## Is there a kinematic backreaction in cosmology?

Posted in The Universe and Stuff with tags , , , , , on March 28, 2017 by telescoper

I just noticed that a paper has appeared on the arXiv with the confident title There is no kinematic backreaction. Normally one can be skeptical about such bold claims, but this one is written by Nick Kaiser and he’s very rarely wrong…

The article has a very clear abstract:

This is an important point of debate, because the inference that the universe is dominated by dark energy (i.e. some component of the cosmic energy density that violates the strong energy condition) relies on the assumption that the distribution of matter is homogeneous and isotropic (i.e. that the Universe obeys the Cosmological Principle). Added to the assumption that the large-scale dynamics of the Universe are described by the general theory of relativity, this means that we evolution of the cosmos is described by the Friedmann equations. It is by comparison with the Friedmann equations that we can infer the existence of dark energy from the apparent change in the cosmic expansion rate over time.

But the Cosmological Principle can only be true in an approximate sense, on very large scales, as the universe does contain galaxies, clusters and superclusters. It has been a topic of some discussion over the past few years as to whether the formation of cosmic structure may influence the expansion rate by requiring extra terms that do not appear in the Friedmann equations.

Nick Kaiser says `no’. It’s a succinct and nicely argued paper but it is entirely Newtonian. It seems to me that if you accept that his argument is correct then the only way you can maintain that backreaction can be significant is by asserting that it is something intrinsically relativistic that is not covered by a Newtonian argument. Since all the relevant velocities are much less than that of light and the metric perturbations generated by density perturbations are small (~10-5) this seems a hard case to argue.

I’d be interested in receiving backreactions to this paper via the comments box below.

## A Quite Interesting Question: How Loud Was the Big Bang?

Posted in The Universe and Stuff with tags , , , , , , , on March 16, 2017 by telescoper

I just found out this morning that this blog got a mention on the QI Podcast. It’s taken a while for this news to reach me, as the item concerned is two years old! You can find this discussion here, about 16 minutes in. And no, it’s not in connection with yawning psychopaths. It was about the vexed question of how loud was the Big Bang?

I’ve posted on this before (here and here)but since I’m very busy again today I  should recycle the discussion, and update it as it relates to the cosmic microwave background, which is what one of the things I work on on the rare occasions on which I get to do anything interesting.

As you probably know the Big Bang theory involves the assumption that the entire Universe – not only the matter and energy but also space-time itself – had its origins in a single event a finite time in the past and it has been expanding ever since. The earliest mathematical models of what we now call the  Big Bang were derived independently by Alexander Friedman and George Lemaître in the 1920s. The term “Big Bang” was later coined by Fred Hoyle as a derogatory description of an idea he couldn’t stomach, but the phrase caught on. Strictly speaking, though, the Big Bang was a misnomer.

Friedman and Lemaître had made mathematical models of universes that obeyed the Cosmological Principle, i.e. in which the matter was distributed in a completely uniform manner throughout space. Sound consists of oscillating fluctuations in the pressure and density of the medium through which it travels. These are longitudinal “acoustic” waves that involve successive compressions and rarefactions of matter, in other words departures from the purely homogeneous state required by the Cosmological Principle. The Friedman-Lemaitre models contained no sound waves so they did not really describe a Big Bang at all, let alone how loud it was.

However, as I have blogged about before, newer versions of the Big Bang theory do contain a mechanism for generating sound waves in the early Universe and, even more importantly, these waves have now been detected and their properties measured.

The above image shows the variations in temperature of the cosmic microwave background as charted by the Planck Satellite. The average temperature of the sky is about 2.73 K but there are variations across the sky that have an rms value of about 0.08 milliKelvin. This corresponds to a fractional variation of a few parts in a hundred thousand relative to the mean temperature. It doesn’t sound like much, but this is evidence for the existence of primordial acoustic waves and therefore of a Big Bang with a genuine “Bang” to it.

A full description of what causes these temperature fluctuations would be very complicated but, roughly speaking, the variation in temperature you corresponds directly to variations in density and pressure arising from sound waves.

So how loud was it?

The waves we are dealing with have wavelengths up to about 200,000 light years and the human ear can only actually hear sound waves with wavelengths up to about 17 metres. In any case the Universe was far too hot and dense for there to have been anyone around listening to the cacophony at the time. In some sense, therefore, it wouldn’t have been loud at all because our ears can’t have heard anything.

Setting aside these rather pedantic objections – I’m never one to allow dull realism to get in the way of a good story- we can get a reasonable value for the loudness in terms of the familiar language of decibels. This defines the level of sound (L) logarithmically in terms of the rms pressure level of the sound wave Prms relative to some reference pressure level Pref

L=20 log10[Prms/Pref].

(the 20 appears because of the fact that the energy carried goes as the square of the amplitude of the wave; in terms of energy there would be a factor 10).

There is no absolute scale for loudness because this expression involves the specification of the reference pressure. We have to set this level by analogy with everyday experience. For sound waves in air this is taken to be about 20 microPascals, or about 2×10-10 times the ambient atmospheric air pressure which is about 100,000 Pa.  This reference is chosen because the limit of audibility for most people corresponds to pressure variations of this order and these consequently have L=0 dB. It seems reasonable to set the reference pressure of the early Universe to be about the same fraction of the ambient pressure then, i.e.

Pref~2×10-10 Pamb.

The physics of how primordial variations in pressure translate into observed fluctuations in the CMB temperature is quite complicated, because the primordial universe consists of a plasma rather than air. Moreover, the actual sound of the Big Bang contains a mixture of wavelengths with slightly different amplitudes. In fact here is the spectrum, showing a distinctive signature that looks, at least in this representation, like a fundamental tone and a series of harmonics…

If you take into account all this structure it all gets a bit messy, but it’s quite easy to get a rough but reasonable estimate by ignoring all these complications. We simply take the rms pressure variation to be the same fraction of ambient pressure as the averaged temperature variation are compared to the average CMB temperature,  i.e.

Prms~ a few ×10-5Pamb.

If we do this, scaling both pressures in logarithm in the equation in proportion to the ambient pressure, the ambient pressure cancels out in the ratio, which turns out to be a few times 10-5. With our definition of the decibel level we find that waves of this amplitude, i.e. corresponding to variations of one part in a hundred thousand of the reference level, give roughly L=100dB while part in ten thousand gives about L=120dB. The sound of the Big Bang therefore peaks at levels just a bit less than 120 dB.

As you can see in the Figure above, this is close to the threshold of pain,  but it’s perhaps not as loud as you might have guessed in response to the initial question. Modern popular beat combos often play their dreadful rock music much louder than the Big Bang….

A useful yardstick is the amplitude  at which the fluctuations in pressure are comparable to the mean pressure. This would give a factor of about 1010 in the logarithm and is pretty much the limit that sound waves can propagate without distortion. These would have L≈190 dB. It is estimated that the 1883 Krakatoa eruption produced a sound level of about 180 dB at a range of 100 miles. The QI podcast also mentions  that blue whales make a noise that corresponds to about 188 decibels. By comparison the Big Bang was little more than a whimper..

PS. If you would like to read more about the actual sound of the Big Bang, have a look at John Cramer’s webpages. You can also download simulations of the actual sound. If you listen to them you will hear that it’s more of  a “Roar” than a “Bang” because the sound waves don’t actually originate at a single well-defined event but are excited incoherently all over the Universe.

## Tension in the Hubble constant

Posted in The Universe and Stuff with tags , , on February 28, 2017 by telescoper

A few months ago I blogged about the apparent “tension” between different measurements of the Hubble constant. Here is an alternative view of the situation, with some recent updates. The plot has thickened a bit, but it’s still unclear to me whether there’s really a significant discrepancy.

Anyway, here’s a totally unscientific poll on the issue! Do feel free to register your vote.

There has been some hand-wringing of late about the tension between the value of the expansion rate of the universe – the famous Hubble constant, H, measured directly from observed redshifts and distances, and that obtained by multi-parameter fits to the cosmic microwave background. Direct determinations consistently give values in the low to mid-70s, like Riess et al. (2016): H = 73.24 ± 1.74 km/s/Mpc while the latest CMB fit from Planck gives H = 67.8 ± 0.9 km/s/Mpc. These are formally discrepant at a modest level: enough to be annoying, but not enough to be conclusive.

The widespread presumption is that there is a subtle systematic error somewhere. Who is to blame depends on what you work on. People who work on the CMB and appreciate its phenomenal sensitivity to cosmic geometry generally presume the problem is with galaxy measurements. To people who work on local galaxies, the CMB value is…

View original post 1,029 more words

## One Hundred Years of the Cosmological Constant

Posted in History, The Universe and Stuff with tags , , , , , , on February 8, 2017 by telescoper

It was exactly one hundred years ago today – on 8th February 1917 – that a paper was published in which Albert Einstein explored the cosmological consequences of his general theory of relativity, in the course of which he introduced the concept of the cosmological constant.

For the record the full reference to the paper is: Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie and it was published in the Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften. You can find the full text of the paper here. There’s also a nice recent discussion of it by Cormac O’Raifeartaigh  and others on the arXiv here.

Here is the first page:

It’s well worth looking at this paper – even if your German is as rudimentary as mine – because the argument Einstein constructs is rather different from what you might imagine (or at least that’s what I thought when I first read it). As you see, it begins with a discussion of a modification of Poisson’s equation for gravity.

As is well known, Einstein introduced the cosmological constant in order to construct a static model of the Universe. The 1917 paper pre-dates the work of Friedman (1923) and Lemaître (1927) that established much of the language and formalism used to describe cosmological models nowadays, so I thought it might be interesting just to recapitulate the idea using modern notation. Actually, in honour of the impending centenary I did this briefly in my lecture on Physics of the Early Universe yesterday.

To simplify matters I’ll just consider a “dust” model, in which pressure can be neglected. In this case, the essential equations governing a cosmological model satisfying the Cosmological Principle are:

$\ddot{a} = -\frac{4\pi G \rho a }{3} +\frac{\Lambda a}{3}$

and

$\dot{a}^2= \frac{8\pi G \rho a^2}{3} +\frac{\Lambda a^2}{3} - kc^2.$

In these equations $a(t)$ is the cosmic scale factor (which measures the relative size of the Universe) and dots are derivatives with respect to cosmological proper time, $t$. The density of matter is $\rho>0$ and the cosmological constant is $\Lambda$. The quantity $k$ is the curvature of the spatial sections of the model, i.e. the surfaces on which $t$ is constant.

Now our task is to find a solution of these equations with $a(t)= A$, say, constant for all time, i.e. that $\dot{a}=0$ and $\ddot{a}=0$ for all time.

The first thing to notice is that if $\Lambda=0$ then this is impossible. One can solve the second equation to make the LHS zero at a particular time by matching the density term to the curvature term, but that only makes a universe that is instantaneously static. The second derivative is non-zero in this case so the system inevitably evolves away from the situation in which $\dot{a}=0$.

With the cosmological constant term included, it is a different story. First make $\ddot{a}=0$  in the first equation, which means that

$\Lambda=4\pi G \rho.$

Now we can make $\dot{a}=0$ in the second equation by setting

$\Lambda a^2 = 4\pi G \rho a^2 = kc^2$

This gives a static universe model, usually called the Einstein universe. Notice that the curvature must be positive, so this a universe of finite spatial extent but with infinite duration.

This idea formed the basis of Einstein’s own cosmological thinking until the early 1930s when observations began to make it clear that the universe was not static at all, but expanding. In that light it seems that adding the cosmological constant wasn’t really justified, and it is often said that Einstein regard its introduction as his “biggest blunder”.

I have two responses to that. One is that general relativity, when combined with the cosmological principle, but without the cosmological constant, requires the universe to be dynamical rather than static. If anything, therefore, you could argue that Einstein’s biggest blunder was to have failed to predict the expansion of the Universe!

The other response is that, far from it being an ad hoc modification of his theory, there are actually sound mathematical reasons for allowing the cosmological constant term. Although Einstein’s original motivation for considering this possibility may have been misguided, he was justified in introducing it. He was right if, perhaps, for the wrong reasons. Nowadays observational evidence suggests that the expansion of the universe may be accelerating. The first equation above tells you that this is only possible if $\Lambda\neq 0$.

Finally, I’ll just mention another thing in the light of the Einstein (1917) paper. It is clear that Einstein thought of the cosmological as a modification of the left hand side of the field equations of general relativity, i.e. the part that expresses the effect of gravity through the curvature of space-time. Nowadays we tend to think of it instead as a peculiar form of energy (called dark energy) that has negative pressure. This sits on the right hand side of the field equations instead of the left so is not so much a modification of the law of gravity as an exotic form of energy. You can see the details in an older post here.

## The Dipole Repeller

Posted in The Universe and Stuff with tags , , , , , , on February 2, 2017 by telescoper

An interesting bit of local cosmology news has been hitting the headlines over the last few days. The story relates to a paper by Yehuda Hoffman et al. published in Nature Astronomy on 30th January. The abstract reads:

Our Local Group of galaxies is moving with respect to the cosmic microwave background (CMB) with a velocity 1 of VCMB = 631 ± 20 km s−1and participates in a bulk flow that extends out to distances of ~20,000 km s−1 or more 2,3,4 . There has been an implicit assumption that overabundances of galaxies induce the Local Group motion 5,6,7 . Yet underdense regions push as much as overdensities attract 8 , but they are deficient in light and consequently difficult to chart. It was suggested a decade ago that an underdensity in the northern hemisphere roughly 15,000 km s−1 away contributes significantly to the observed flow 9 . We show here that repulsion from an underdensity is important and that the dominant influences causing the observed flow are a single attractor — associated with the Shapley concentration — and a single previously unidentified repeller, which contribute roughly equally to the CMB dipole. The bulk flow is closely anti-aligned with the repeller out to 16,000 ± 4,500 km s−1. This ‘dipole repeller’ is predicted to be associated with a void in the distribution of galaxies.

The effect of this “void in the distribution of galaxies” has been described in rather lurid terms as “Milky Way being pushed through space by cosmic dead zone” in a Guardian piece on this research.

If you’re confused by this into thinking that some sort of anti-gravity is at play, then it isn’t really anything so exotic. If the Universe were completely homogeneous and isotropic – as our simplest models assume – then it would be expanding at the same rate in all directions.  This would be a pure “Hubble flow“, with galaxies appearing to recede from an observer with a speed proportional to their distance:

But the Universe isn’t exactly smooth. As well as the galaxies themselves, there are clusters, filaments and sheets of galaxies and a corresponding collection of void regions, together forming a huge and complex “cosmic web” of large-scale structure. This distorts the Hubble flow by inducing peculiar motions (i.e. departures from the pure expansion). A part of the Universe which is denser than average (e.g. a cluster or supercluster) expands less  quickly than average, a part which is less dense (i.e. a void) expands more quickly than average. Relative to the global expansion rate, clusters represent a “pull” and voids represent a “push”. That’s really all there is to it.

The difficult part about this kind of study is measuring a sufficient number of peculiar motions of galaxies around our own to make a detailed map of what’s going on in the local velocity field. That’s particularly hard for galaxies near the plane of the Milky Way disk as they tend to be obscured by dust. Nevertheless, after plugging away at this for many years, the authors of the Nature paper have generated some fascinating results. It seems that our Galaxy and other members of the Local Group lie between a dense supercluster (often called the Shapley concentration) and an underdense region, so the peculiar velocity field around us has an approximately dipole structure.

They’ve even made a nice video to show you what’s going on, so I don’t have to explain any further!

## Fake News of the Holographic Universe

Posted in Astrohype, The Universe and Stuff with tags , , , , , , on February 1, 2017 by telescoper

It has been a very busy day today but I thought I’d grab a few minutes to rant about something inspired by a cosmological topic but that I’m afraid is symptomatic of malaise that extends far wider than fundamental science.

The other day I found a news item with the title Study reveals substantial evidence of holographic universe. You can find a fairly detailed discussion of the holographic principle here, but the name is fairly self-explanatory: the familiar hologram is a two-dimensional object that contains enough information to reconstruct a three-dimensional object. The holographic principle extends this to the idea that information pertaining to a higher-dimensional space may reside on a lower-dimensional boundary of that space. It’s an idea which has gained some traction in the context of the black hole information paradox, for example.

There are people far more knowledgeable about the holographic principle than me, but naturally what grabbed my attention was the title of the news item: Study reveals substantial evidence of holographic universe. That got me really excited, as I wasn’t previously aware that there was any observed property of the Universe that showed any unambiguous evidence for the holographic interpretation or indeed that models based on this model could describe the available data better than the standard ΛCDM cosmological model. Naturally I went to the original paper on the arXiv by Niayesh Ashfordi et al. to which the news item relates. Here is the abstract:

We test a class of holographic models for the very early universe against cosmological observations and find that they are competitive to the standard ΛCDM model of cosmology. These models are based on three dimensional perturbative super-renormalizable Quantum Field Theory (QFT), and while they predict a different power spectrum from the standard power-law used in ΛCDM, they still provide an excellent fit to data (within their regime of validity). By comparing the Bayesian evidence for the models, we find that ΛCDM does a better job globally, while the holographic models provide a (marginally) better fit to data without very low multipoles (i.e. l≲30), where the dual QFT becomes non-perturbative. Observations can be used to exclude some QFT models, while we also find models satisfying all phenomenological constraints: the data rules out the dual theory being Yang-Mills theory coupled to fermions only, but allows for Yang-Mills theory coupled to non-minimal scalars with quartic interactions. Lattice simulations of 3d QFT’s can provide non-perturbative predictions for large-angle statistics of the cosmic microwave background, and potentially explain its apparent anomalies.

The third sentence (highlighted) states explicitly that according to the Bayesian evidence (see here for a review of this) the holographic models do not fit the data even as well as the standard model (unless some of the CMB measurements are excluded, and then they’re only slightly better)

I think the holographic principle is a very interesting idea and it may indeed at some point prove to provide a deeper understanding of our universe than our current models. Nevertheless it seems clear to me that the title of this news article is extremely misleading. Current observations do not really provide any evidence in favour of the holographic models, and certainly not “substantial evidence”.

The wider point should be obvious. We scientists rightly bemoan the era of “fake news”. We like to think that we occupy the high ground, by rigorously weighing up the evidence, drawing conclusions as objectively as possible, and reporting our findings with a balanced view of the uncertainties and caveats. That’s what we should be doing. Unless we do that we’re not communicating science but engaged in propaganda, and that’s a very dangerous game to play as it endangers the already fragile trust the public place in science.

The authors of the paper are not entirely to blame as they did not write the piece that kicked off this rant, which seems to have been produced by the press office at the University of Southampton, but they should not have consented to it being released with such a misleading title.

## How the Nonbaryonic Dark Matter Theory Grew [CEA]

Posted in The Universe and Stuff with tags , , on January 24, 2017 by telescoper

Another arXiver post, this time from the great Jim Peebles. Always a skeptic about dark matter, especially cold dark matter, it is the hallmark of a great scientist that he weighs up the evidence as objectively as possible.

This is a long review, but well worth reading for its important insights and historical perspective. I agree that the case for non-baryonic dark matter is compelling, but it is also far from proved and it’s still possible that an alternative, equally or more compelling, theory will be found.

http://arxiv.org/abs/1701.05837

The evidence is that the mass of the universe is dominated by an exotic nonbaryonic form of matter largely draped around the galaxies. It approximates an initially low pressure gas of particles that interact only with gravity, but we know little more than that. Searches for detection thus must follow many difficult paths to a great discovery, what the universe is made of. The nonbaryonic picture grew out of a convergence of evidence and ideas in the early 1980s. Developments two decades later considerably improved the evidence, and advances since then have made the case for nonbaryonic dark matter compelling.