Category Archives: Cosmology 101

BB problem 2: the horizon problem

A second question concerning the Big Bang model of the universe has become known as the Horizon Problem. Essentially, the very homogeneity of the universe, as measured from the cosmic background radiation (see previous post), requires some explanation.

The problem concerns the finite age of the universe versus the finite speed of light. When you do the math, it turns out that the furthest flung regions of the universe are further apart than light could have travelled in the age of the universe. A simple claculation shows that the furthest regions could never have been in thermal contact – yet they have the same temperature to 1 part in 100,000.

So we have a paradox: the homogeneity of the background radiation suggests that all of the observable universe was once in contact long enough to reach thermal equilibrium, while simple calculations based on rewinding the Hubble graph suggest that the universe is too big for this to have happened in the time available.

Artist’s impression of the horizon problem

What is the solution to the paradox? One interesting solution could be that the speed of light in the very early universe was different from what we measure today. A less drastic solution is that we have made an unjustified assumption – namely, by extrapolating the Hubble slope back to the very early universe, we have superimposed an expansion rate of one era on an earlier era we know nothing about.. more on this later.

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The BB singularity: implications for a creator?

Before looking at further questions concerning the Big Bang model, let’s consider the possible implications of the singularity problem (see previous post) for religion, as this topic often arises in the media.

Our best description of gravity (the dominant force in the universe at large) is Einstein’s general theory of relativity. Applied to the cosmos, general relativity has made some spectacular predictions that have since been verified by experiment (the expanding universe in particular). However, it is true that the theory breaks down as we rewind the clock of the expanding universe all the way back to time zero (the equations blow up to infinity).

Some religiously-minded scientists consider this significant, suggesting that we may be coming to a limit to what the human mind may comprehend about the work of a creator and this is also the view of many theologians. I heard several interesting talks on this topic at Cambridge last year, see the July posts on Cosmology Day at the Faraday Institute here.

Implications for a creator?

However, it’s important to emphasize that most cosmologists would say that the uncertainty really arises from quantum physics. We already know that general relativity is incomplete because it doesn’t incorporate quantum theory (the theory that describes the world of the very small with extreme accuracy). Since the space and time of the infant universe will be of quantum dimensions, we will not be able to describe it until we have a successful quantum theory of gravity. In other words, our current lack of a clear picture of the birth of the universe simply arises from a well-known limitation of the theory of relativity. In time, theoreticians will hopefully find a quantum version of relativity and we will have a clearer picture – so no there are no real implications for religion, one way or the other. I made this point in a public talk on the Big Bang last year (see post on this here), and you can find my description of the lecture in the July issue of Physics World 2008.

Interestingly, one thing we do know from quantum theory is that, even with a successful theory of quantum gravity, some uncertainty will always apply to the first instant of the universe. This is because one of the central tenets of quantum physics is that an inherent fuzziness pertains to the properties of phenomena on the smallest scales (not just a fuzziness in measurement, as many philosophers wrongly believe). This is a direct consequence of the famous Heisenberg Uncertainty Principle. Applied to the Big Bang model, Heisenberg uncertainty predicts that there is no exact point in time called time zero – a trade off between time and energy ensures an in-built fuzziness around this (and any other) instant in time.

The Heisenberg Uncertainty Principle also has implications for the ‘something from nothing’ question. The trade off between time and energy of quantum theory predicts that particles of matter can ‘borrow energy’ to come into existence out of a vacuum, provided their lifetime is short enough. This bizarre behaviour of the smallest constituents of matter has been verified by experiment beyond a shadow of a doubt. Amazingly, it is actually possible in principle that the matter of the entire universe came into being this way, and then had its lifetime extended by a process known as inflation (more on inflation later).

In summary, most cosmologists would argue that there are no real implications for or against religion arising fom the singularity of the Big Bang model, particularly when quantum effects are considered. Indeed, quantum theory even predicts that the entire universe may be a free lunch!

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BB problem 1: the singularity

While the evidence for the Big Bang model is very convincing (see posts below), many questions remain. The first and most obvious is the singularity problem. In essence, the problem is that while the BB model gives us much information on the evolution of the universe after the Bang, it gives little information about the Bang itself. What banged? What does time zero really mean?

The Big Bang model predicts that the matter, energy, space and time of our universe all came into being in a faction of the first instant and that the universe has been expanding and cooling ever since. The problem is that as we rewind the clock of an expanding universe and the intergalatic distances shrink to zero, relativity predicts that the temperature and density of the universe must increase to infinity (just as the function f(x) = 1/x approaches infinity as x approaches zero – known as a singularity in mathematics). What does this mean physically?

A singularity appears as the distance approaches zero

At first, it was thought that the singularity might be a facet of the simplfying assumptions used in applying the equations of general relativity to the universe. However, in the 1970s, Hawking and Penrose published a number of theorems showing that classical relativity predicts that an expanding universe must originate in a singularity, assuming only some very general conditions. (The most important general condition is a restriction on the behaviour of matter at high energy known as the strong energy condition – of course one way out of the problem is to assume that this condition does not apply, more on this later).

Hawking: an expanding universe must begin in a singularity

The most obvious solution to the singularity problem is to realise that when one is considering an extremely young universe (i.e. a universe of atomic dimensions), quantum effects will become important. However, these cannot be described as we do not have a quantum theory of gravity (i.e. we do not yet have a version of general relativity that takes quantum physics into account, hence the name classical general relativity). Until we do, we can say little of the universe in the time when it was of atomic dimensions or smaller.

In other words, the prediction of an initial singularity may well be a limitation of current theoretical physics, rather than a facet of reality. This incompleteness of the Big Bang model is well recognized, and it is the main reason one talks about the Big Bang model rather than the Big Bang theory. ..

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Note on theory: one of the great challenges of modern physics is  to reconcile general relativity and quantum theory, the two great pillars of modern physics. Gravity is now the only one of the four interactions that we cannot currently describe as a quantum field theory. Most of the time, this doesn’t matter, as gravity typically deals with the world of the very large, while quantum theory deals with the world of the very small. However, when we when we attempt to describe gravity on small scales – (i.e.black holes or Big Bangs), the mutal incompatibility of the two theories becomes a major stumbling block…

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Putting it all together: the Big Bang model

Putting the three planks of evidence together (see below), we are led to The Big Bang model : a model that posits that the universe began as a superhot, superdense singularity that has been expanding and cooling ever since. Although we don’t know much about the initial singularity , there is very strong evidence for the evolution of the universe from this state – so the name Big Bang is a bit of a misnomer! Let’s summarize the evidence once more before we examine the cracks:

1. The expansion of the universe: it’s been known since 1929 that far-away galaxies are receding away from each other at a speed proportional to their distance (Hubble’s Law). This is surprisingly easy to measure as the light emitted by moving galaxies is red-shifted by the Doppler effect. Following the famous Hubble graph back down to the origin led Georges Lemaitre to the idea of a Universe bursting out from a tiny volume (the primeval atom) . Nowadays, we say the Universe began as a superhot, superdense explosion of space, time , matter and radiation, expanding and cooling as time goes on.

Best of all, the slope of the Hubble graph gives an immediate estimate for the age of the universe: the modern value of this figure agrees exactly with that expected from independent estimates (the age of the oldest stars etc)

2. The composition of the elements: if the universe began as some sort of tiny dense fireball, it would have been too hot for atoms to form at first. Calculations by Gamow suggested that a universe made up of about 75% Hydrogen and 25 % Helium should have evolved after a certain time. Guess what – the figures match our universe (it was later realised that all the other elements are fused in dying stars and account for about 0.1%).

3. The cosmic backround radiation: Alpher, Herman and Gamow also suggested that radiation left over from the very early universe might still be observable. (The reason is once atoms began to form, the scattering of light becomes reduced and the universe becomes transparent). Such radiation would be hugely redshifted and freezing cold, but it should be there. Just such radiation was found by Penzias and Wilson in 1965, using the world’s first radiotelescope. Since the background radiation offers a real glimpse of the very early universe, much of modern cosmology is concerned with getting more and more accurate measurements of this ‘cosmic fossil’, using satellite telescopes such as COBE and WMAP.

And that’s the model..

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Poscript

Of course, the model is not perfect. The most obvious problem is the singularity itself – can the universe once really have been infinitely hot and infinitely dense, or is this a feature of our limited understanding of gravity on the quantum scale? There are other problems too, such as the horizon and flatness problems. More on this next day..

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The third plank of evidence: cosmic radiation

The discovery of the expansion of the universe and the subsequent estimate of the age of the universe (once the distance scale was sorted out) was a key step in the development of the Big Bang model. Another step was the correct prediction of the Hydrogen and Helium content of the universe from Big Bang nucleosynthesis by Gamow (see post below). However, it was a third piece of evidence that was to prove the most convincing of all – the discovery of radiation left over from the hot young universe, now known as the cosmic microwave background (CMB).

Two of Gamov’s students, Ralph Alpher and Robert Herman, continued with his interest in the early universe. In particular, they calculated that as the early universe expanded and cooled, atoms would form after about 100,000 years (a process known as recombination). At this time, radiation left over from the cataclysmic origin of the universe that had been continually scattered by elementary particles would no longer be scattered. The two young scientists postulated that the universe would become transparent to radiation from this time onwards, and that this radiation might even be observable in today’s universe (like a cosmic fossil).  They calculated that it would be isotropic, homogeneous, of black body spectrum and extremely low temperature . Most intriguingly, the radiation would be Doppler shifted (by billions of years of universe expansion) from the extreme high-energy part of the electromagnetic spectrum all the way down to microwave frequencies, the least energetic part of the energy spectrum.

Sadly, no-one paid much attention to this prediction. (At the time, the Big Bang estimate of the age of the universe was way off and Gamov’s initial work on the nucleosynthesis of the heavier elements was also wrong). However, in 1965, Penzias and Wilson, two engineers at Bell Lab, detected an unexpected background noise in data they obtained with the world’s most sensitive radiotelescope. Having spent a year trying to eliminate it, they concluded that the source was extra-galactic and contacted the theoretician Bob Dicke at Princeton. Dicke was amazed. The Princeton group had been working on the theory of cosmic background radiation and drawing up plans for the construction of an experiment to search for it – now the Bell Lab  astronomers already had the  data  (“Boys, we’ve been scooped!”). The two groups published their findings, experiment and theoretical explanation side by side, in a famous issue of the Astrophysics Journal.

The world of science was stunned. This was convincing evidence indeed for the Big Bang model (there is no alternate explanation for the spectrum of the CMB) and the debate was effectively over. Penzias and Wilson were awarded the Nobel Prize and Dicke became instantly famous. (As a bonus, the redshift of the CMB was also extremely convincing evidence that space is indeed expanding, as the radiation isn’t going anywhere).

Penzias and Wilson with their giant antenna in the backgound

There is a sad postscript, however. Neither group was aware of the work of Alpher and Herman twenty years earlier and it was a long time before the work of the Gamow group was acknowledged. Ironic that the Nobel went to two astronomers who knew little of cosmology and that the great work of the theoreticians who predicted the CMB went unsung until recently.

Today, much of modern cosmology is concerned with the study of the CMB with ever more precision, using more and more sopisticated space telescopes. In particular, the COBE satellite  showed the blackbody spectrum of the radiation in precise detail in 1992, while the WMAP mission gave us priceless information on perturbations in the spectrum in 2006. More on this later….

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The second plank of evidence: nucleosynthesis

The second plank of evidence for the Big Bang model lies in the area of nucleosynthesis. In English, this means that the abundance of the elements seen in the universe at large matches what one would expect in a universe that began in a state that was almost infinitely hot and infinitely dense.

The great Russian theoretician George Gamow was one of the first to take Lemaitre’s prediction of an early universe the size of an atom seriously (see post below). However, Gamow went even further. A specialist in nuclear physics, he calculated that the temperatures in the early universe would have been too high for atoms to form. Instead, matter would have existed as elementary particles, only gradually forming atoms as the universe expanded and cooled in the first few minutes.

Applying simple mathematics to the expanding universe led to a surprising result – that the matter of our universe should be composed almost entirely of the simplest two elements, Hydrogen and Helium (specifically, about 75% H and about 25% He). This prediction turned out to be correct – all the other elements of the Periodic Table account for about 0.1% of the matter of the universe!

The irrepressible George Gamow

This was an impressive early victory for the Big Bang model – however, it failed to explain where the other elements came from (Gamow’s own belief that the other elements are also made in the Big Bang was soon shown to be false, as the universe cools too quickly). It was later shown that all the other elements are ‘cooked in the stars’.

Essentially, what happens is this: a young star burns Hydrogen as fuel, fusing it into Helium, a process that balances the intense inward gravitational force on the star. As the star ages, it runs out of fuel to burn, becomes denser and the temperature increases. Helium then fuses into Lithium, Lithium into the next element, and so on. This process continues right down to Iron. At this point, some stars lose the battle with gravity, turning into neutron stars or even black holes.

Others have a different fate. By a process of accretion of a nearby star, they go supernova –  a cataclsmic process at extreme temperatures during which all the heavy elements of the Periodic Table are fused in turn, and then all spat out in one great explosion…

And that’s where you and I, and all the little children and everything we see about us comes from….stardust!

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Note: an interesting sidenote is that the formation of carbon in the fusion chain of stars was long a stumbling block. The puzzle was eventually solved by the British astrophysicist Fred Hoyle, by postulating the existence of a new, unkown isotope of carbon. He badgered an American experimental group to look for this isotope and they soon found it. The riddle of the formation of heavier elements was solved….but Hoyle was to become a controversial figure despite this great success. He was bitterly opposed to the Big Bang model on philosophical grounds – as the evidence mounted, he concocted ever more convoluted alternative models, refusing to concede defeat right up until his death. More on this later…

Note 2: the above is a simplified version of Big Bang nucleosynthesis. In fact, traces of Lithium and Berellium were also formed in the Bang, you can read the details here

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The first plank of evidence: Hubble’s law

This week, our 1st years finally get to the first plank of evidence for the Big Bang in their introductory course in cosmology. Having covered the work of Kepler, Galileo, Newton and Einstein, and the theoretical debate between Einstein’s static universe and Friedmann’s dynamic one, they have reached the point where it’s time to introduce the first piece of experimental evidence in modern cosmology – Hubble’s law.

As every schoolgirl knows, Hubble discovered that distant galaxies are moving away from us (or any other point) with a velocity that is proportional to their distance. This is the crux of the evidence for the expanding universe and a major piece of the evidence for the Big Bang.

The law arose from Hubble’s observation of distant galaxies and is usually written as

v = Hd

where v is the recessional velocity of a galaxy, d is the displacement of the galaxy from us and H is the Hubble ‘constant’, or the slope of the graph.

The velocity of a galaxy is measured as a Doppler redshift of the light it emits and is relatively easy to measure. However, the measurement of the distance of a given galaxy is trickier (it is done using stars known as Cepheid variables.). In fact, Hubble had a major systematic error in his distance calculations, an error that was not corrected for decades.

Hubble’s graph was an important advance, for it settled the debate between a static and expanding universe (leading Einstein to label his cosmological constant, introduced to the equations of GR to force a static universe, ‘his greatest blunder’). The graph also immediately hinted at a universe that might once have been very much smaller – perhaps even as small as an atom, as first suggested by the mathematician Georges Lemaitre. (To see this, trace your finger down the slope of the graph towards the origin). This is the model now known as the Big Bang model of the origin of the universe.

However, one problem with the new model immediately emerged. It is easily shown that the age of such a universe can be calculated as the inverse of the slope of the Hubble graph (1/H): unfortunately this calculation gave an answer that was far younger (not older) than the known age of some stars! This observation severely weakened the Big Bang hypothesis and it was only years later that it was discovered that the error lay in Hubble’s estimation of stellar distances (the x-axis). Nowadays, estimates of the age of the universe from updated and expanded Hubble graphs agree exactly with the age calculated from several independent phenomena.

Hubble’s graph contains many subtleties so here are a few other points:

1. Of course the galaxies aren’t really moving at all. General relativity predicts that it’s really space that’s expanding and the galaxies ride the wave.

2. A question arises when Hubble’s law is applied to one galaxy only – surely any object that has a velocity that is proportional to its displacement it must be accelerating? (since its displacement is changing). I wrote a post on this very question a while ago, and got some very interesting answers…see post on Hubble Puzzle

3. Not all galaxies are moving away from one another – for example, our nearest galaxy is approaching us, due to local gravitation effects. Woody Allen has a famous skit on this in the film ‘Annie Hall’, you can see the clip on YouTube here (thanks Dave!)

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