COSMOLOGY: The Big Bang Model Of The Universe And The Cosmic Background Radiation.
The current model for the origin and nature of the Universe begins with a seeming impossibility and ends in Uncertainty. The impossibility is that at the beginning Everything must have been a single point – a singularity. This is not only difficult to imagine but it also means that no known laws of physics could apply.
The success of the model is that once we are past that first impossible moment, the laws of physics are able to explain most of the Universe’s observable features. Of course, there are still many gaps in the theories and many observations that don’t fit very well. There are also missing observations: no one has detected gravitational waves, let alone gravitons, the particles that theory predicts carry the gravitational force. There is also the puzzle that most of the mass that must be in the Universe to explain gravitational effects seems to be undetectable.
There follows a summary of the evolution of the Universe described by the standard Big Bang model, together with some of the main evidence in favour of the model.
DURING THE FIRST THREE MINUTES
If we run the film of the expanding Universe backwards. We reach a point where everything – spacetime, radiation and matter – is compressed into dimensions incredibly smaller than the size of a proton. At this very earliest stage, the four fundamental forces (interactions) of nature formed one single unified force, often called supergravity.
At 10-43 seconds
The micro-Universe has expanded to be about 10-35 m across at a temperature of 1032 K, with a mass-energy density of 1097 kg m-3. Nothing surrounds it, not even a space or ‘vacuum’ since the Universe is all there is. At this time, ordinary gravity splits away (decouples) from the original single force.
Expansion continues, and the tightly packed highly energetic photons convert some of their energy into a sea of virtual quarks which combine to form larger virtual particles and antiparticles. Virtual particles of matter exist for only a very short time. This is allowed by the Heisenberg uncertainty principle, provided that their mass-energy and lifetimes multiply to a smaller value than the Planck constant h.
Timeline of the metric expansion of space, where space (including hypothetical non-observable portions of the universe) is represented at each time by the circular sections. On the left, the dramatic expansion occurs in the inflationary epoch; and at the center, the expansion accelerates
NASA/WMAP Science Team - Original version: NASA; modified by Cherkash, Public domain
After 10-35 seconds: a sudden rapid inflation
The Universe has been expanding steadily, while cooling. But at about 10-35 s, the strong force separates out, leaving the electromagnetic and the weak forces coupled together as the electroweak force. With the separation of the strong forces, there is a sudden increase in the rate of expansion, an inflation, which lasts until 10-30 s have elapsed. In this time, the Universe has expanded by a factor of 1050, to become about the size of an orange.
By the end of this period of inflation, the Universe has cooled from 1032 K to about 1026 K. Real particles can now be formed from photons which have enough energy to produce particle-antiparticle pairs: quarks and antiquarks, electrons and positrons. So photons become fewer and less energetic. As expansion and cooling continue, the quarks combine to form very massive but short-lived particles (hyperons), and eventually the stable protons and antiprotons.
At one microsecond
A microsecond is a very long time in the early Universe. At this time it has reached the size of the Solar System and its temperature has dropped to 1013 K, too low for the creation of any more heavy particles from photons. In fact, the quantity of matter is now decreasing rapidly as protons combine with antiprotons, annihilating each other.
If protons and antiprotons had been created in exactly equal quantities, the Universe would now consist entirely of radiation, all at too low an energy to create more particles. Fortunately, there was an excess of protons over antiprotons in the ratio 10,000,000,001 to 10,000,000,000. This left enough protons over to make all the stars and galaxies that now exist.
At one second
The temperature has fallen to 1010 K, at which photons no longer have enough energy to create electron-positron pairs. There is a second great matter-antimatter annihilation as those that existed meet. This creates more photons. But again, there is an excess of matter (electrons) over antimatter (positrons) which is just enough to match the protons’ charge – so that the total electric charge in the Universe is zero.
At this stage, the Universe is a hot plasma consisting of photons, electrons and protons in equal proportions. There is also a very large but unknown number of neutrinos.
Neutrons are produced by collisions between protons and electrons. But neutrons are unstable, and another equilibrium develops between creation and decay which eventually produces two neutrons for every 14 protons.
Later, at a slightly lower temperature, protons and neutrons can combine on collision to form the nuclei of deuterium (hydrogen with 1 proton, 1 neutron) and then helium. (The ratio of neutrons to protons, predicted by nuclear and particle theory, should have produced a hydrogen-helium ratio of 75 per cent to 25 per cent by mass. This ratio is confirmed by present-day observation.) Any larger nuclei are broken up by collision until the plasma cools down further.
Panoramic view of the entire near-infrared sky reveals the distribution of galaxies beyond the Milky Way. Galaxies are color-coded by redshift.
IPAC/Caltech, by Thomas Jarrett, Public domain.
At three minutes
Eventually, during the next three minutes, the stable isotopes of the light nuclei lithium (7Li) and beryllium (9Be) are formed – but in very tiny amounts. By this time, the average distance between particles is so large that they are extremely unlikely to meet and form larger nuclei. This process has to wait until nucleosynthesis in stars begins.
DURING THE NEXT 300 000 YEARS
In its first 300 000 years, the Universe is first a plasma consisting of electrons, protons and helium nuclei. All atoms are ionised. Photons are scattered by the charged particles and cannot travel without losing energy by collisions. We say the Universe at this stage is ‘opaque’ to radiation.
Eventually, the temperature drops to about 3000 K and nuclei rapidly capture electrons to form neutral atoms which photon energies are too low to break up. The universe becomes transparent to its own radiation.
When the temperature falls a lot more, the maximum wavelength of the radiation is about 1 mm, in the near infrared. It is from this stage of the Universe’s evolution that a relic of radiation at that time, cosmic background radiation, is still detectable. This radiation is roughly the same from all directions and shows a pattern of intensity at a range of wavelengths characteristic of black body radiation of a Universe which has cooled to about 3 K as it expanded.
EXPLAINING THE COSMIC BACKGROUND RADIATION
The existence of a low-temperature radiation that fills all space was discovered by accident in 1965. It had been predicted as early as 1948 by George Gamow, Ralph Alpher and Robert Hermann, but later forgotten.
Arno Penzias and Robert Wilson, physicists working for the Bell Telephone Company, were testing a small, very sensitive radio telescope they had designed and built to detect radiation of 7 cm wavelength. They found a high level of ‘noise’ in the system which they couldn’t eliminate. They also found that, unlike most noise in radio telescopes, it didn’t vary with time of day or with the direction the telescope pointed. Eventually, they accepted that the signal wasn’t noise in the machine but radiation of cosmological origin.
At a nearby university, physicists were reinventing the theories of Gamow, Alpher and Hermann, and the report of Penzias’ and Wilson’s discovery seemed convincing evidence in favour of the Big Bang model, which at the time had little evidence to support it.
Since then, many very accurate measurements have been made on the background radiation and have confirmed it as a relic of the primal universal radiation.
One problem with the radiation was that it was too uniform to be true! The variation and clustering of mass in the Universe was expected to be matched by a similar – if not so dramatic – variation in radiation density: whatever had caused matter not to be distributed uniformly should also have affected the radiation.
The ‘lumpiness’ of the radiation was first measured by the Cosmic Background Explorer (COBE) satellite experiment in 1992. A much more detailed measurement was made by the Wilkinson Microwave Anisotropy Probe (WMAP) in 2006. In its figure, the darker shades show regions of lower radiation intensity coming from regions where, about 14 billion years ago, there was more matter. Its gravitational effect reduced the intensity of the radiation. The difference in intensity is tiny: a few parts in 100 000. Detailed study of the data supports the theory of early cosmic inflation.
This graphic illustrates the evolution of satellites designed to measure ancient light leftover from the big bang that created our universe 13.8 billion years ago. Called the cosmic microwave background, this light reveals secrets of the universe's origins, fate, ingredients and more.
CRITICAL DENSITY AND THE FUTURE OF THE UNIVERSE
We need Einstein’s theory of general relativity for a full explanation of an expanding Universe. But the Newtonian model is good enough for us to construct some possible scenarios. Think of a galaxy at the edge of a large spherical volume of space inside the Universe. It contains clusters of galaxies, all moving apart from each other. Newtonian theory says that only galaxies inside the spherical volume will affect the motion of the galaxy. The effects of galaxies outside the sphere cancel each other out. Our chosen galaxy (and all others, because we can choose any sphere as long as it is large enough) will have a force on it tending to slow down its outward movement.
What eventually happens to the galaxy depends on much the same factors that decide whether an object thrown upwards from Earth will fall back or go off the planet having been given the escape velocity. This is essentially a battle between the kinetic energy of the galaxy and its gravitational potential energy.
Think about a galaxy of mass m at distance R from us. The sphere centred on us with a surface at the galaxy contains a mass M. According to Newton’s law of gravity the force pulling inwards on the galaxy is
F = GMm/R2 [1]
And the mass M in terms of the mean density ρ of the space inside the sphere
M = (4/3 ) πR3ρ [2]
By Hubble’s law (v = HD) the galaxy is separating from us with a speed v such that
v = HR [3]
Does the galaxy have enough speed to escape’? If it does then the Universe will keep expanding forever. Escape velocity is a well-known idea and is given by the relationship
v2=2GM/R [4]
With the quantities now referring to the sphere and the movement of the galaxy. Using equations 2 and 4 we can put the possible escape velocity in terms of the density of the space inside the sphere:
v2 = 2G(4/3) πR2ρ
The escape velocity will be just reached when the density has critical value ρc such that
ρc = v2/[(8/3)GπR2]
But we know that v = HR, so substituting for v we have
ρc = H2R2/[(8/3)GπR2]
which simplifies to
ρc = 3H2/8Gπ
The large uncertain quantity here is H, the Hubble constant. Accepting the value favoured in my previous post on COSMOLOGY: Clusters and Superclusters of Galaxies and The Expanding Universe, the critical density is about 5 × 10-27 kg m-3 (about 1 hydrogen atom per cubic metre). You can also check this value for yourself.
The density of the Universe is not easy to measure. One way is to add up all the matter we can see in stars and galaxies, make some corrections for the clouds of invisible hydrogen gas and other small particles and hope for the best.
Cosmologists discuss the future of the Universe using the density parameter Ω which is the ratio of the measured density of the Universe to the critical density:
Ω = ρ/ρc
There are three possible fates for the universe.
1. Ω =1: the Universe will keep expanding but more and more slowly and eventually, at some time in the infinite future, come to a stop. It is a flat Universe.
2. Ω < 1: the Universe expands forever and ends up with a finite velocity at infinity. It is an open Universe.
3. Ω > 1: the Universe will eventually stop expanding and its gravity will start pulling it backwards. It ends up in a hot dense phase – quite possibly as it started in a Big Crunch. This is a closed Universe.
The terms flat, open and closed are linked to the various geometries of space that fit Einstein’s general theory of relativity.
To summarise: if there is too little matter we have scenarios 1 and 2, if enough scenario 3 will occur. If ordinary matter were responsible for the fate of the Universe, scenario 2 occurs. But read on.
NINETY PER CENT OF THE UNIVERSE IS MISSING
Estimates of the density of matter in the Universe that are based on the matter we can actually see give very low values – about 4 × 1028 kg m-3, or one hydrogen atom to every 10 m3. To keep the Universe expanding steadily, as in scenario 1 above, we need about 70 atoms in this volume of space. However, when astronomers measure the gravitational pull of the material in a galaxy, or even a supercluster of galaxies, they find that the visible material contributes only about 10 per cent of the gravitational mass.
The invisible material does not affect the light output, so is unlikely to be clouds of dust. (Even gas clouds form only 5 to 15 per cent of the mass of a galaxy.) The search is now on for the missing material. It could exist as unknown forms of matter such as weakly interacting particles (WIMPs), dead dark stars and planets (MACHOs) or heavy neutrinos. There could also be black holes, just small enough (which has been confirmed already).
AND ANOTHER THING… DARK ENERGY
One of the most valuable indicators of cosmological distance is a very bright type of object called a type Ia supernova. They are valuable because not only are they very bright (and so can be detected even when they are very far away) but they all have almost exactly the same well-known maximum brightness. This allows distances to be measured for a range of galaxies in which they appear. Research teams working with these objects discovered (and announced in 1998) a quite unexpected result, linking the distances of the host galaxies with their rate of recession (z value).
Light takes time to travel. When we observe a distant galaxy we are looking at a stage of the Universe up to 10 billion years old. The surprising discovery was that the Universe is not expanding at a steady rate: H0 is not constant with time. The Universe is expanding faster now than it was a billion years ago; it is accelerating. The theoretical implication of this discovery is that Einstein was right: his first model of the Universe contained a quantity called a cosmological constant which predicted the acceleration that has now been discovered. But back in the 1920s Hubble’s work contradicted the existence of the cosmological constant and Einstein came to refer to it as his ‘greatest mistake. An accelerating Universe is not a constant energy system as considered in the scenarios above, rather the quantity of energy it contains must increase with time. This has been called dark energy, or quintessence, and has the effect of counteracting gravity. This energy causes space itself to expand faster and faster.
Chart shows the proportion of different components of the universe – about 95% is dark matter and dark energy.
Had the effect been strongly in existence in the early Universe it would have stopped the gravitational collapse that has produced stars and galaxies, suggesting again that the dark energy is increasing with time. It is estimated to be now about two-thirds of the total energy in the Universe. The increase from a very small value over time can be explained by saying that the energy is proportional to the volume of space, and so increases naturally as space expands.
It may be composed of particles and the search is now on for evidence of this, which I’m sure our dear Professor 
SUMMARY
After you might have read through these posts of mine on cosmology, starting with:
- COSMOLOGY: The strange darkness, Olbers' Paradox and the main features of the Universe.
- COSMOLOGY: Clusters and Superclusters of Galaxies and The Expanding Universe
I’m quite sure, we should all have been able to:
- Understand why Olbers’ paradox suggests that a static, infinite Universe is an impossibility.
- Know that the Universe consists of stars and interstellar material grouped in units: galaxies, clusters of galaxies and superclusters.
- Know how the distances to stars and distant objects can be measured.
- Understand how the Doppler effect is used to measure the velocities of galaxies.
- Know about the observed expansion of the Universe on a large scale, red shift, Hubble’s law and the Hubble constant.
- Know the standard Big Bang model of the Universe, the importance of particle physics in describing the first minutes of its evolution and be able to give evidence in support of the model (cosmic background radiation, cosmic abundance of elements).
- Know the age and possible fates of the Universe, linked to its density and the value of the Hubble constant.
Thanks for reading.
REFERENCES
https://en.wikipedia.org/wiki/Cosmic_microwave_background
https://en.wikipedia.org/wiki/Cosmic_background_radiation
What-is-the-critical-density-of-the-universe?