Archive for Inflation

How solid is the BICEP2 B-mode result?

Posted in The Universe and Stuff with tags , , on March 18, 2014 by telescoper

Another wordpress post about BICEP2 – by astrophysicist Phil Bull – with some comments on possible issues with the data…

Lumps 'n' Bumps

Phew! An exciting day indeed, so I’ll jot down a few notes to recap what happened.

The BICEP2/Keck experiments detected B-modes at large angular scales in the polarisation of the CMB. They released two papers and some data online just as the announcement was made, which you can find here. Not all of the data mind, but it’s plenty to go on for now.

Their interpretation of the data is that they detect a bump at low-ell that is characteristic of primordial B-modes generated by inflation. If true, this is super exciting, as it gives us a (sort of, but not really) direct detection of gravitational waves, and opens up a new window on the very early Universe (and hence extremely high energy scales). People are even saying it’s a probe of quantum gravity, which I guess is sort of true. Furthermore, they find a best-fit value of the…

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BICEP2: New Evidence Of Cosmic Inflation!

Posted in The Universe and Stuff with tags , , on March 18, 2014 by telescoper

Following on from yesterday’s news, here’s a more detailed analysis of the implications of the BICEP2 result from Matt Straessler’s blog. I certainly agree with the statement highlighted in red in his post:

Until this measurement/discovery is confirmed by another experiment, you should consider it provisional. Although this is too large a signal to be likely to be due to a pure statistical fluke, it could still be due to a mistake or problem, or due to something other than gravitational waves from inflation.

Of Particular Significance

[For your reference if you can’t follow this post: My History of the Universe, and a primer to help you understand what’s going on today.]

I’m still updating this post as more information comes in and as I understand more of what’s in the BICEP2 paper and data. Talking to and listening to experts, I’d describe the mood as cautiously optimistic; some people are worried about certain weird features of the data, while others seem less concerned about them… typical when a new discovery is claimed.  I’m disturbed that the media is declaring victory before the scientific community is ready to.  That didn’t happen with the Higgs discovery, where the media was, wisely, far more patient.

The Main Data

Here’s BICEP2’s data!  The black dots at the bottom of this figure, showing evidence of B-mode polarization both at small scales (“Multipole” >> 100, where it is due to gravitational…

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BICEP2DAY

Posted in Astrohype, The Universe and Stuff with tags , , , , on March 17, 2014 by telescoper

Well, it’s official that this afternoon’s announcement of a “major discovery” is going to be from the BICEP team, and it specifically concerns the BICEP2 CMB telescope experiment. I’ve just got back to Sussex (after a weekend in Cardiff) and will be following the events in among other things I have to do before going off to give a lecture at 5pm GMT.

The schedule of events is as follows: there will be a special webcast presenting the first results from the BICEP2 CMB telescope. The webcast will begin with a presentation for scientists 10:45-11:30 EDT, followed by a news conference 12:00-1:00 EDT.

You can join the webcast from the link at http://www.cfa.harvard.edu/news/news_conferences.html

Papers and data products will be available at 10:45 EDT from http://bicepkeck.org/

EDT is four hours behind Greenwich Mean Time so the webcast will begin at 14:45 GMT, i.e. in about half an hour.

In the mean time, for those of you wondering what these BICEPS are all about, here is a useful graphic in which a Harvard astrophysicist demonstrates the possibilities:

biceps

LIVE BLOG:

14:36 The press conference server has gone down. There’s no truth in the rumour that ex-members of the Clover collaboration have sabotaged it.

14:42 There’s a grave danger that this press conference will run into tea time.

14:45 The BICEP2 papers are now live at http://bicepkeck.org/

14:48 Straight to the headline: R=0.2 (+0.07, -0.05) with R=0 rejected at about 7 sigma, if you like things stated in such terms…

14:53 Here’s the crucial graph. Results a bit higher than the expected  signal at l in range 200-300?

Bi7-IpDCEAA7frU

15:06 The news avalanche has started, e.g. here at the BBC, but there is some concern about the shape of the spectrum.

15:10 I’m not getting anything from the press conference, so may have missed important details. It seems to me though that there’s a significant possibility of some of the polarization signal in E and B not being cosmological. This is a very interesting result, but I’d prefer to reserve judgement until it is confirmed by other experiments.

15:35 Despite the press hype there’s still some scepticism among cosmologists arising from the strange-looking shape of the spectrum. I’m not convinced myself. Anyway, I have to sign off now in order to prepare a lecture..

16:20 Back-of-the-envelope time: if the result is correct then the inflationary energy scale is about 2×1016 GeV. That’s just two orders of magnitude below the Planck scale…

18:19 Returned from my 5pm Theoretical Physics lecture. Couldn’t resist spending 30 minutes talking about BICEP2, though I did tell them it’s not in the examination.

18:25 Main points of controversy:

  1. there seems to be evidence of leakage of temperature into polarization (lines in Fig. 5);
  2. there’s an excess in the B-B spectrum at l~250 shown above;
  3. there’s an excess at low l in the E-E spectrum
  4. there’s a deficit at low l in the cross-correlation with Keck

There may be a connection between 1. and 2.-4. If 2.-4 are real then they may be evidence of something interesting that requires more than a straightforward modification of inflation (such as might include just a running of the spectral index).

18:35 Other controversy: why has this result been announced before the paper has been published or even peer-reviewed?

Some B-Mode Background

Posted in Astrohype, Science Politics, The Universe and Stuff with tags , , , , , , , , , , , on March 15, 2014 by telescoper

Well, in case you hadn’t noticed, the cosmology rumour mill has gone into overdrive this weekend primarily concerning the possibility that an experiment known as BICEP (an acronym formed from Background Imaging of Cosmic Extragalactic Polarization). These rumours have been circulating since it was announced last week that the Harvard-Smithsonian Center for Astrophysics (CfA) will host a press conference  on Monday, March 17th, to announce “a major discovery”. The grapevine is full of possibilities, but it seems fairly clear that the “major discovery” is related to one of the most exciting challenges facing the current generation of cosmologists, namely to locate in the pattern of fluctuations in the cosmic microwave background evidence for the primordial gravitational waves predicted by models of the Universe that involve inflation.

Anyway, I thought I’d add a bit of background on here to help those interested make sense of whatever is announced on Monday evening.

Looking only at the temperature variation across the sky, it is not possible to distinguish between tensor  (gravitational wave) and scalar (density wave) contributions  (both of which are predicted to be excited during the inflationary epoch).  However, scattering of photons off electrons is expected to leave the radiation slightly polarized (at the level of a few percent). This gives us additional information in the form of the  polarization angle at each point on the sky and this extra clue should, in principle, enable us to disentangle the tensor and scalar components.

The polarization signal can be decomposed into two basic types depending on whether the pattern has  odd or even parity, as shown in the nice diagram (from a paper by James Bartlett)

The top row shows the E-mode (which look the same when reflected in a mirror and can be produced by either scalar or tensor modes) and the bottom shows the B-mode (which have a definite handedness that changes when mirror-reflected and which can’t be generated by scalar modes because they can’t have odd parity).

The B-mode is therefore (at least in principle)  a clean diagnostic of the presence of gravitational waves in the early Universe. Unfortunately, however, the B-mode is predicted to be very small, about 100 times smaller than the E-mode, and foreground contamination is likely to be a very serious issue for any experiment trying to detect it. To be convinced that what is being measured is cosmological rather than some sort of contaminant one would have to see the signal repeated across a range of different wavelengths.

Moreover, primordial gravitational waves are not the only way that a cosmological B-mode signal could be generated. Less than a year ago, a paper appeared on the arXiv by Hanson et al. from SPTpol, an experiment which aims to measure the polarization of the cosmic microwave background using the South Pole Telescope. The principal result of this paper was to demonstrate a convincing detection of the so-called “B-mode” of polarization from gravitational lensing of the microwave background photons as they pass through the gravitational field generated by the matter distributed through the Universe. Gravitational lensing can produce the same kind of shearing effect that gravitational waves generate, so it’s important to separate this “line-of-sight” effect from truly primordial signals.

So we wait with bated breath to see exactly what is announced on Monday. In particular, it will be extremely interesting to see whether the new results from BICEP are consistent with the recently published conclusions from Planck. Although Planck has not yet released the analysis of its own polarization data, analysis of the temperature fluctuations yields a (somewhat model-dependent) conclusion that the ratio of tensor to scalar contributions to the CMB pattern is no more than about 11 per cent, usually phrased in the terms, i.e. R<0.11. A quick (and possibly inaccurate) back-of-the-envelope calculation using the published expected sensitivity of BICEP suggests that if they have made a detection it might be above that limit. That would be really interesting because it might indicate that something is going on which is not consistent with the standard framework. The limits on R arising from temperature studies alone assume that both scalar and tensor perturbations are generated by a relatively simple inflationary model belonging to a class in which there is a direct relationship between the relative amplitudes of the two modes (and the shape of the perturbation spectrum). So far everything we have learned from CMB analysis is broadly consistent with this simplifying assumption being correct. Are we about to see evidence that the early Universe was more complex than we thought? We'll just have to wait and see…

Incidentally, once upon a time there was a British experiment called Clover (involving the Universities of  Cardiff, Oxford, Cambridge and Manchester) which was designed to detect the primordial B-mode signal from its vantage point in Chile. I won’t describe it in more detail here, for reasons which will become obvious.

The chance to get involved in a high-profile cosmological experiment was one of the reasons I moved to Cardiff in 2007, and I was looking forward to seeing the data arriving for analysis. Although I’m primarily a theorist, I have some experience in advanced statistical methods that might have been useful in analysing the output.  Unfortunately, however, none of that actually happened. Because of its budget crisis, and despite the fact that it had spent a large amount (£4.5M) on it already,  STFC decided to withdraw the funding needed to complete it (£2.5M)  and cancelled the Clover experiment. Had it gone ahead it would probably have had two years’ data in the bag by now.

It wasn’t clear that Clover would have won the race to detect the B-mode cosmological polarization, but it’s a real shame it was withdrawn as a non-starter. C’est la vie.

Is Inflation Testable?

Posted in The Universe and Stuff with tags , , , , , , , , on March 4, 2014 by telescoper

It seems the little poll about cosmic inflation I posted last week with humorous intent has ruffled a few feathers, but at least it gives me the excuse to wheel out an updated and edited version of an old piece I wrote on the subject.

Just over thirty  years ago a young physicist came up with what seemed at first to be an absurd idea: that, for a brief moment in the very distant past, just after the Big Bang, something weird happened to gravity that made it push rather than pull.  During this time the Universe went through an ultra-short episode of ultra-fast expansion. The physicist in question, Alan Guth, couldn’t prove that this “inflation” had happened nor could he suggest a compelling physical reason why it should, but the idea seemed nevertheless to solve several major problems in cosmology.

Three decades later, Guth is a professor at MIT and inflation is now well established as an essential component of the standard model of cosmology. But should it be? After all, we still don’t know what caused it and there is little direct evidence that it actually took place. Data from probes of the cosmic microwave background seem to be consistent with the idea that inflation happened, but how confident can we be that it is really a part of the Universe’s history?

According to the Big Bang theory, the Universe was born in a dense fireball which has been expanding and cooling for about 14 billion years. The basic elements of this theory have been in place for over eighty years, but it is only in the last decade or so that a detailed model has been constructed which fits most of the available observations with reasonable precision. The problem is that the Big Bang model is seriously incomplete. The fact that we do not understand the nature of the dark matter and dark energy that appears to fill the Universe is a serious shortcoming. Even worse, we have no way at all of describing the very beginning of the Universe, which appears in the equations used by cosmologists as a “singularity”- a point of infinite density that defies any sensible theoretical calculation. We have no way to define a priori the initial conditions that determine the subsequent evolution of the Big Bang, so we have to try to infer from observations, rather than deduce by theory, the parameters that govern it.

The establishment of the new standard model (known in the trade as the “concordance” cosmology) is now allowing astrophysicists to turn back the clock in order to understand the very early stages of the Universe’s history and hopefully to understand the answer to the ultimate question of what happened at the Big Bang itself and thus answer the question “How did the Universe Begin?”

Paradoxically, it is observations on the largest scales accessible to technology that provide the best clues about the earliest stages of cosmic evolution. In effect, the Universe acts like a microscope: primordial structures smaller than atoms are blown up to astronomical scales by the expansion of the Universe. This also allows particle physicists to use cosmological observations to probe structures too small to be resolved in laboratory experiments.

Our ability to reconstruct the history of our Universe, or at least to attempt this feat, depends on the fact that light travels with a finite speed. The further away we see a light source, the further back in time its light was emitted. We can now observe light from stars in distant galaxies emitted when the Universe was less than one-sixth of its current size. In fact we can see even further back than this using microwave radiation rather than optical light. Our Universe is bathed in a faint glow of microwaves produced when it was about one-thousandth of its current size and had a temperature of thousands of degrees, rather than the chilly three degrees above absolute zero that characterizes the present-day Universe. The existence of this cosmic background radiation is one of the key pieces of evidence in favour of the Big Bang model; it was first detected in 1964 by Arno Penzias and Robert Wilson who subsequently won the Nobel Prize for their discovery.

The process by which the standard cosmological model was assembled has been a gradual one, but the latest step was taken by the European Space Agency’s Planck mission . I’ve blogged about the implications of the Planck results for cosmic inflation in more technical detail here. In a nutshell, for several years this satellite mapped  the properties of the cosmic microwave background and how it varies across the sky. Small variations in the temperature of the sky result from sound waves excited in the hot plasma of the primordial fireball. These have characteristic properties that allow us to probe the early Universe in much the same way that solar astronomers use observations of the surface of the Sun to understand its inner structure,  a technique known as helioseismology. The detection of the primaeval sound waves is one of the triumphs of modern cosmology, not least because their amplitude tells us precisely how loud the Big Bang really was.

The pattern of fluctuations in the cosmic radiation also allows us to probe one of the exciting predictions of Einstein’s general theory of relativity: that space should be curved by the presence of matter or energy. Measurements from Planck and its predecessor WMAP reveal that our Universe is very special: it has very little curvature, and so has a very finely balanced energy budget: the positive energy of the expansion almost exactly cancels the negative energy relating of gravitational attraction. The Universe is (very nearly) flat.

The observed geometry of the Universe provides a strong piece of evidence that there is an mysterious and overwhelming preponderance of dark stuff in our Universe. We can’t see this dark matter and dark energy directly, but we know it must be there because we know the overall budget is balanced. If only economics were as simple as physics.

Computer Simulation of the Cosmic Web

The concordance cosmology has been constructed not only from observations of the cosmic microwave background, but also using hints supplied by observations of distant supernovae and by the so-called “cosmic web” – the pattern seen in the large-scale distribution of galaxies which appears to match the properties calculated from computer simulations like the one shown above, courtesy of Volker Springel. The picture that has emerged to account for these disparate clues is consistent with the idea that the Universe is dominated by a blend of dark energy and dark matter, and in which the early stages of cosmic evolution involved an episode of accelerated expansion called inflation.

A quarter of a century ago, our understanding of the state of the Universe was much less precise than today’s concordance cosmology. In those days it was a domain in which theoretical speculation dominated over measurement and observation. Available technology simply wasn’t up to the task of performing large-scale galaxy surveys or detecting slight ripples in the cosmic microwave background. The lack of stringent experimental constraints made cosmology a theorists’ paradise in which many imaginative and esoteric ideas blossomed. Not all of these survived to be included in the concordance model, but inflation proved to be one of the hardiest (and indeed most beautiful) flowers in the cosmological garden.

Although some of the concepts involved had been formulated in the 1970s by Alexei Starobinsky, it was Alan Guth who in 1981 produced the paper in which the inflationary Universe picture first crystallized. At this time cosmologists didn’t know that the Universe was as flat as we now think it to be, but it was still a puzzle to understand why it was even anywhere near flat. There was no particular reason why the Universe should not be extremely curved. After all, the great theoretical breakthrough of Einstein’s general theory of relativity was the realization that space could be curved. Wasn’t it a bit strange that after all the effort needed to establish the connection between energy and curvature, our Universe decided to be flat? Of all the possible initial conditions for the Universe, isn’t this very improbable? As well as being nearly flat, our Universe is also astonishingly smooth. Although it contains galaxies that cluster into immense chains over a hundred million light years long, on scales of billions of light years it is almost featureless. This also seems surprising. Why is the celestial tablecloth so immaculately ironed?

Guth grappled with these questions and realized that they could be resolved rather elegantly if only the force of gravity could be persuaded to change its sign for a very short time just after the Big Bang. If gravity could push rather than pull, then the expansion of the Universe could speed up rather than slow down. Then the Universe could inflate by an enormous factor (1060 or more) in next to no time and, even if it were initially curved and wrinkled, all memory of this messy starting configuration would be lost. Our present-day Universe would be very flat and very smooth no matter how it had started out.

But how could this bizarre period of anti-gravity be realized? Guth hit upon a simple physical mechanism by which inflation might just work in practice. It relied on the fact that in the extreme conditions pertaining just after the Big Bang, matter does not behave according to the classical laws describing gases and liquids but instead must be described by quantum field theory. The simplest type of quantum field is called a scalar field; such objects are associated with particles that have no spin. Modern particle theory involves many scalar fields which are not observed in low-energy interactions, but which may well dominate affairs at the extreme energies of the primordial fireball.

Classical fluids can undergo what is called a phase transition if they are heated or cooled. Water for example, exists in the form of steam at high temperature but it condenses into a liquid as it cools. A similar thing happens with scalar fields: their configuration is expected to change as the Universe expands and cools. Phase transitions do not happen instantaneously, however, and sometimes the substance involved gets trapped in an uncomfortable state in between where it was and where it wants to be. Guth realized that if a scalar field got stuck in such a “false” state, energy – in a form known as vacuum energy – could become available to drive the Universe into accelerated expansion.We don’t know which scalar field of the many that may exist theoretically is responsible for generating inflation, but whatever it is, it is now dubbed the inflaton.

This mechanism is an echo of a much earlier idea introduced to the world of cosmology by Albert Einstein in 1916. He didn’t use the term vacuum energy; he called it a cosmological constant. He also didn’t imagine that it arose from quantum fields but considered it to be a modification of the law of gravity. Nevertheless, Einstein’s cosmological constant idea was incorporated by Willem de Sitter into a theoretical model of an accelerating Universe. This is essentially the same mathematics that is used in modern inflationary cosmology.  The connection between scalar fields and the cosmological constant may also eventually explain why our Universe seems to be accelerating now, but that would require a scalar field with a much lower effective energy scale than that required to drive inflation. Perhaps dark energy is some kind of shadow of the inflaton

Guth wasn’t the sole creator of inflation. Andy Albrecht and Paul Steinhardt, Andrei Linde, Alexei Starobinsky, and many others, produced different and, in some cases, more compelling variations on the basic theme. It was almost as if it was an idea whose time had come. Suddenly inflation was an indispensable part of cosmological theory. Literally hundreds of versions of it appeared in the leading scientific journals: old inflation, new inflation, chaotic inflation, extended inflation, and so on. Out of this activity came the realization that a phase transition as such wasn’t really necessary, all that mattered was that the field should find itself in a configuration where the vacuum energy dominated. It was also realized that other theories not involving scalar fields could behave as if they did. Modified gravity theories or theories with extra space-time dimensions provide ways of mimicking scalar fields with rather different physics. And if inflation could work with one scalar field, why not have inflation with two or more? The only problem was that there wasn’t a shred of evidence that inflation had actually happened.

This episode provides a fascinating glimpse into the historical and sociological development of cosmology in the eighties and nineties. Inflation is undoubtedly a beautiful idea. But the problems it solves were theoretical problems, not observational ones. For example, the apparent fine-tuning of the flatness of the Universe can be traced back to the absence of a theory of initial conditions for the Universe. Inflation turns an initially curved universe into a flat one, but the fact that the Universe appears to be flat doesn’t prove that inflation happened. There are initial conditions that lead to present-day flatness even without the intervention of an inflationary epoch. One might argue that these are special and therefore “improbable”, and consequently that it is more probable that inflation happened than that it didn’t. But on the other hand, without a proper theory of the initial conditions, how can we say which are more probable? Based on this kind of argument alone, we would probably never really know whether we live in an inflationary Universe or not.

But there is another thread in the story of inflation that makes it much more compelling as a scientific theory because it makes direct contact with observations. Although it was not the original motivation for the idea, Guth and others realized very early on that if a scalar field were responsible for inflation then it should be governed by the usual rules governing quantum fields. One of the things that quantum physics tells us is that nothing evolves entirely smoothly. Heisenberg’s famous Uncertainty Principle imposes a degree of unpredictability of the behaviour of the inflaton. The most important ramification of this is that although inflation smooths away any primordial wrinkles in the fabric of space-time, in the process it lays down others of its own. The inflationary wrinkles are really ripples, and are caused by wave-like fluctuations in the density of matter travelling through the Universe like sound waves travelling through air. Without these fluctuations the cosmos would be smooth and featureless, containing no variations in density or pressure and therefore no sound waves. Even if it began in a fireball, such a Universe would be silent. Inflation puts the Bang in Big Bang.

The acoustic oscillations generated by inflation have a broad spectrum (they comprise oscillations with a wide range of wavelengths), they are of small amplitude (about one hundred thousandth of the background); they are spatially random and have Gaussian statistics (like waves on the surface of the sea; this is the most disordered state); they are adiabatic (matter and radiation fluctuate together) and they are formed coherently.  This last point is perhaps the most important. Because inflation happens so rapidly all of the acoustic “modes” are excited at the same time. Hitting a metal pipe with a hammer generates a wide range of sound frequencies, but all the different modes of the start their oscillations at the same time. The result is not just random noise but something moderately tuneful. The Big Bang wasn’t exactly melodic, but there is a discernible relic of the coherent nature of the sound waves in the pattern of cosmic microwave temperature fluctuations seen in the Cosmic Microwave Background. The acoustic peaks seen in the  Planck  angular spectrum  provide compelling evidence that whatever generated the pattern did so coherently.

Planck_power_spectrum_orig
There are very few alternative theories on the table that are capable of reproducing these results, but does this mean that inflation really happened? Do they “prove” inflation is correct? More generally, is the idea of inflation even testable?

So did inflation really happen? Does Planck prove it? Will we ever know?

It is difficult to talk sensibly about scientific proof of phenomena that are so far removed from everyday experience. At what level can we prove anything in astronomy, even on the relatively small scale of the Solar System? We all accept that the Earth goes around the Sun, but do we really even know for sure that the Universe is expanding? I would say that the latter hypothesis has survived so many tests and is consistent with so many other aspects of cosmology that it has become, for pragmatic reasons, an indispensable part our world view. I would hesitate, though, to say that it was proven beyond all reasonable doubt. The same goes for inflation. It is a beautiful idea that fits snugly within the standard cosmological and binds many parts of it together. But that doesn’t necessarily make it true. Many theories are beautiful, but that is not sufficient to prove them right.

When generating theoretical ideas scientists should be fearlessly radical, but when it comes to interpreting evidence we should all be unflinchingly conservative. The Planck measurements have also provided a tantalizing glimpse into the future of cosmology, and yet more stringent tests of the standard framework that currently underpins it. Primordial fluctuations produce not only a pattern of temperature variations over the sky, but also a corresponding pattern of polarization. This is fiendishly difficult to measure, partly because it is such a weak signal (only a few percent of the temperature signal) and partly because the primordial microwaves are heavily polluted by polarized radiation from our own Galaxy. Polarization data from Planck are yet to be released; the fiendish data analysis challenge involved is the reason for the delay.  But there is a crucial target that justifies these endeavours. Inflation does not just produce acoustic waves, it also generates different modes of fluctuation, called gravitational waves, that involve twisting deformations of space-time. Inflationary models connect the properties of acoustic and gravitational fluctuations so if the latter can be detected the implications for the theory are profound. Gravitational waves produce very particular form of polarization pattern (called the B-mode) which can’t be generated by acoustic waves so this seems a promising way to test inflation. Unfortunately the B-mode signal is expected to be very weak and the experience of WMAP suggests it might be swamped by foregrounds. But it is definitely worth a go, because it would add considerably to the evidence in favour of inflation as an element of physical reality.

But would even detection of primordial gravitational waves really test inflation? Not really. The problem with inflation is that it is a name given to a very general idea, and there are many (perhaps infinitely many) different ways of implementing the details, so one can devise versions of the inflationary scenario that produce a wide range of outcomes. It is therefore unlikely that there will be a magic bullet that will kill inflation dead. What is more likely is a gradual process of reducing the theoretical slack as much as possible with observational data, such as is happening in particle physics. For example, we have not yet identified the inflaton field (nor indeed any reasonable candidate for it) but we are gradually improving constraints on the allowed parameter space. Progress in this mode of science is evolutionary not revolutionary.

Many critics of inflation argue that it is not a scientific theory because it is not falsifiable. I don’t think falsifiability is a useful concept in this context; see my many posts relating to Karl Popper. Testability is a more appropriate criterion. What matters is that we have a systematic way of deciding which of a set of competing models is the best when it comes to confrontation with data. In the case of inflation we simply don’t have a compelling model to test it against. For the time being therefore, like it or not, cosmic inflation is clearly the best model we have. Maybe someday a worthy challenger will enter the arena, but this has not happened yet.

Most working cosmologists are as aware of the difficulty of testing inflation as they are of its elegance. There are also those  who talk as if inflation were an absolute truth, and those who assert that it is not a proper scientific theory (because it isn’t falsifiable). I can’t agree with either of these factions. The truth is that we don’t know how the Universe really began; we just work on the best ideas available and try to reduce our level of ignorance in any way we can. We can hardly expect  the secrets of the Universe to be so easily accessible to our little monkey brains.

Inflation and the Multiverse

Posted in Astrohype, The Universe and Stuff with tags , , , , , , on January 6, 2014 by telescoper

I was quite excited when I discovered, via Twitter, a paper on the arXiv with the title Quantum Fluctuations in Cosmology and How They Lead to a Multiverse, which was written by one of the architects of the inflationary universe scenario, Alan Guth. Despite numerous attempts to understand the argument how inflation leads to a Multiverse I’ve never really succeeded. To me it always seemed like  a version of the Mind Projection Fallacy inspired by a frequentist interpretation of probability: the construction of notional ensembles for the purposes of calculation in quantum mechanics does not imply that such ensembles are realized in nature. In fact I’ve never found much more substance in articles about this issue than the assertion that Quantum Physics = Woo! = Multiverse.

Anyway, since the paper I found is a review article I hoped it would help teach me the error of my ways. Here is the abstract

This article discusses density perturbations in inflationary models, offering a pedagogical description of how these perturbations are generated by quantum fluctuations in the early universe. A key feature of inflation is that that rapid expansion can stretch microscopic fluctuations to cosmological proportions. I discuss also another important conseqence of quantum fluctuations: the fact that almost all inflationary models become eternal, so that once inflation starts, it never stops.

My eye was drawn to the phrase “almost all inflationary models”.  I had hoped to see “almost all” used in its strict mathematical sense, ie “apart from a set of measure zero” with the measure being fully specified. Disappointingly, it isn’t.   Guth discusses the consequences of the tail  the inflationary potential V (for large values of the inflaton field ϕ) on the long-term evolution of inflationary dynamics and then states

Since V3/2/|V ′| grows without bound as ϕ → ∞ for most potentials under consideration, almost all models allow for eternal inflation.

This means, to me, most models people have constructed but doesn’t mean all possible models. I don’t doubt that some inflationary models  become eternal, but would have preferred a more rigorous statement.  This is particularly strange because Guth spends the last section of his paper discussing the “measure problem”:

While the multiverse picture looks very plausible in the context of inflationary cosmology — at least to me — it raises a thorny and unsolved problem, known as the “measure problem.” Specifically, we do not know how to define probabilities in the multiverse.

The measure problem to my mind also extends to the space of all possible inflationary theories.

And then there’s the title, which, I remind you, is Quantum Fluctuations in Cosmology and How They Lead to a Multiverse. Guth’s argument consists of going through the (standard) calculation of the spectrum of cosmological density fluctuations (which does fit a host of observational data). He then states:

Since the density perturbation calculations have been incredibly successful, it seems to make sense to take seriously the assumptions behind these calculations, and follow them where they lead. I have to admit that there is no clear consensus among cosmologists, but to many of us the assumptions seem to be pointing to eternal inflation, and the multiverse.

I have to admit that I get a bit annoyed when I read a paper in which the actual conclusions are much weaker than implied by the title, but that seems to be par for the course in this field.

For the record, I’ll state that I am an agnostic about the multiverse. It may be a correct idea, it may not. I will say, however, that I still haven’t found any article that puts it on a firm scientific footing. That may well, of course, just be a measure of my ignorance. If you know of one, please let me know through the comments box.

The Inflationary Bubble

Posted in The Universe and Stuff with tags , , , , on July 9, 2013 by telescoper

The Summer School I’m attending on Inflation and the CMB got under way yesterday morning with a couple of lectures (90 minutes each) by Andrei Linde, one of the pioneers of the theory of cosmic inflation. I enjoyed the first part of the session, but then he went off into the technical details of a specific model for which there seemed previous little in the way of physical motivation or testable consequences. There’s an occupational hazard for people working on inflation which is that they become so absorbed by their calculations that they forget that they’re supposed to be doing science. It sometimes appears that this field has reached a critical density of activity which means that it’s in danger of forming a closed universe completely incapable of communicating with the world outside and perhaps of collapsing in on itself.

The other thing I didn’t like was the evangelism about the multiverse, which is widespread amongst theorists these days. I’ve stated my position about this before so I won’t repeat my objections here. I will, however, lodge an objection to the way Prof. Linde answered a question about whether the multiverse theory was a testable of various fine-tuning problems in cosmology by saying

Ihe multiverse is the only known explanation so in a sense it has already been tested.

I don’t mind particularly if theories are not testable with current technology. New ideas often have to wait a very long time before equipment and techniques are developed to test them, but Linde’s response is rather symptomatic of a frame of mind that does not consider testability important at all. The worst offenders in this regard are certain string theorists who seem to thing string theory is so compelling in its own right that it just has to be the one true description of how the Universe works, even if the framework it provides is unable to make any predictions at all.

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Germany Calling…

Posted in Biographical, Books, Talks and Reviews, The Universe and Stuff with tags , , , , on July 7, 2013 by telescoper

Just a quick post to break radio silence and announce my arrival in the picturesque town of Bad Honnef, spa town in Germany near Bonn in the Rhein-Sieg district of North Rhine-Westphalia. We’re right on the banks of the Rhine actually, and there are some fine views of castles and hills to be had all round.

To get here I took my life in my hands and flew with a German budget airline called Germanwings from Heathrow to nearby Bonn-Cologne airport. I mean it’s near to Bad Honnef, not to Heathrow. Apart from the fact that I had to queue for an hour at check-in because the staff apparently didn’t know how to operate the computer system, and the flight was delayed leaving because it was delayed on the way in, it wasn’t actually too bad; we arrived only about 25 minutes late and I was able to have a few beers and some food when I arrived at my destination.

The reason for this expedition is that I’m giving two lectures at the Deutschen Physikalischen Gesellschaft (henceforth DPG) Summer School on Inflation and the CMB. The list of other speakers is very impressive so I assume that some form of administrative error is responsible for my invitation, and especially for the fact that I’ve got to give two lectures while everyone else is just giving one…

Anyway, it’s lovely weather here – although a little on the toasty side for my cold English blood – and I hope to get the chance to take a few pictures as well as some updates from the meeting. I also hope to find out why this place is called Bad Honnef. I know I’ve only been here a few hours, but it seems to me that, as Honnefs go, it’s really not bad at all…

Has Planck closed the window on the Early Universe?

Posted in The Universe and Stuff with tags , , , , , , , , on April 7, 2013 by telescoper

A combination of circumstances – including being a bit poorly – has made me rather late in getting around to reading the papers released by the Planck consortium a couple of weeks ago. I’ve had a bit of time this Sunday so I decided to have a look. Naturally I went straight for, er, paper No. 24, which you can find on the arXiv, here.

I picked this one to start with because it’s about primordial non-Gaussianity. This is an important topic because the simplest theories of cosmological inflation predict the generation of small-amplitude irregularities in the early Universe that form a statistically homogeneous and isotropic Gaussian random field. This means that the perturbations (usually defined in terms of departures of the metric from a pure Robertson-Walker form) are defined by probability distributions which are invariant under translations and rotations in 3D space.

In a nutshell, such perturbations arise quite simply in inflationary cosmology as zero-point oscillations of a scalar quantum field, in a very similar way the Gaussian distributions that arise from the quantized harmonic oscillator. Assuming the fluctuations are small in amplitude the scalar field evolves according to

\ddot{\Phi} +3H\dot{\Phi} + V^{\prime}(\Phi),

which is similar to that describing a ball rolling down a potential V, under the action of a force given by the derivative V^{\prime}, opposed by a “frictional” force depending on the ball’s speed; in the inflationary context the frictional force depends on the expansion rate H(\Phi, \dot{\Phi}). If the slope of the potential is relatively shallow then there is a slow-rolling regime during which the kinetic energy of the field is negligible compared to its potential energy; the term in \ddot{\phi} then becomes negligible in the above equation. The universe then enters a near-exponential phase of expansion, during which the small Gaussian quantum fluctuations in \Phi become Gaussian classical metric perturbations.

On the one hand, Gaussian fluctuations are great for a theorist because so many of their statistical properties can be calculated analytically: I played around a lot with them in my PhD thesis many moons ago, long before Planck, in fact long before any fluctuations in the cosmic microwave background were measured at all! The problem is that if we keep finding that everything is consistent with the Gaussian hypothesis then we have problems.

The point about this slow-rolling regime is that it is an attractor solution that resembles the physical description of a body falling through the air: eventually such a body reaches a terminal velocity defined by the balance between gravity and air resistance, but independent of how high and how fast it started. The problem is that if you want to know where a body moving at terminal velocity started falling from, you’re stumped (unless you have other evidence). All dynamical memory of the initial conditions is lost when you reach the attractor solution. The problem for early Universe cosmologists is similar. If everything we measure is consistent with having been generated during a simple slow-rolling inflationary regime, then there is no way of recovering any information about what happened beforehand because nothing we can observe remembers it. The early Universe will remain a closed book forever.

So what does all this have to do with Planck? Well, one of the most important things that the Planck collaboration has been looking for is evidence of non-Gaussianity that could be indicative of primordial physics more complicated than that included in the simplest inflationary models (e.g.  multiple scalar fields, more complicated dynamics, etc).  Departures from the standard model might just keep the window on the early Universe open.

A simple way of defining a parameter that describes the level of non-Gaussianity is as follows:

\phi = \phi_{G} + f_{NL} \left( \phi_{G}^2 -< \phi_{G}^2 > \right)

the parameter f_{NL} describes a quadratic contribution to the overall metric perturbation \phi: you can think of this as being like a power series expansion of the total fluctuation in terms of a Gaussian component \phi_{G}; the term in angle brackets is just there to ensure the whole thing averages to zero. This definition of non-Gaussianity is not the only one possible, but it’s the simplest and it’s the one for which Planck has produced the most dramatic result:

f_{NL}=2.7 \pm 5.8,

which is clearly consistent with zero. If this doesn’t look impressive, bear in mind that the typical fluctuation in the metric inferred from cosmological measurements is of order 10^{-5}. The quadratic terms are therefore of order 10^{-10}, so the upper limit on the level of non-Gaussianity allowed by Planck really is minuscule. This is one of the reasons why some people have described the best-fitting model emerging from Planck as the Maximally Boring Universe

So it looks like only very unwise investors will be buying shares in cosmological non-Gaussianity at least in the short-term. More fundamentally we may be approaching the limit of what we can learn about inflation in particular, or even the early Universe in general, using the traditional techniques of observational cosmology. But there remain very intriguing questions that may yet shed light on the pre-inflationary epoch. Among these are the large-scale anomalies seen in the very same Planck data that have put such stringent limits on non-Gaussianity. But that question, described in Planck Paper 23, will have to wait for another day…

The Cosmic Tightrope

Posted in The Universe and Stuff with tags , , on May 3, 2009 by telescoper

Here’s a thought experiment for you.

Imagine you are standing outside a sealed room. The contents of the room are hidden from you, except for a small window covered by a curtain. You are told that you can open the curtain once and only briefly to take a peep at what is inside, and you may do this whenever you feel the urge.

You are told what is in the room. It is bare except for a tightrope suspended across it about two metres in the air. Inside the room is a man who at some time in the past – you’re not told when – began walking along the tightrope. His instructions were to carry on walking backwards and forwards along the tightrope until he falls off, either through fatigue or lack of balance. Once he falls he must lie motionless on the floor.

You are not told whether he is skilled in tightrope-walking or not, so you have no way of telling whether he can stay on the rope for a long time or a short time. Neither are you told when he started his stint as a stuntman.

What do you expect to see when you eventually pull the curtain?

Well, if the man does fall off sometime it will clearly take him a very short time to drop to the floor. Once there he has to stay there.One outcome therefore appears very unlikely: that at the instant you open the curtain, you see him in mid-air between a rope and a hard place.

Whether you expect him to be on the rope or on the floor depends on information you do not have. If he is a trained circus artist, like the great Charles Blondin here, he might well be capable of walking to and fro along the tightrope for days. If not, he would probably only manage a few steps before crashing to the ground. Either way it remains unlikely that you catch a glimpse of him in mid-air during his downward transit. Unless, of course, someone is playing a trick on you and someone has told the guy to jump when he sees the curtain move.

This probably seems to have very little to do with physical cosmology, but now forget about tightropes and think about the behaviour of the mathematical models that describe the Big Bang. To keep things simple, I’m going to ignore the cosmological constant and just consider how things depend on one parameter, the density parameter Ω0. This is basically the ratio between the present density of the matter in the Universe compared to what it would have to be to cause the expansion of the Universe eventually to halt. To put it a slightly different way, it measures the total energy of the Universe. If Ω0>1 then the total energy of the Universe is negative: its (negative) gravitational potential energy dominates over the (positive) kinetic energy. If Ω0<1 then the total energy is positive: kinetic trumps potential. If Ω0=1 exactly then the Universe has zero total energy: energy is precisely balanced, like the man on the tightrope.

A key point, however, is that the trade-off between positive and negative energy contributions changes with time. The result of this is that Ω is not fixed at the same value forever, but changes with cosmic epoch; we use Ω0 to denote the value that it takes now, at cosmic time t0, but it changes with time.

At the beginning, at the Big Bang itself,  all the Friedmann models begin with Ω arbitrarily close to unity at arbitrarily early times, i.e. the limit as t tends to zero is Ω=1.

In the case in which the Universe emerges from the Big bang with a value of Ω just a tiny bit greater than one then it expands to a maximum at which point the expansion stops. During this process Ω grows without bound. Gravitational energy wins out over its kinetic opponent.

If, on the other hand, Ω sets out slightly less than unity – and I mean slightly, one part in 1060 will do – the Universe evolves to a state where it is very close to zero. In this case kinetic energy is the winner  and Ω ends up on the ground, mathematically speaking.

In the compromise situation with total energy zero, this exact balance always applies. The universe is always described by Ω=1. It walks the cosmic tightrope. But any small deviation early on results in runaway expansion or catastrophic recollapse. To get anywhere close to Ω=1 now – I mean even within a factor ten either way – the Universe has to be finely tuned.

A slightly different way of describing this is to think instead about the radius of curvature of the Universe. In general relativity the curvature of space is determined by the energy (and momentum) density. If the Universe has zero total energy it is flat, so it doesn’t have any curvature at all so its curvature radius is infinite. If it has positive total energy the curvature radius is finite and positive, in much the same way that a sphere has positive curvature. In the opposite case it has negative curvature, like a saddle. I’ve blogged about this before.

I hope you can now see how this relates to the curious case of the tightrope walker.

If the case Ω0= 1 applied to our Universe then we can conclude that something trained it to have a fine sense of equilibrium. Without knowing anything about what happened at the initial singularity we might therefore be pre-disposed to assign some degree of probability that this is the case, just as we might be prepared to imagine that our room contained a skilled practitioner of the art of one-dimensional high-level perambulation.

On the other hand, we might equally suspect that the Universe started off slightly over-dense or slightly under-dense, at which point it should either have re-collapsed by now or have expanded so quickly as to be virtually empty.

About fifteen years ago, Guillaume Evrard and I tried to put this argument on firmer mathematical grounds by assigning a sensible prior probability to Ω based on nothing other than the assumption that our Universe is described by a Friedmann model.

The result we got was that it should be of the form

P(\Omega) \propto \Omega^{-1}(\Omega-1)^{-1}.

I was very pleased with this result, which is based on a principle advanced by physicist Ed Jaynes, but I have no space to go through the mathematics here. Note, however, that this prior has three interesting properties: it is infinite at Ω=0 and Ω=1, and it has a very long “tail” for very large values of Ω. It’s not a very well-behaved measure, in the sense that it can’t be integrated over, but that’s not an unusual state of affairs in this game. In fact it is an improper prior.

I think of this prior as being the probabilistic equivalent of Mark Twain’s description of a horse:

dangerous at both ends, and uncomfortable in the middle.

Of course the prior probability doesn’t tell usall that much. To make further progress we have to make measurements, form a likelihood and then, like good Bayesians, work out the posterior probability . In fields where there is a lot of reliable data the prior becomes irrelevant and the likelihood rules the roost. We weren’t in that situation in 1995 – and we’re arguably still not – so we should still be guided, to some extent by what the prior tells us.

The form we found suggests that we can indeed reasonably assign most of our prior probability to the three special cases I have described. Since we also know that the Universe is neither totally empty nor ready to collapse, it does indicate that, in the absence of compelling evidence to the contrary, it is quite reasonable to have a prior preference for the case Ω=1.  Until the late 1980s there was indeed a strong ideological preference for models with Ω=1 exactly, but not because of the rather simple argument given above but because of the idea of cosmic inflation.

From recent observations we now know, or think we know, that Ω is roughly 0.26. To put it another way, this means that the Universe has roughly 26% of the density it would need to have to halt the cosmic expansion at some point in the future. Curiously, this corresponds precisely to the unlikely or “fine-tuned” case where our Universe is in between  two states in which we might have expected it to lie.

Even if you accept my argument that Ω=1 is a special case that is in principle possible, it is still the case that it requires the Universe to have been set up with very precisely defined initial conditions. Cosmology can always appeal to special initial conditions to get itself out of trouble because we don’t know how to describe the beginning properly, but it is much more satisfactory if properties of our Universe are explained by understanding the physical processes involved rather than by simply saying that “things are the way they are because they were the way they were.” The latter statement remains true, but it does not enhance our understanding significantly. It’s better to look for a more fundamental explanation because, even if the search is ultimately fruitless, we might turn over a few interesting stones along the way.

The reasoning behind cosmic inflation admits the possibility that, for a very short period in its very early stages, the Universe went through a phase where it was dominated by a third form of energy, vacuum energy. This forces the cosmic expansion to accelerate. This drastically changes the arguments I gave above. Without inflation the case with Ω=1 is unstable: a slight perturbation to the Universe sends it diverging towards a Big Crunch or a Big Freeze. While inflationary dynamics dominate, however, this case has a very different behaviour. Not only stable, it becomes an attractor to which all possible universes converge. Whatever the pre-inflationary initial conditions, the Universe will emerge from inflation with Ω very close to unity. Inflation trains our Universe to walk the tightrope.

So how can we reconcile inflation with current observations that suggest a low matter density? The key to this question is that what inflation really does is expand the Universe by such a large factor that the curvature radius becomes infinitesimally small. If there is only “ordinary” matter in the Universe then this requires that the universe have the critical density. However, in Einstein’s theory the curvature is zero only if the total energy is zero. If there are other contributions to the global energy budget besides that associated with familiar material then one can have a low value of the matter density as well as zero curvature. The missing link is dark energy, and the independent evidence we now have for it provides a neat resolution of this problem.

Or does it? Although spatial curvature doesn’t really care about what form of energy causes it, it is surprising to some extent that the dark matter and dark energy densities are similar. To many minds this unexplained coincidence is a blemish on the face of an otherwise rather attractive structure.

It can be argued that there are initial conditions for non-inflationary models that lead to a Universe like ours. This is true. It is not logically necessary to have inflation in order for the Friedmann models to describe a Universe like the one we live in. On the other hand, it does seem to be a reasonable argument that the set of initial data that is consistent with observations is larger in models with inflation than in those without it. It is rational therefore to say that inflation is more probable to have happened than the alternative.

I am not totally convinced by this reasoning myself, because we still do not know how to put a reasonable measure on the space of possibilities existing prior to inflation. This would have to emerge from a theory of quantum gravity which we don’t have. Nevertheless, inflation is a truly beautiful idea that provides a framework for understanding the early Universe that is both elegant and compelling. So much so, in fact, that I almost believe it.