The Afterglow of Creation

Thursday, 15 April 2010
Museum of London

Subject:






Overview

Astronomers have learnt about the early universe from the discovery in 1965 and subsequent observations of the radiation left over from the Big Bang. Jodrell Bank receivers are aboard the Planck spacecraft now observing this afterglow with unequalled clarity. What might it tell us about the past and future of our universe?






Transcript of the lecture

 

The Afterglow of Creation

 How Vesto Slipher and Edwin Hubble showed that the Universe was expanding

 

Professor Ian Morison

15/4/2010

 When the spectra of galaxies were first observed in the early 1900's it was found that their observed spectral lines, such as those of hydrogen and calcium, were shifted from the positions of the lines when observed in the laboratory.  In the closest galaxies the lines were shifted toward the blue end of the spectrum, but for galaxies beyond our local group, the lines were shifted towards the red.  This effect is called a "redshift" or "blueshift" and the simple explanation attributes this effect to the speed of approach or recession of the galaxy, similar to the falling pitch of a receding train whistle, which we know of as the Doppler effect.  For speeds which are small compared to the speed of light, then the simple formula:

                                       Δf/f =   Δl/l    =   v/c

may be used.   Here, f is the frequency, l is the wavelength, Df and Dl are changes in frequency and wavelength, v is the velocity of approach or recession and c is the speed of light. 

Some of the earliest observations of red and blue shifts were made by the American astronomer Vesto Slipher.  In 1913 he discovered that the Andromeda galaxy had a blueshift of 300 km/s.  This implies that Andromeda and the Milky Way galaxies are approaching each other due to the gravitational attraction between them but not, as might first appear, by 300 km/sec.  Our Sun is orbiting the centre of our galaxy at about 220 km/second and taking this into account, the actual approach speed is nearer 100 km/sec. By 1915 Slipher had measured the shifts for 15 galaxies, 11 of which were redshifted.  Two years later, a further 6 redshifts had been measured and it became obvious that only the nearer galaxies (those within our local group) showed blueshifts.  From the measured shifts, and using the Doppler formula given above he was able to calculate the velocities of approach or recession of these galaxies.  These data were used by Edwin Hubble in what was perhaps the greatest observational discovery of the last century, and it is perhaps a little unfair that Slipher has not been given more recognition.

In the late 1920's Edwin Hubble, using the 100" Hooker Telescope on Mount Wilson, measured the distances of galaxies in which he could observe a type of very bright variable star called Cepheid Variables which vary in brightness with very regular periods - a method that has been described in the previous chapter. He combined these measurements with those of their speed of approach or recession (provided by Slipher) of their host galaxies (measured from the blue or red shifts in their spectral lines) to produce a plot of speed against distance.  All, except the closest galaxies, were receding from us and he found that the greater the distance, the greater the apparent speed of recession.  From this he derived "Hubble's Law" in which the speed of recession and distance were directly proportional and related by "Hubble's Constant" or H0.  The value that is derived from his original data was ~500 km/sec/Mpc. Such a linear relationship is a direct result of observing a universe that is expanding uniformly, so Hubble had shown that we live within an expanding universe.   The use of the word "constant" is perhaps misleading.  It would only be a real constant if the universe expanded linearly throughout the whole of its existence. It has not - which is why the subscript is used.  H0 is the current value of Hubble's Constant!

Consider the very simple one dimensional universe shown below.  Initially the three components are 10 miles apart.  Let this universe expand uniformly by a factor of two in one hour to give the situation.  As seen from the left hand component, the middle components will have appeared to have moved 10 miles in one hour whilst the right hand component will have appeared to move 20 miles - the apparent recession velocity is proportional to the distance.

If one makes the simple assumption that the universe has expanded at a uniform rate throughout its existence, then it is possible to backtrack in time until the universe would have had no size - its origin - and hence estimate the age, known as the Hubble Age, of the universe.  This is very simply given by 1/H0 and, using 500 km/sec/Mpc, one derives an age of about 2000 million years: 

                                    1/H0     =    1 Mpc  / 500 km/sec

                                                =    3.26 million light years/ 500 km/sec

                                                =   3.26 x 106 x 365 x 24 x 3600 x 3 x 105 sec / 500

                                                =   3.26 x 106 x 3 x 105 years / 500

                                                =   1.96 x 109 years 

                                                =   ~ 2 Billion years

In fact, the real age must be less than this as the universe would have been expanding faster in the past and the actual age would be 2/3 that of the Hubble Age or ~1300 million years old.

So Hubble's work showed that the Universe may have started in a singularity - which later became known as the "Big Bang". This name was coined by Fred Hoyle who felt that the idea was wrong - and it was meant to be a derogatory name!

This result obviously became a problem as the age of the solar system was determined (~ 4500 million years) and calculations relating to the evolution of stars made by Hoyle and others indicated that some stars must be much older than that, ~ 10 to 12 thousand million years old.   During the blackouts of World War II, Walter Baade used the 100" telescope to study the stars in the Andromeda Galaxy and discovered that there were, in fact, two types of Cepheid variable.  Those observed by Hubble were 4 times brighter than those that had been used for the distance calibration, and this lead to the doubling of the measured galaxy distances.  As a result, Hubble's constant reduced to ~250 km/sec/Mpc.  There still remained many problems in estimating distances, but gradually the observations have been refined and, as a result, the estimate of Hubble's constant has reduced in value to about 70 km/sec/Mpc.  One of the best determinations is that made by a "key project" of the Hubble Space Telescope that observed almost 800 Cepheid variable stars in 19 galaxies out to a distance of 108 million light-years.

Combined with some other measurements they derived a value of:

                                                H0 =72+/-8 km s-1 Mpc-1.

 

Observations of gravitational lenses give a totally independent method of determining the Hubble Constant and their best value to date is:

                                                H0 =71+/-6 km s-1 Mpc-1.

 

These are in very good agreement so it is unlikely that the true value of Hubble's constant will differ greatly from this.

Predictions of a "Hot" Big Bang and hence the presence of radiation within the Universe.

Two American scientists, George Gamow and Robert Dicke independently predicted that very high temperatures must have existed at the time of the Big Bang - both for somewhat the wrong reasons!   If so, the Universe would then have been filled with very high energy photons, initially in the form of gamma rays.  As the Universe has expanded the radiation has become less energetic and would now be in the far infra red and very short wave radio parts of the spectrum.  But this means that if one could place a thermometer in the space between the galaxies it would not read absolute zero but a value of a few degrees above absolute zero.  This radiation is now normally called the Cosmic Microwave Backgroundradiation (CMB) but has had alternate names such as the Relict Radiation and the name of this lecture The Afterglow of Creation.

In 1948, Gamow produced an important paper with his student Ralph Alpher, which was published as "The Origin of Chemical Elements". [Gamow had the name of Hans Bethe listed as one of the authors on the article even though he had played no part in its preparation.  The paper became known as the Alpher-Bethe-Gamow theory to make a pun on the first three letters of the Greek alphabet, alpha, beta and gamma!]

The paper showed how the present levels of hydrogen and helium in the universe (which are thought to make up ~98% of all matter) could be largely explained by reactions that occurred during the "big bang". This lent theoretical support to the Big Bang theory, although it did not explain the presence of elements heavier than helium.  In this paper, no estimate of the strength of the present day residual CMB was made but shortly afterwards his students Ralph Alpher and Robert Herman predicted that the afterglow of the big bang would have cooled down after billions of years, and would now fill the universe with a radiation whose effective temperature was five degrees above absolute zero.  The names of Alpher and Herman have been largely ignored since then which is somewhat unfair.  Their prediction was essentially forgotten about for 20 years and even they thought, incorrectly, that the technology available then would be unable to detect such weak radiation.  

In fact, Gamow had hoped that all the elements could have been made in the Big Bang so the overall thrust of his idea was wrong and this is perhaps why his work was largely forgotten. 

Ironically, the effective temperature of the universe had been measured by this time - but by a chemist - and this did not become common knowledge for many years after.  CN is a radical which can exist in space caused by the photo dissociation of HCN in dense molecular clouds.  It was first discovered in 1941 by A. McKellar using a coude spectrograph mounted on the 100-inch Hooker telescope on Mt. Wilson.  CN has some excited rotational vibration levels and McKellar observed one that corresponded to an effective temperature of 2.3 degrees!  This implied that the CN lay in a bath of radiation at this effective temperature - the first observation of the CMB!

The other prediction was made by Robert Dicke, a physicist at Princton University.  He, like Hoyle, did not like the idea of a singular start to the Universe (what was there before?)  and came up with the idea of the oscillating Universe in which the Universe expands up to a maximum size and then collapses again to a singularity (called the Big Crunch) of the maximum density possible before expanding again.  Since Gamow's failure to explain the formation of the elements heavier than Helium, Hoyle and others had showed how the heavier elements had been formed in stars.  Thus to start afresh with a new expanding universe, all the heavier elements had to be destroyed.  Dicke realized that extreme heat - temperatures of at least a billion degrees - would do the job nicely as the heavy elements would crash together and split up into their constituent protons, neutrons and electrons.

An undeniable consequence is that such a hot phase in the life of the early universe would be intense radiation - which would cool as the Universe expands and give rise to the CMB.

But here was a difference, Dicke had been a pioneer in the field of radio astronomy and realized this radiation, now largely in the microwave part of the spectrum, should be able to be detected and recruited two young physicists, David Wilkinson and Peter Roll, to build a horn receiver and detector to look for what they called "the Primeval Fireball".  They began work in the spring of 1964. 

The serendipitous discovery of the Cosmic Microwave background  

Arno Penzias and Robert Wilson at the Holmdale antenna with which they discovered the CMB

 Our story now moves to the Bell Telephone Laboratories where two young radio astronomers, Arno Penzias and Robert Wilson had been given use of the telescope and receiver that had been used for the very first passive satellite communication experiments using a large aluminum covered balloon called "Echo".  It had been designed to minimise any extraneous noise that might enter the horn shaped telescope and the receiver was one of the best in the world at that time.  They tested it thoroughly and found that there was more background noise produced by the system than they expected.  They wondered if it might have been caused by pigeons nesting within the horn - being at ~290 K they would radiate radio noise - and bought a pigeon trap (now in the Smithsonian Air and Space Museum in Washington) to catch the pigeons.  They used the internal mail system to send them 40 miles away to the Bell Telephone Whippany site where they were released but, as pigeons do, they returned and had to be "removed" by a local pigeon expert.  During their time within the horn antenna, the pigeons had covered much of the interior with what, in their letter to the journal 'science' was called "a white dielectric substance" - we might call it "guano".  This was cleaned out as well but having removed both the pigeons and the guano there was no substantial difference.  The excess noise remained the same wherever they pointed the telescope - it came equally from all parts of the sky. 

Another radio astronomer, Bernie Burke, when told of the problem suggested that they contact Robert Dicke at Princeton University.  As mentioned above, Dicke had independently theorised that the universe should be filled with radiation resulting from the big-bang and his students were building a horn antenna on top of the Physics department in order to detect it.  Learning of  Penzias and Wilson's observations, Dicke immediately realised that his group had been "scooped" and told them that the excess noise was not caused within their horn antenna or receiver but that their observations agreed exactly with predictions that the universe would be filled with radiation left over from the Big Bang.  Dicke was soon able to confirm their result, and it was perhaps a little unfair that he did not share in the Nobel Prize that was awarded to Penzias and Wilson. 

The cause of the Cosmic Microwave Background - as we now believe

 We believe that the universe began in a burst of inflation that expanded a volume of space smaller than a proton by a factor of perhaps 1060 up to the size of order a metre in diameter in a time of less than 10-23 second.  This released a massive amount of energy.   Half of the gravitational potential energy that arose from this inflationary period was converted into kinetic energy from which arose an almost identical number of particles and antiparticles, but with a very small excess of matter particles (~1 part in several billion).  All the antiparticles annihilated with their respective particles leaving a relatively small number of particles in a bath of radiation.  This radiation is now called the "Cosmic Microwave Background" (CMB).

As the universe expanded and cooled there finally came a time, ~380,000 years after the origin, when the typical photon energy became low enough to allow atoms to form.  There were then no free electrons left to scatter radiation so the universe became transparent.  This is thus as far back in time as we are able to see.  At this time the universe had a temperature of ~3000K.  As the radiation and matter were then in thermal equilibrium, the radiation would have a very well defined power spectrum - known as the black body spectrum -  with a peak of energy in the yellow part of the visible spectrum.  Since that time, the universe has expanded by about 1000 times.  The wavelengths of the photons that made up the CMB will also have expanded by 1000 times and so will now be in the far infrared and radio part of the spectrum - but would still have a black body spectrum.  The effective black body temperature of this radiation will have fallen by just the same factor and would thus now be ~3K.

This prediction agrees well with the average temperature, now measured, of the CMB of 2.725K.  However it was not until 1992, nearly thirty years later, that measurements made by the COBE spacecraft were able to show that the CMB had the precise "blackbody spectrum" that would result from the Big Bang scenario.  Since then, it has been very difficult to refute the fact that there was a "hot" Big Bang.

The Cosmic Background Explorer (COBE)

The Cosmic Background Explorer (COBE) was a satellite whose goals were to investigate the cosmic microwave background radiation of the universe.  COBE was originally planned to be launched on a Space Shuttle mission STS-82-B in 1988 from Vandenberg Air Force Base, but the Challenger explosion delayed this plan and eventually, having redesigned it to drastically reduce its weight, COBE was placed into sun-synchronous orbit on November 18, 1989 aboard a Delta rocket.

Its first significant result was not long in coming, using the Far-InfraRed Absolute Spectrophotometer FIRAS - a spectrophotometer used to measure the spectrum of the CMB - and with just 9 minutes worth of data COBE was able to plot a spectrum where the error bars on the data points lay within the theoretical Black Body Curve that should have been seen if the CMB really was the radiation from a time when the radiation and matter were in thermal equilibrium.

The second significant result came from the Differential Microwave Radiometer DMR a microwave instrument that would map variations (or anisotropies) in the CMB.   The ground based results, with their limited accuracy, showed a uniform CMB temperature, but COBE's greater sensitivity soon showed that the temperature was not constant across the sky it was slightly hotter in the direction of the constellation Leo in the sky, and slightly cooler in the opposite direction towards Aquarius..

The "Dipole" signature in the CMB emission - the small "blobs" are effects from our galaxy.  The hottest region is +3.5 mK above the average and the coolest -3.5 mK below the average.

 Such an observation was predicted, as the Solar system is moving through space orbiting the centre of our Galaxy and so our motion would mean that photons arriving from the direction of motion are boosted in energy - and hence appear "hotter" whilst those from behind lose energy and thus appear cooler.   But, to everyone's surprise, the direction of motion determined from these observations was not aligned with the orbital motion of the Solar System around the Galaxy, but was in nearly the opposite direction!   This means that our Galaxy and the whole local group of galaxies are moving with a speed of more than two million miles per hour (600 km/sec or ~1/500 the speed of light) with respect to the Universe at large!  What could cause this?   It appears to be a result of the clustering and super clustering of galaxies in our local (within 100 million light years) neighborhood so that there is a net gravitational pull towards the direction of Leo. 

Incidentally, the COBE DMR observations clearly show changes in the observed velocity of 30 kilometers per second - a 5% effect - due to the motion of the Earth around the Sun - good evidence that Galileo was right!  

The face of God

The most significant observation made by COBE - and initially its most controversial one "was when NASA and Berkley announced that COBE had detected the expected fluctuations in the CMB.  Against the advice of some of the team, it was decided to accompany the press release with a, now famous, image.  This image did show tiny fluctuations in temperature - but they did not show the fluctuations in the CMB.  Information accompanying the image did try to make this clear but was subtle and widely ignored by the press. 

First COBE map of the CMB which does not show the fluctuation of the CMB

The majority of the fluctuations were caused by noise and only about 10% of the signal was attributed to the CMB.  The point was that the fluctuations were just a little greater than would have been expected by noise and thus, statistically, indicate the presence of underlying fluctuations.  Suppose you randomly shook sand over a metre square flat wooden board.  It would then be covered by piles of sand and you could measure the highest peaks that occurred - let's say that they were ~ 5 cm high.  Now sprinkle the sand randomly over a metre square board which has a rough surface having surface irregularities with peaks of, say, 1 cm.  You might now expect that the highest peaks were a little higher, perhaps 6 cm rather than 5 cm, and you could deduce that the board below was not smooth and even estimate its roughness.   This is exactly how the COBE team deduced the presence of the background fluctuations.  When asked by someone in the audience at the Press Conference how important this result was George Smoot said "Well, if you are a religious person, it's like seeing the face of God."  This naturally gave rise to intense media interest! 

Following two more years of data the noise in the original map was reduced to such a degree that the real structure of the CMB fluctuations became apparent.

Fluctuations on the CMB as observed by COBE after 4 years of observations

John Mather and George Smoot received the Nobel prize for Physics in 2006 for this work which the Nobel Prize Committee said had begun the period of "precision" cosmology.   

The cause of the Fluctuations in the CMB

Why are these small variations present?  To answer this we need to understand a little about "dark matter".  Though not yet directly detected, its presence has been inferred from a wide variety of observations. 

As described above, for ~380,000 years following the big bang, the matter and radiation were interacting as the energy of the photons was sufficient to ionize the atoms giving rise to a plasma of nuclei and free electrons.  This gives rise to two results:

1: The radiation and matter are in thermal equilibrium and the radiation will thus have a black body spectrum as was proven by the COBE observations.

2: The plasma of nuclei and electrons will be very homogeneous as the photons act rather like a whisk beating up a mix of ingredients.

It is the second of these that is important to the argument that follows.  When the temperature drops to the point that atoms can form the matter can begin to clump under gravity to form stars and galaxies.  Simulations have shown that, as the initial gas is so uniformly distributed, it would take perhaps 8 to 10 billion years for regions of the gas to become sufficiently dense for this to happen.  But we know that galaxies came into existence around 1 billion years after the Big Bang.  Something must have aided the process.  We believe that this was non-baryonic dark matter.  As this would not have been coupled to the radiation, it could have begun to gravitationally "clump" immediately after the Big Bang.  Thus when the normal matter became decoupled from the photons, there were "gravitational wells" in place formed by concentrations of dark matter. The normal matter could then quickly fall into these wells, rapidly increasing its density and thus greatly accelerating the process of galaxy formation.

 The concentrations of dark matter that existed at the time the CMB originated have an observable effect due to the fact that if radiation has to "climb out" of a gravitational potential well it will suffer a type of red shift called the "gravitational red shift".  So the photons of the CMB that left regions where the dark matter had clumped would have had longer wavelengths than those that left regions with less dark matter.  This causes the effective blackbody temperature of photons coming from denser regions of dark matter to be less than those from sparser regions - thus giving rise to the temperature fluctuations that are observed.  As such observations can directly tell us about the universe as it was just 380,000 or so years after its origin it is not surprising that they are so valuable to cosmologists! 

WMAP

Observations by the COBE spacecraft first showed that the CMB did not have a totally uniform temperature and, since then, observations from the WMAP spacecraft, balloons and high mountain tops have been able to make maps of these so called "ripples" in the CMB - temperature fluctuations in the observed temperature of typically 60 micro Kelvin.

The Wilkinson Microwave Anisotropy Probe (WMAP) was originally known as the Microwave Anisotropy Probe (MAP) but was renamed after the death of one of the pioneers of CMB observations, Dave Wilkinson, who sadly died of cancer whilst its data was being analysed.  The WMAP spacecraft was launched on 30 June 2001 and flew to the to the Sun-Earth L2 Lagrangian point, arriving there on 1 October 2001.   This lies at a distance of 1.5 million km from the Earth directly away from the Sun.   In general, as one moves further away from the Sun, a planet (or satellite) will orbit more slowly, but if it lies on the Sun-Earth line the additional gravitational pull from the Earth will add to that from the Sun and the satellite will orbit more rapidly.  So, at just the right distance, a satellite can be made to orbit in one Earth year and so move round the Sun in consort to the Earth.  This position is L2.  Here, always observing the half of the sky away from the Sun it can produce a map of the sky in 6 months. WMAP completed its first all sky survey in April 2002.

The fundamental problem in producing an all sky map is the contamination of forground emission from our own galaxy and other, more distant radio sources.  To overcome this, WMAP observes in five frequencies which allows these to be determined and subtracted from the map.  Synchrotron radiation, from electrons spiraling round the magnetic field of the galaxy, dominate the low frequencies whilst emissions from dust dominate the higher frequencies.  These emissions contribute different amounts to the five frequencies, thus permitting their identification and subtraction leaving a map without any evidence of the fact that it was made within our galaxy!  ("Amazing" says the author of this transcript!)

The 3-year WMAP data alone showed that the universe must contain dark matter and that the age of the universe is 13.7 billion years old.  The 5-year data included new evidence for the cosmic neutrino background, showed that it took over half a billion years for the first stars to reionize the universe, and provided new constraints on cosmic inflation.

At a time ~400,000 years after the Big Bang, WMAP showed that 10% of the universe was made up of neutrinos, 12% of atoms, 15% of photons and 63% dark matter. The contribution of dark energy at the time was negligible.

The seven-year WMAP data were released on 26 January 2010.  According to this data the Universe is 13.75 ±0.11 billion years old and confirmed some asymmetries in the data that will be discussed below.  As of April 2010, the WMAP spacecraft continues to take data in perfect working order and will continue to make observation until September 2010

All-sky map of the CMB ripples produced by WMAP in February 2003

 Observations from balloons and the ground

Boomerang and Maxima Balloon Flights and Very Small Array (VSA) on Mount Teide, Tenerife, and Cosmic Background Imager (CBI) in the Atacama Desert, Chile.

 Observations of the CMB are greatly hampered by the presence of water vapour and so balloon flights such as Boomerang and Maxima and ground based antenna arrays such as the Very Small Array and the Cosmic Background Imager located in high, dry locations have been used to observe relatively small regions of the sky but with higher resolution than that yet achieved by all sky satellite imagers.  They have thus greatly aided the extension of the power spectrum, discussed below, to smaller angular scales.

The Planck Mission

Planck is a space observatory built by the European Space Agency which will complement and improve upon observations made by NASA's Wilkinson Microwave Anisotropy Probe  of the cosmic microwave background.  Planck was launched into orbit on the 14th May 2009 and flown to the same L2 region as WMAP where it was injected into its final "figure of 8" orbit on July 3rd by which time the high frequency receivers systems has reached the operational temperature of just 1/10 a degree above absolute zero.  It has the ability to make observations at smaller angular scales than WMAP and has significantly higher sensitivity.  In addition, it is making observations at 9 wavelengths rather than the 5 made by WMAP which should help remove the "foreground" contamination of the CMB data.  Two of the receiver systems were designed and built at the Jodrell Bank Observatory and are the most sensitive receivers ever made at their operating wavelengths.

Though the main objective of the mission is to observe the total intensity and polarization of the primordial CMB, it will create a catalogue of galaxy clusters using the Sunyaev-Zel'dovich effect and observe the effects of gravitational lensing on the CMB.  In order to remove the effects of the Milky Way from the raw images it will make detailed observations of the local interstellar medium, the galactic synchrotron emission and magnetic field.

In September 2009 (with the author present) ESA announced the preliminary results from the Planck First Light Survey (performed to demonstrate the stability of the instruments and the ability to calibrate them over long periods). The results indicated that the data quality is excellent.

These images are from an identical segment of the WMAP and Planck images. The top image is that made by the WMAP spacecraft and the bottom is from the first light Planck image of a region above and to the left of the galactic centre.  The centre image has been made by the author by overlaying the two images with a transparency of 50%.  The dark area in this image is where there is no Planck data.  The fact that the bright area looks "clean" and the colours are still well saturated shows a very high degree of agreement between the two images - though you will see that (as expected) the Planck image has a significantly higher resolution.   This will allow it to extend the CMB power spectrum to higher spatial frequencies that will give insights into both "inflation" and the relative amounts of normal and non-baryonic (dark) matter in the Universe.  On 17 March 2010 the first Planck photos were published, showing dust concentration within 500 light years from the Sun.

Planck started its first All-Sky Survey on 13 August 2009 followed by the second on the 14th February 2010.   By this time 95% of the sky had been observed with 100% sky coverage being expected by mid-June 2010.  The first preliminary results are expected by December 2010 with its final results released towards the end of 2012.

What have the observations of the CMB told us about the universe?

1] The curvature of space and hence the density of the universe.

The photons that make up the CMB have traveled across space for billions of years and will thus have been affected by the curvature of space. This curvature is a function of the amount of matter (and energy) in space and hence its density.  If the density is higher than some critical amount, the space will be positively curved (like, in 2 dimensions, on the surface of a sphere).  If the density is critical, Euclidian geometry holds true and is said to be "flat".  If the density is less than this the space will be negatively curved (like, in 2 dimensions, on the surface of a saddle).

Theory tells us the expected angular scale of the fluctuations of the CMB.  If we observed it through flat space then we would see exactly this angular scale.  If, however, we observed it thought positively curved space - which acts rather like a convex lens - we would observe a larger pattern than predicted, and if we observed it thought negatively curved space - which acts rather like a concave lens - we would observe a smaller pattern than predicted.  It is possible to simulate the expected pattern of fluctuations if space were negatively curved, positively curved or flat and these can be compared with observations. 

The upper part of the diagram shows the fluctuations observed by the Boomerang Balloon Experiment.  Below are the simulations of what would be expected if space were either flat or positively or negatively curved.  I think that it is fairly obvious that the "flat" pattern agrees most closely with that observed.

These observations can be put on a more quantative basis by analyzing the relative amounts of structure seen at different angular scales. Looking at the "blobs" in the boomerang data does it appear that there is a significant amount of structure seen on scale sizes of order one degree?   I do hope that you might agree.

The power in the CMB fluctuations as a function of angular scale using WMAP data at low angular scales and balloon and ground based - such as Jodrell Bank's Very Small Array (VSA) - data at the higher angular scales

In fact the peak in the plot is at ~0.8 degrees which is exactly what we would expect if space were "flat" and the WMAP results show that space is "flat" to an accuracy of 1%.  This important result this leads to value of the density of the universe which is 9.9 x 10-30 g/cm3, which is equivalent to only 5.9 protons per cubic meter.  This is in terms of mass, but we now know that a major part is in the form of energy. (Mass and energy being related by a well known formula!)

2] The relative amounts of the various components in the universe

4% Normal matter:  This implies that 96 % of the energy density in the universe is in a form that has never been directly detected in the laboratory!

23% Dark Matter:  The major part of which is Cold Dark Matter (Cold = relatively massive particles moving slowly) Dark matter is likely to be composed of one or more species of sub-atomic particles that interact very weakly with ordinary matter.  As we have seen, dark matter plays a very important part in the formation of the galaxies and has significant gravitational effects. Particle physicists have many plausible candidates and experiments are just on the verge of their detection.  This 23% includes a small proportion of Hot Dark Matter.   (Hot = light particle particles moving at speeds close to that of light)  Fast moving neutrinos make a small contribution to the dark matter total but too great a component of HDN would have prevented the early clumping of gas in the universe, delaying the emergence of the first stars and galaxies.  However, WMAP is able to see evidence that a sea of cosmic neutrinos do exist in numbers that are expected from other lines of reasoning.

73% Dark Energy: In the 1990's, observations of supernova were used to trace the expansion history of the universe over relatively recent times showing that the expansion appeared to be speeding up, rather than slowing down.  If 73% of the energy density in the universe is in the form of dark energy, which has a gravitationally repulsive effect, it is just the right amount to explain both the flatness of the universe and the observed accelerated expansion.

3] The Time and Redshift of  Reionization

The Reionization redshift relates to the time when the first stars formed and the ultraviolet light produced by them able to split electrons off hydrogen atoms giving ionized Hydrogen.  It is termed reionization as when the universe was hot - up to about 380,000 years after the origin of the universe, the hydrogen had been previously ionized.  At that time, when the atoms formed and cooled, the universe entered the so called "Dark Ages" which lasted until the universe was again filled with light from the first stars.  WMAP showed that this began at a redshift of 11 and was completed by a redshift of 7 corresponding to a time starting just 400 million years after the Big band and lasting for ~500 million years. 

4] The age of the Universe

The 7 year data from WMAP gave the age of the Universe as 13.75 ±0.11 billion years old. That's pretty precise!

Build your own Universe

There is an excellent piece of software produced by the WMAP team which can be found by putting "WMAP CMB Power Spectrum Analyzer" into Google.  This shows how the CMB spectrum would appear with varying values of the amounts of Normal and Dark matter and the relative amount of Dark Energy.  It is important to set the value of Hubble's constant to 73, the Reionization redshift to 11 and the spectral index to 0.95 first.

The Spectral Index is a measure of the relative amounts of fluctuations on different scales in the very early universe.

As they say, you can build your own universe and see what WMAP would have observed!

Does it all add up?

Well almost, there are some unexplained asymmetries in the data with one half of the sky 'starkly differing' from the other.  This is not necessarily anomalous but is being investigated.  The other interesting feature is the large "cold" spot seen below the centre-right of the WMAP plot.  One intriguing theory is that this is the result of the interaction of "our" universe with a second that formed with ours in the initial inflationary period when two "bubbles", not one, formed together.  Could this be the first evidence of another universe beyond our own?  Probably not, but you never know??.

©Professor Ian Morison, Gresham College 2010

Two good books:

•         Afterglow of Creation- Marcus Chown- Faber and Faber

•         Wrinkles in Time -  George Smoot -   Avon Books