Science week in Ireland: was Einstein wrong?

This week is Science Week in Ireland, with science events taking place all over the country. There are talks and demonstrations on every aspect of science you can think of, from a demonstration of animal magic at Killaloe in County Limerick to astronomy at the Crawford Observatory of University College Cork.

This evening, I will give a public lecture on the Big Bang in Trinity College, hosted by Astronomy Ireland. We’re still in the International Year of Astronomy, celebrating the 400th anniversary of Galileo’s use of the telescope to establish the heliocentric model of the solar system, so it’s highly appropriate to have a lecture describing another paradigm shift in science brought to us by astronomy: the discovery of the expanding universe and the big bang model that followed. I’m delighted to be giving the lecture as Astronomy Ireland do a fantastic job of promoting astronomy and science around the country, with night-classes in astronomy, public viewings of astronomical events and regular public science lectures. It’s also fun to tell the story of the discovery of the big bang model to people with an interest in astronomy, as many of them already know most of the facts, but from a slightly different perspective. Indeed, much of what we know of cosmology really comes from astronomical observation. You can find a poster, a summary of the lecture and the slides I will use here.

As I write this post, I’m sitting in the RTE canteen having done an interview promoting the lecture on Today with Pat Kenny, the flagship radio show of RTE, the Irish broadcasting corporation. (The last time I was at RTE I was auditioning for deputy work with the  Concert Orchestra but that’s another story!). I think the interview went well, it was certainly good fun. Unlike a lot of scientists I quite enjoy talking to the media, it’s a challenge getting deep ideas across in a short interview without sounding completely incomprehensible! I also find this particular radio show very good and listen in whenever I can.

Astronomy Ireland marketed the lecture as ‘The Big Bang: Was Einstein Wrong? which is quite a good hook, so the interview touched on this quite a bit. Of course the answer is YES, it refers to a famous Einstein gaffe. When E. applied the general theory of relativity, his new theory of space, time and gravity, to the entire universe, it predicted a universe that was changing in time (space and time expanding). No evidence for such a thing existed at the time, so Einstein then introduced an extra term into the equations of relativity to force the universe to be static. Such fudge-factors are always risky in science and sure enough it turned out to be a big mistake. In 1929, the American astronomer Edwin Hubble established unequivocally that faraway galaxies are rushing away from one another and mathematicians realised that the universe is indeed expanding. Einstein immediately dropped the spurious term (known as the cosmological constant), declaring it his ‘greatest blunder’. You can listen to a podcast of the interview here, I hope I got the point across!

Einstein: right about relativity, but missed the prediction of the expanding universe

On Tuesday evening, I’ll give a repeat of the lecture in Waterford,in the main Auditorium of our college. On Wednesday, there is a talk on on the legacy of Charles Darwin at Waterford City Hall, which should be very good, I hope to attend myself. Both these lectures have been organised by CALMAST, the science communication group at WIT. All in all, it’s going be a busy week.

Update: I can see why media interviews are important, we had to change venue to the largest lecture theatre in trinity last night as we got a turnout of about 500! I think the lecture went well, I certainly enjoyed it.

Current status of the concordance model

This week I’m studying a very nice article on the ArXiv by L.Perivolaropoulos on recent observational challenges to the ΛCDM model (thanks Bee).

The ΛCDM model is the technical name given to the concordance model of Big Bang cosmology (see final post in cosmology 101 series). Essentially, the model is the best attempt to account for the three main strands of observational evidence: the measurements of the cosmic microwave background, the measurements of the large scale structure of the universe by gravitational lensing, and the supernova measurements of the accelerated expansion of the universe. CDM stands for Cold Dark Matter, the postulate that much of the matter holding the galaxies and galaxy clusters together is unseen – i.e. does not couple with the electromagnetic interaction (see previous post on Dark Matter). Λ refers to the so-called cosmological constant -  i.e.  the ‘dark energy’ term thought to be responsible for the current acceleration of the universe expansion (see previous post on dark energy here).

The matter-energy composition of the universe according to ΛCDM

However, cosmologists are well aware that there is an alternative: the ΛCDM model could simply be wrong, and the postulates of dark matter and dark energy completely spurious, if our underlying theory of gravity – general relativity – does not apply at the largest scales. Both postulates arise from the attempt to shoehorn the observational data into gravitational theory, and it is always possible that the underlying theory is incomplete (after all, we know GR breaks down at the smallest scales). There is a very nice discussion of this in Perivolaropoulos’ s paper, in the context of six experimental observations that have emerged in the last few years that don’t seem to fit easily into the ΛCDM model.

Of course, given the spectacular success of general relativity in explaining so many aspects of our universe so far, the betting money is on relativity being correct, while the new observational data may modified as more measurements are made (this has happened countless times before). Either way, it’s a really nice update on the current state of play and shows how good science is done – not to mention the usefulness of the ArXiv database.

Update

Over on the DiscoverScience blog, Sean Carroll also has very nice post on a specific challenge to the concordance model from measurements of the large scale structure of the universe by weak gravitational lensing. Again, both the post and the discussion afterwards are excellent and give a good idea of how this sort of science is done.

It’’s worth mentioning that both dark matter and dark energy are favourite targets of skeptics, philosophers of science and other commentators. To be sure, they both probably seem like an obvious fix to an outsider, particularly given their postulated prevalence relative to ordinary matter (our universe is estimated to comprise 73% dark energy, 23%  dark matter and only 4% ordinary matter!). However, in this sort of debate, it’s important to listen to the experts. While keeping an open mind, most cosmologists seem convinced that dark matter almost certainly exists. The general line is that you can see it – by its gravitational effect, not electromagnetic. This is perfectly feasible if dark matter is made up of WIMPS (weakly interacting massive particles), a not unreasonable proposition. Such particles may even be detected at the LHC, which would be very exciting. It should also be remembered that the existence of dark matter is also invoked to account for the nucleosynthesis of the elements, a seperate plank of the big bang model. Finally, there are now strong experimental hints of the existence of dark matter from studies of galaxy collisions

Evidence for dark matter in the bullet cluster

As for dark energy, it is certainly true that this is a lot more speculative, and could turn out to be one of many different things  (see wiki for a good summary). However, it’s important to note that the postulate does not arise solely from the supernova measurements – there are also indirect evuidence of dark energy from measurements of the cosmic microwave background.

Binary black holes, gravitational waves and numerical relativity

We had an excellent turn-out for yesterday’s superb Institute of Physics seminar even though we are in the last hectic week of the teaching semester (thanks to the organisational skills of the WIT maths/physics seminar group). The talk ‘Binary black holes, gravitational waves and numerical relativity’ was given by Dr Joan Centrella, head of the Gravitational Astrophysics Laboratory at NASA’s Goddard Space Flight Centre. Dr Centrella is a distinguished relativist, well known for her work in the simulation of black hole mergers and she certainly didn’t disappoint.

The lecture started with an overview of massive black holes, intermediate black holes and gravitational waves. Just as general relativity predicts that a large mass will curve spacetime, it predicts that moving mass will cause ripples in the curvature of spacetime – known as gravitational waves. Of course, such disturbances will be extremely difficult to detect due to the weakness of the gravitational interaction. Indeed, while many of the spectacular predictions of general relativity have been verified (the bending of light in a gravitational field, time dilation in a gravitational field, black holes and even the expanding universe) the direct detection of gravitational waves is possibly the last great test of relativity. The speaker explained that the best chance of seeing the phenomenon directly is by studying the most explosive events known: black hole mergers.

There was a brief description of the indirect observation of gravitational waves, in particular the Hulse-Taylor pulsar. This is a binary pulsar found in 1974, whose orbit has been observed to be gradually shrinking due to the radiation of energy by gravitational waves: the two stars will merge in about 300 million years. Interesting that Hulse got the Nobel for work done while still a postgraduate, while Jocelyn Bell was overlooked for her discovery of pulsars – see post on IoP meeting below.

Centrella then gave an overview of direct searches for gravitational waves, both earth-bound (LIGO) and space-based (LISA). LIGO, the Large Interferometer Gravitational Wave Observatory, is basically a huge Michelson interferometer, complete with laser source, beam splitter and mirrors – the arms of the interferometer are several kilometers in length! LISA, the Laser Interferometer Space Antenna, is an astounding project: a joint NASA/ESA mission, it will consist of three separate mini-spacecraft, each with its own laser source, maintained in an equilateral triangle that will form a giant Michelson interferometer in space. Minute disturbances in spacetime by a passing gravitational wave will be measured as tiny changes in relative arm length (having taken all other factors into account). A crucial difference between the two systems is the target: while LIGO searches for intermediate black hole events, LISA will search for massive BH events (a much stronger source in a different region of the spectrum).

LIGO (California)

LISA (artist’s impression)

Dr Centrella then described her own field: the use of numerical methods and algorithims to solve the equations of general relativity for the particular case of relativistic binary systems and their associated gravitational waves. She gave a great overview of historic problems in the area and recent breakthroughs in the field, from the puncture method to the Lazarus approach. I won’t attempt to summarize this part of the talk, but there is a nice overview of the field here and I should have a link to the slides from the talk in a day or two.

Dr Centrella with a scale model of one of the LISA spacecraft

All in all, this was a superb lecture, courtesy of the Institute of Physics. It was clear the audience enjoyed the lecture thoroughly and there were plenty of queries at question time – indeed the lecture would have continued for another hour had we not whisked the speaker off for dinner. In answer to my own question on the detection of gravitational waves from the Big Bang itself, Dr Centrella pointed out that one would certainly to see expect a signal from cosmic inflation – however these waves would be in a very different region of the spectrum from that studied by either LIGO or LISA. ..

Update: Joan has been in contact to say you can get a review article she wrote on the subject for the Scidac Review here; she has also done a podcast for Sky and Telescope with movies of the simulations here. She also has two comments and corrections to the text above; rather than paraphrase them I have put them verbatim in the comments section!

Update II: there is a wonderful article on gravitational waves and the early universe by Craig Hogan in the June 2007 edition of Physics World, which you can access here if you’re a member

The standard model of cosmology

The previous 12 posts listed the main discoveries of modern cosmology in chronological order: putting all this information together leads to the Standard Model of cosmology (not to be confused with the Standard Model of particle physics). We conclude our short course with a simple overview of the standard model (also known as the Concordance Model). You will notice that it is also a brief history of time. Keep in mind that what follows is a model: the strength of the evidence for each phenomenon varies (see specific posts on each topic starting here).

1. The Big Bang

• The universe began approximately 13.7 billion years ago when it began expanding from an almost inconceivably hot, dense state.  Ever since, the cosmos has been expanding and cooling, eventually reaching the cold, sparse state we see today.

• In the first 10^-34 seconds, the universe experiences a brief period of extremely fast expansion known as inflation. This period smooths out initial inhomogeneities, leaving the universe with the homogeneity and isotropy we see today. Quantum mechanical fluctuations during this process are imprinted on the universe as density fluctuations that later seed the formation of structure.

• The infant universe is a soup of matter and energy in which particle/antiparticle pairs are constantly born and annihilated.  As the universe cools, it becomes too cold to produce heavier particles, while the creation of lighter particles continues until temperatures cool to a few billion Kelvin.  At this point, most of the remaining particle/antiparticle pairs are annihilated.  A small amount of matter survives due to a slight asymmetry in the decay of between matter and antimatter.

• After a few minutes, nuclei of the light elements (hydrogen, helium and lithium) are formed by the combination of free protons and neutrons, a process known as nucleosynthesis.

• After about 100,000 years, the universe is cold enough for free nuclei and electrons to to combine into atoms (recombination).  At this point, the universe becomes transparent due to reduced scattering by free electrons.  Radiation now permeates the universe – seen today as the cosmic microwave background. By this time, dark matter (unaffected by the behavior of the baryonic matter) has already begun to collapse into halos.

• After a few hundred million years, galaxies and stars form, as baryonic gas and dust collapse to the center of the pre-existing dark matter halos.

A brief history of time

2. The Composition of the Universe

• Baryonic Matter: ~3% of the mass in the universe
  This is ordinary matter composed of protons, neutrons, and electrons.  It comprises gas, dust, stars, planets, people, etc.

• Cold Dark Matter: ~23%
  This is the “missing mass” of the universe.  It comprises the dark matter halos that surround galaxies and galaxy clusters, and aids in the formation of structure in the universe. Dark matter is believed to be composed of weakly interacting massive particles or WIMPs.

• Dark Energy: ~73%
• Observations of distant supernovae suggest that the expansion of the universe is currently accelerating.  This observation is backed up by the flatness of the universe as measured from the cosmic microwave background.  Cosmologists believe that the acceleration may be caused by some kind of energy of the vacuum, possibly left over from inflation.

Matter/energy  composition of the universe

That concludes our short course in cosmology. You can find details on any of the topics above  by scrolling through the last 12 posts of this blog. Alternately, you can find slides from a lecture I gave on the subject (The Big Bang – Theory or Established Fact?) by clicking here

Update

There is a really nice one-page web summary of all of the above on the Talkorigins Archive here, and for readers requiring a slightly more advanced treatment, there is a good review of the current state of play in cosmology on the ARXIV here

A brief history of cosmology

The last 12 posts described each of the main topics of modern cosmology: from the predictions of general relativity to the three main planks of evidence for the Big Bang, from the theory of inflation to the most recent measurements of the cosmic microwave background. All of this theory and experiment has been put together to form what is known as the Standard Model of cosmology. Before we describe the Standard Model, let’s briefly review the main discoveries in chronological order (you can read a seperate post on each starting here)

****************************

A Brief History of Cosmology

1.  The general theory of relativity (Einstein, 1916) and the prediction of a dynamic universe (Friedmann, 1919)

2. The observation of the expanding universe (Hubble’s Law, 1929)

3. Rewinding the Hubble graph: the ‘primeval atom’ and the calculation of the age of the universe (Lemaitre, 1929)

4. The Big Bang model and the problem of the singularity

5. The prediction of the abundances of H and He from the BB model (Gamow, 1945)

6. The predicton of the cosmic microwave background (CMB) from the BB model (Alphaer, Heuer and Gamow, 1949)

7. The detection of the cosmic microwave background (Penzias and Wilson, 1965)

8. The CMB puzzles of flatness, homogeneity and galaxy formation (1965 -)

9. The theory of inflation (Guth, Linde and Steinhardt, 1981-82)

10. The COBE study of the CMB -  support for the BB model and inflation (1992)

11. Dark energy – the supernova measurements of an accelerating universe (1998)

12. The WMAP study of the CMB – more support for inflation and dark energy (2005)

**************************************************

I gave a talk on the Big Bang to our astronomy class at WIT last night, describing most of the above topics. It was great fun, with a lengthy question and answer session afterwards, fielded by both me and well-known astronomer Emmet Mordaunt who normally takes the class. You can find the slides for the talk here.

Dark Energy

In 1998, a totally unexpected result from astronomy caused a dramatic rethink of the Big Bang model. Measurements of the light emitted by a certain supernova suggested that it was further away than predicted by the Hubble constant. In other words, the exploding star did not lie on the straight line of the Hubble graph! This is a startling discovery as it implies that the expansion of the universe is not constant - instead the expansion is currently accelerating (see a description of the experiment here).

Skeptics at first suggested the result might arise from an error in the measurement of stellar distance – however, a similar observation was reported by a different group within two years. Further, independent support for the result soon emerged from measurements of the cosmic microwave background (CMB). In 2002, precision measurements of the CMB by the WMAP satellite suggested a universe with geometry that is flat to within 1%. This result is completely inexplicable in the context of the known density of the matter of the universe (both ordinary and dark). The known density of matter points to a universe with Ω = 0.3, a long way from flatness (Ω =1). Hence the CMB measurements suggest that there is a great deal of matter/energy in the uiverse unaccounted for.

As a result, cosmologists now talk about a new phenomenon; a form of energy that is pushing the universe outward, causing the expansion to accelerate and the geometry to be flat. The phenomenon is labelled Dark Energy : the physical cause for dark energy is thought to be some sort of vacuum energy. However, it should be pointed out that the numbers don’t yet stack up – detailed calculations suggests that the postulated vacuum energy would cause an accelerated expansion many orders of magnitude greater than that observed…this is a major area of research at the moment.

Putting Dark Energy together with Dark Matter, cosmologists postulate that ordinary matter, dark matter and dark energy all add up to the critical density required for the geometry of the universe to be flat (as measured). In other words, the current model of the universe can be summed up by

Density ord matter (4%) + Dens dark matter (22%) + Dens dark energy (74%) = 100%

or Ω_M (0.04) + Ω_DM (0.22) + Ω_DE (0.74) = 1

*************************************************

Technical notes:

1. Is Dark Energy compatible with relativity?

Yes, but note that an accelerating universe is not predicted by the Friedmann equation, i.e. does not feature in any of the Friedmann universes (see post on the expanding universe below). Going back to 1st principles, when one applies the equations of general relativity to the cosmos, an extra term must be added in order to account for the accelerating expansion. This is rather reminiscent of the manner in which Einstein himself , dismayed by the prediction of a dynamic universe, originally added a term to his equations in order to keep the universe static (the positive cosmological constant) . Now we apply a term to the other side of the equation for the opposite reason.

Revised Friedmann graphs of the evolution of the universe

2. Is Dark Energy compatible with inflation?

Yes, for two reasons:

1. The fact that the expansion is accelerating now makes the suggestion of an exponential expansion in the first instants a lot less fanciful.

2. While the current accleration is many orders of magnitude less than that of inflation, it may be that the cause is some energy left over from inflation – more on this later.

Dark Matter

The posts below constitute a brief introduction to the Big Bang model: the three planks of evidence, the problems of singularity, horizon and flatness, and the theory of inflation. Before we go on to discuss the Standard Model of cosmology (yes, there is such a thing), two further concepts are necessary: the old puzzle of Dark Matter and the new puzzle of Dark Energy.

Dark matter is thought to make up about 70% of the matter of the universe. Although we can’t see it, we presume it exists because of its gravitational effect on visible matter. Put differently, we don’t insist that all matter be ‘visible’ i.e. interact with the electromagnetic force. Instead, we include the possibility that some matter may be seen only by its gravitational effect on other matter.

DM was first postulated by Fritz Zwicky in the 1930s to account for a discrepancy between the calculated velocity of spiral galaxies and that observed. Nowadays, it has been proposed to account for the motion of many astrophysical phenomena from the smaller scales to the largest e.g. local stellar dynamics, galaxy rotation, galaxy cluster dynamics, X-ray halos, gravitational lensing and cluster streaming.

Calculations for galaxy rotation based on ordinary matter (curve A) and experimental points (curve B)

A second pointer of evidence for Dark Matter comes from cosmology, in particular from the cosmic microwave background (see post below). In order to to relate the miniscule variations in temperature seen in the CMB to galaxy formation in the early universe, all current models invoke the existence of DM. Even more importantly, the existence of DM is necessary to provide enough gravity to explain the flatness of the universe, as measured from the CMB (in conjunction with the postulate of dark energy – see next week).

It should be pointed out that not everyone agrees with the postulate of Dark Matter. Skeptics point to the possibility that our laws of gravity (both Newtonian and Einsteinian) may be failing at the largest scales – a theory known as modified Newtonian dynamics or MOND. However, most cosmologists now consider this possibility unlikely, due to the astrophysical and cosmological evidence above.

Best of all, the first hint of direct evidence DM was reported in a study of galaxy collision in 2007. If Dark Matter really exists, one might expect to observe ‘galaxy splitting’ in the case of galaxy collision. This is because the DM of each galaxy should interact little with the other, while the ordinary matter of each will interact strongly (just as a couple crossing a crowded room soon become separated if one is more social than the other!). Researchers at the University of Arizona are pretty sure this is exactly what they observed (see here). A similar result was reported by NASA in September 2008.

The famous bullet cluster collision (2007)

What could Dark Matter be made up of? Clearly, DM particles must be weakly interacting (otherwise we would see them) and possibly massive – i.e. weakly interacting massive particles or WIMPs. It is currently thought that the most likely candidates might be supersymmetric particles. (As we saw before, the theory of supersymmetry (SUSY) arises out of attempts to unify three of the fundamental forces – the theory postulates that every normal particle has a heavier supersymmetric partner). It turns out the most likely candidiate for DM is the neutralino, the lightest SUSY particle which cannot decay further.

Many groups around the world have been constructing experiments to look for particles that might be candidates for Dark Matter – you can find a post on a lecture on this subject by Tim Sumner of the Zeplin III experiment here and there is a very good overview of the Zeplin experiment itself here . However, this is straying into the area of particle physics; for cosmologists, establishing the existence of DM unequivocally is the real challenge.

The mechanism of inflation

The theory of inflation (below) offers a very neat explanation for the homogeneity and flatness of our universe, i.e. offers a very neat solution to the horizon and flatness problems of the Big Bang model. But what physical mechanism could have caused inflation? What could cause the infant universe to undergo a psychotic, exponential expansion in the first fractions of an instant?

The basic idea is that the infant universe may have undergone a phase transition. In particle physics, it has long been predicted that the quarks in the quark-gluon plasma must have undergone a phase transition to become trapped in hadrons in the first billionth of a second. Cosmologists now believe that, even earlier in the history of the universe, the fundamental constituents of matter/energy may have undergone a phase transition at even higher energies. Under certain circumstances, such a phase transition would be accompanied by the appearance of energy in empty space (so-called vacuum energy). Calculations show that this vacuum energy could act as an enormous force of repulsion, causing a rapid, exponential expansion of spacetime.

Technically speaking, it is thought that the very early universe cooled into a metastable state of false vacuum - it was then nudged towards genuine equilibrium by a process of quantum tunnelling. However, it was soon shown that the latter process is too violent to result in the universe we observe today. Instead, Linde , Albrecht and Steinhardt calculated that a more realistic model is a universe that moves from false vacuum to equilibrium via a gradual process as shown below.

New inflation vs old inflation

Finally, it was assumed in all the early versions of inflation theory that the vacuum energy liberated by the phase transition disappeared immediately after the hyper-expansion. However, it has recently been discovered that the rate of expansion of the universe is currently accelerating! This observation was a great surprise as it is not predicted by any of the Friedmann models; it is now believed that the cause of the acceleration (known as dark energy) may be a small amount of vacuum energy left over from inflation….more on this next week.

Update: if you can’t wait, there is a very nice summary of dark energy here

The theory of inflation

We have discussed the three main planks of evidence for the Big Bang model: the Hubble expansion graph (and consequent estimate of the age of the universe), the abundance of hydrogen and helium, and the cosmic background radiation. These leave little room for doubt that the basic model is correct. On the other hand, close examination of the model raises many questions – in particular the singularity, horizon and flatness problems (see posts below). Another problem is that it is not clear from the model how perturbations in the early universe led to the large scale structure of galaxies and galaxy clusters seen today.

A possible solution to these puzzles is the theory of inflation. First proposed by Alan Guth in 1981, inflation posits that in the very first fractions of an instant after the Bang, the young universe underwent an exponentially fast expansion (faster than the speed of light) – totally unike the Hubble expansion we see today. This does not violate principles of relativity, since relativity sets no constraints on the behaviour of spacetime itself.

An inflationary expansion of the very early universe offers a simple solution to the horizon problem: if the universe expanded arbitrarily fast, even the farthest flung points could once have been in thermal contact. In other words, the properties of distant points in the universe would not be determined by a competition between the finite speed of light and the finite age of the universe, as previously thought.

Inflation also offers a neat solution to the flatness problem: it was soon shown that, instead of deviations from flatness quickly leading to a runaway open or closed universe, deviations in an inflationary universe tend to be driven back towards flatness. The geometrical equivalent of this is to imagine a balloon being inflated to enormously large dimensions – of course the surface is driven towards flatness.

This is a simplified overview of the theory of inflation – the main point is that inflation offers a version of the Big Bang model in which the universe is driven towards the critical value of flatness/ mass density that exists today, far from accepting it as lucky coincidence.

What is most impressive about the theory is that, contrary to public perception, inflation was not originaly posited in order to address problems in Big Bang cosmology. In fact, the theory arose in an attempt to address certain puzzles in Grand Unified Theory (the branch of particle physics that seeks to unify the strong interaction with the electro-weak interaction). Guth’s proposal was at first treated with incredulity by the cosmological community – however, it was quickly realised that it offered an intriguing solution to the problems above.

As so often, the original model of inflation was found to contain a fatal mathematical flaw (the end of inflation was incompatible with the known universe). This flaw was soon overcome in a modified version of inflation by Linde and Steinhardt. Nowadays, many versions of inflationary models have been posited: which particular version is correct remains to be seen, but strong theoretical and experimental support for an inflationary universe has been forthcoming (more on this next day).

BB problem 3: the flatness problem

Another question concerning the Big Bang model concerns the geometry of the universe and has become known as the Flatness Problem.

Recall that a key prediction of general relativity is that matter distorts spacetime – i.e. the force of gravity is essentially a distortion of spacetime by mass. Hence the curvature of the spacetime of our universe will be determined by the density of matter in it. Assuming only that the universe is homogenous and isotropic, it can be shown from general relativity that three distinct types of universe are possible (first calculated by Alexander Friedmann).

If the universe has a high enough density of matter, gravity will triumph over the energy of expansion as time goes on and space will be pulled in on itself, much like a sphere (closed universe). On the other hand, if the universe has a low enough density of matter, gravity eventually loses the battle with the energy of expansion and space will curve outwards (open universe). A third but unlikely possibility is that the curvature of space caused by matter could be exactly balanced by the energy of expansion – in this case space would not be curved but have Euclidean geometry (flat universe).

Friedmann universes: 3 possibilities

We say the above mathematically by defining a flatness parameter Ω to be the ratio of the actual density of matter d to the critical density d_c required for flatness i.e. Ω = d/d_c . Hence we characterize an open,closed or flat universe as Ω < 1, Ω >1 and Ω = 1 respectively.

So what’s the problem? In the late 1960s, calculations by Bob Dicke showed that even the slightest deviation (1 in10¹⁵)  from flatness in the early universe would quickly lead to either a runaway closed or a runaway open universe.  As observation and mass calculations suggest that we live in neither of these, there is a clear implication that the geometry of the early universe must have been exactly flat. But why should the early universe have been so finely balanced between the energy of gravity and the energy of expansion? A curious example of fine tuning indeed…

This mystery has come back to the fore in recent years: measurements of the cosmic microwave background are strongly indicative of a universe that is exactly flat (at least to 1%) at the time of recombination. So now we also have experimental evidence of an exact balance between the density of matter in the universe and the energy of expansion. Again, why such a precise balancing act?