Dark Horizons

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.

15 Responses to “Dark Horizons”

  1. Anton Garrett Says:

    The problems all seem to be about the rate of expansion at various epochs after the big bang, and the rate of change of *that*. Personally I think it is more mature to say “We don’t know yet” in answer to some questions than to postulate bizarre answers. Theorists are not going to be unemployed by abstaining in the meanwhile from the wild and the far out, as Peter’s example shows. I suspect that the answers, when they come, will be stimulated by further data. What experiments might have a bearing?

    • telescoper Says:


      That’s definitely the issue behind dark energy, and there are experiments proposed to measure this more accurately in various ways such as the European Space Agency’s Euclid satellite which was recently shortlisted for selection as a medium-sized mission. There’s also the related question of the relationship between spatial curvature and energy density. We assume this is as described by GR, hence the importance of CMB measurements which strongly suggest flat spatial sections.

      For dark matter, the only really definitive tests would either be direct detection of the particles passing through the earth or by creating particles at the LHC. The former is extremely difficult, the latter perhaps less likely to convince skeptics. The creation of a few events at the LHC is not proof that the same thing happened 13.7 billion years ago.

      The dark flow nonsense claim arose from studies of the Sunyaev-Zel’dovich effect. I haven’t thought about this in detail, but it seems likely that Planck will provide lots of new data for this kind of study.

      As you say, the correct answer at the moment to many questions is “We don’t know”, but I guess that doesn’t make for interesting TV..


  2. John Peacock Says:

    Peter: I am provoked to a small rant about terminology. “is general relativity right?” is an interesting question, but it’s not usually one that cosmology research addresses. To me, general relativity is a statement that valid physics equations need to be written in a generally covariant form, most transparently by using quantities that are invariant under general coordinate transformations (by analogy with special relativity, where the coordinate transformations are Lorentz transformations only). The perfect example of this is when you write gravity as an action principle, in terms of a gravitational Lagrangian. Einstein’s suggestion for this Lagrangian was the simple Ricci scalar, R (leaving aside dark energy). A valid and interesting exercise is to attempt to account for cosmic acceleration by generalizing this to f(R) – but this is still covariant, and still uses a metric, so it still deserves to be described as a valid piece of physics in general relativity. When people say “testing general relativity”, they really mean “testing Einstein gravity”. The more radical idea of a genuine failure of GR (e.g. there is no metric to consider, or valid equations are not covariant) is much less frequently discussed.

  3. What cosmology really needs is a healthy dose of credulity, not skepticism: as Martin Rees has said, there is more evidence that advances have been missed (for a time) because we didn’t take theory seriously enough (e.g. Alpher & Herman’s CMB prediction), than because we put too much trust in the current paradigm.

    What we really have is an “effective cosmology”, an intermediate-energy theory which increasingly resembles cartography within the observable universe, because if you test the theory thoroughly enough you can throw away the theory and work directly with the measurements; but which must always fade into speculation in the far future and near the big bang, because we can never be sure we have found all the physics we need to know. Meanwhile, cosmology marches on.

  4. Anton Garrett Says:

    Peter, John: I was going to suggest that we distinguish between the *principle* of general relativity and the *theory* of general relativity*. But the former already has a name – it is the equivalence principle. So surely ‘GR’ is interchangeable in meaning with Einstein’s field eqns, and Peter’s original usage is acceptable?

  5. John Peacock Says:

    Anton: I disagree. Einstein has two theories: L = R or L = R + 2 Lambda. Which of these is GR? If we eventually prove that L = R + 0.000001 R^2, we’ll still write textbooks about general relativity – the name is clearly broader than a specific Lagrangian. In any case, it’s not necessary to have the ambiguity about the definition of the GR term – just say we’re testing “einstein gravity”.

    But I’m happy to agree with you about the centrality of the equivalence principle. That was one of the things I learned from Weinberg’s wonderful book, whereas too many geometrical authors seem to regard the EP as a subsidiary theme.

  6. telescoper Says:


    It’s quite a subtle point that John makes because there’s a whole class of theories derived from modified Lagrangians that are conformally equivalent to Einstein gravity but with a funny energy-momentum tensor. Gravity theories with a quadratic Lagrangian can, for example, be cast in a form that represents Einstein gravity with a scalar field, which is the sort of thing inflationary cosmologists like to have anyway. So I think John is right to pull me up for seeming to imply that such theories are not GR.

    It’s not really my area but I’d be interested to know what if any non-metric gravity theories people have dreamt up recently or whether there are any with non-covariant field equations. I understand even MOND can be written in a covariant form, although I have never really felt the urge to explore MOND in any detail.


  7. Anton Garrett Says:


    Weinberg’s book is wonderful. I wanted the best books on my shelf across many areas of physics (including areas I do/did not work in); I also prune my collection from time to time. I still have Weinberg’s book and would not contemplate getting rid of it, but Misner-Thorne-Wheeler left my shelves a while ago. Steve Gull’s comment on MSW was pretty good: “I thought it couldn’t possibly be that difficult.”


  8. telescoper Says:


    There is a long awaited update of Weinberg’s book Gravitation and Cosmology, but it’s only about the Cosmology. Still pretty good though. I got to review it for Science so I got a free copy.


  9. Anton Garrett Says:

    I saw Weinberg’s new book when last up in Cambridge from the sticks (not yet the Styx…) and it never occurred to me that it was an update of his earlier book; I took it as something different. It looked well up to his usual standard.

  10. John Peacock Says:

    I agree with Steve Gull about MTW. When I first wanted to learn what GR was all about, it was the first book I picked up – and it left me profoundly depressed about the chance of ever having the slightest insight into the subject. So it was a revelation to discover Weinberg, especially the magical p70-75, where he obtains the whole of GR except the field equations just from special relativity and the equivalence principle. People criticise Weinberg’s book for being a mass of old-fashioned index manipulation as against the geometric elegance of MTW (with perhaps some justice), but any such criticism is a small price to pay for the utter clarity of his physical insight. With MTW, the fact that spacetime has a metric is just taken as a given, whereas Weinberg shows how you *deduce* it.

    I think MTW was in many ways ahead of its time, and there are admirable things in it. But I would never recommend it to a student who didn’t already have a pretty sound understanding of the subject. I would never dream of parting with my copy – except that I don’t own one. After a few years of initial distaste, I decided that I should really own such a classic; but it’s never come down all that much in price. Just checked: 80 quid on Amazon – I can’t believe it costs nearly this much to print, and you’d think the publishers would have taken enough profit over nearly 40 years that they could consider making it more widely available. Maybe when I retire…

    As for Weinberg’s recent book, it’s a different beast to the 1972 one, both in terms of the ground it covers and in style. It’s more similar to his QFT books: full of hard sums, and very good in its way, but not displaying the insight of the original text.

    • telescoper Says:

      I like the new Weinberg book a lot, but it’s a very different kettle of fish to the original.

      Wiley published by cosmology book (the one with Francesco Lucchin) and their rep told me the policy was to increase the price as the sales went down in such a way that the income stayed roughly constant. Not sure why they do that, but it explains why the original Weinberg is so expensive.

  11. Tom Shanks Says:

    “To me, general relativity is a statement that valid physics equations need to be written in a generally covariant form, most transparently by using quantities that are invariant under general coordinate transformations (by analogy with special relativity, where the coordinate transformations are Lorentz transformations only). ” JAP

    Prompted by the above into putting head above parapet and heading off at slight tangent –

    I was never as impressed by general covariance as Lorentz invariance. Lorentz invariance demands frame velocity doesnt appear in physical equn but general covariance allows the gravitational field/acceleration ie the metric to appear in the affine connection. So the only demand is that physical equations take the same form whatever the grav field, not that the grav field doesnt appear. Weinberg’s old book calls this a chiral symmetry as I recall. Whatever that means(!), I suggest the analogy between general covariance and Lorentz invariance is not quite as strong as JAP implies. Discuss!

  12. Your commentary, including…
    “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.”
    “Part of this is that no other theory has been developed to the point where we know what predictions it can make.”
    …suggests lack of awareness of binary mechanics, developed from the relativistic Dirac equation. For a confirmed prediction, see, for example, “Gravity increased by lunar surface temperature” DOI 10.7293/Physics.70081909.
    Congratulations on otherwise fine commentary on legacy physics prior to quantization of space and time.

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