ways in which some exotic particles can end up in a slow-motion state without being massive.

So why do so many of us think the dark matter is cold? The answer to that is threefold. First, this is by far the simplest hypothesis to work on. In other words, good old Occam’s Razor. It’s simple because if the dark matter is cold there is no relevant physical scale associated with the speed of the particles. Everything is just dominated by the gravity, which means there are fewer equations to solve. Not that it’s exactly easy even in this case: huge supercomputers are needed to crunch the numbers.

The second reason is that particle physics has suggested a number of plausible candidates for non-baryonic candidates which could be cold dark matter particles. A favourite theoretical idea is supersymmetry, which predicts that standard model particles have counterparts that could be interesting from a cosmological point of view, such as the fermionic counterparts of standard model bosons. Some of these candidates could even be produced experimentally by the Large Hadron Collider.

The final reason is that CDM seems to work, at least on large scales. The pattern of galaxy clustering on large scales as measured by galaxy redshift surveys seems to fit very well with predictions of the theory, as do the observed properties of the cosmic microwave background.

However, one place where CDM is known to have a problem is on small scales. By small of course I mean in cosmological terms; we’re still talking about many thousands of light-years! There’s been a niggling worry for some time that the internal structure of galaxies, especially in their central regions,  isn’t quite what we expect on the basis of the CDM theory. Neither do the properties of the small satellite galaxies (“dwarfs”) seen orbiting the Milky Way seem to match what what we’d expect theoretically.

The above picture is taken from the BBC website. I’ve included it partly for a bit of decoration, but also to point out that the pictures are both computer simulations, not actual astronomical observations.

Anyway, the mismatch between the properties of dwarf galaxies and the predictions of CDM theory, while not being exactly new, is certainly a potential Achilles’ Heel for the otherwise successful model. Calculating the matter distribution on small scales however is a fearsome computational challenge requiring enormously high resolution. The disagreement may therefore be simply because the simulations are not good enough; “sub-grid” physics may be confusing us.

On the other hand, one should certainly not dismiss the possibility that CDM might actually be wrong. If the dark matter were not cold, but warm (or perhaps merely tepid), then it would produce less small-scale structure whilst not messing up the good fit to large-scale structure that we get with CDM.

So is the Dark Matter Cold or Warm or something else altogether? The correct answer is that we don’t know for sure, and as a matter of fact I think CDM is still favourite. But if the LHC rules out supersymmetric CDM candidates and the astronomical measurements continue to defy the theoretical predictions then the case for cold dark matter would be very much weakened. That might annoy some of its advocates in the cosmological community, such as Carlos Frenk (who is extensively quoted in the article), but it would at least mean that the hunt for the true nature of dark matter would be getting warmer.


Posted in The Universe and Stuff with tags , , , , , , , on June 2, 2011 by telescoper

Just a quickie this fine summer morning to pass on the news – for those of you who haven’t heard yet – that this year’s Gruber Prize for Cosmology has been awarded to Marc Davis (Berkeley, USA), George Efstathiou (Cambridge, UK), Carlos Frenk (Durham, UK) and Simon White (Garching, Germany). This prestigious award is given for their pioneering work on the Cold Dark Matter model of structure formation, which included some of the first large-scale N-body computer simulations. The “Gang of Four” produced a number of papers during the 1980s that established the idea that galaxies form by hierarchical clustering from small initial fluctuations in a matter distribution dominated by massive collisionless non-baryonic particles, the most famous of their papers being pretty universally referred to as DEFW.

In fact, if you’ll forgive me going on a trip down memory lane, that paper, published in 1985, was one of the first papers I read when I started my research degree the same year at Sussex. It was back in the days when everyone seemed to use a VAX for big computing jobs and the simulations presented in that paper involved a mere 323 = 32768 particles. You could probably run that kind of simulation on a mobile phone these days!

This early work on Cold Dark Matter wasn’t the final word, of course. Subsequent observational evidence for an accelerating Universe resulting in our standard cosmological model being modifiel to include an additional (large) component of dark energy in addition to dark matter. Nevertheless, the core ideas presented by DEFW established the basic foundations of structure formation upon which the current standard model is built.

Incidentally, you can read an interesting account of the discovery of the accelerating universe here; a cosmologist by the name of “George F. Stathew” plays a prominent role in that piece and it’s curious I’ve never heard of him before now.

Each of the four winners gets a share of the $500000 Gruber Prize, i.e. in “normalized” terms, they get $125000 each. Why is it so controversial to suggest dividing citation counts the same way? The DEFW paper has about 1500 citations according to ADS, so I think it’s quite reasonable to award the authors 370-odd each towards their respective h-indices. That’s still a pretty good result by any bibliometric standard!

The four also get a Gold Medal each to wear at parties, although by my previous logic they should have to share one between them. Perhaps George might consider donating his to Arsenal Football Club, as their trophy cabinet is looking rather empty these days?

None of the winners are Australian undergraduates, so this award probably won’t be considered newsworthy by the mass media. Believe it or not, however, the Gruber Prize is held in even higher regard by cosmologists than the Templeton Prize, so I’d like to take this opportunity to congratulate them myself for their thoroughly well-deserved honour!

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.