100 Years of Cosmology

 

100 YEARS IN COSMOLOGY
 ASTRONOMY IN WONDERLAND - CURIOUSER AND CURIOUSER
(By Robert Bee)
 
INTRODUCTION:
This series of articles explains how the last 100 years of astronomical investigations have altered our understanding of the universe from a static, unchanging and ageless one to a dynamic, expanding and absolutely weird one that would make even Lewis Carroll’s head spin. In that relatively short period, the cosmos left its comfortable but naively simple form and moved towards a universe that progressively became ‘curiouser and curiouser’. 
 
It is an evolving story, very much like a mystery novel as clues are progressively discovered by the detective and, as each new clue is revealed, the plot thickens. Red herrings abound.
 
 
 
Sadly, for reasons of space constraints, it will have to be a Readers Digest condensed version, with much fine detail and many contributing players omitted. Hopefully, you will still grasp an essence of the story and the science it contains. Through it all there is a single thread – what is the ultimate fate of the universe?
 
We start in the early 1900s. 
At this time, before the 1920s, astronomers, even with the benefit of giant telescopes like the Yerkes 40 inch refractor – the largest in the world then – and the Hale 60 inch reflector at Mount Wilson, still thought that those wispy ‘spiral nebulae’ were all gassy clouds within our own Milky Way galaxy. In fact, the cosmological model of the time was that the Milky Way and all the objects visible within it comprised the entire universe.
 
 
 
 
It was also thought that the universe was static, all the stars and nebulae (including those mysterious spiral nebulae) were fixed in space, unmoving. The Universe always was and always will be as they saw it. No beginning, no end. That blissful state of cosmological ‘ignorance’ is where our story begins.
 
In 1908 Henrietta Leavitt, working for the Harvard Observatory, laboriously sifted through photographic plates of the Large Magellanic Cloud (taken by its observatory in Peru) and identified Cepheid Variable stars. She discovered the principle that the brighter Cepheids had the longer periods and was able to translate this to a means of measuring the distances to very distant objects by measuring the Cepheid’s period and observing its apparent brightness. This was to be of vital importance for what was to come. A copy of Leavitt’s history making plot of Cepheid variables in the LMC is shown below, with the trending very obvious.
 
 
    
 
 Henrietta Leavitt
 
 
In 1912, Vesto Slipher (from Lowell Observatory) took many spectra (about 41) of the so-called spiral nebulae which seemed to populate the Milky Way. 
 
 
 
Vesto Slipher
 
Slipher was studying the spiral nebulae as part of his work for Percival Lowell who believed passionately in life on Mars. It was thought these spiral nebulae may be solar systems in formation so to take their spectra was a logical extension of his work. To his surprise, he found that in most of them the recognisable spectral lines (absorption lines from elements in the star light) were further towards the red end of the spectra than their counterparts in the laboratory. Examples of this concept are shown in the image below.
 
 
 
 
 
This is a type of Doppler Shift called ‘red shift,’ a phenomenon we are now well aware of. 
 
The formula for Red shift is: z = (λobseremit)  - 1 =  (λobser - λemit )/ λemit   
 where λ (lambda) is the wavelength of the light.
 
In fact, measurement of the red shift gave a direct value of the speed (velocity) the object was moving away from us. (In the case of the Andromeda ‘nebula’ and a small number of others, it was in fact a blue shift, giving the velocity with which they were moving towards us.) This told Slipher that the majority of these ‘spiral nebulae’ were moving away from us, but at that time, it was not understood why. He may have thought it was some property of the formation of a solar system. Slipher’s study did not include an estimate of the nebulae’s distances so he had no reason at that time to intuit that they were in fact outside our Milky Way. His data on the red shifts of these nebulae, however, were to be very valuable to others.
 
In 1917, Einstein published his now famous General Theory of Relativity which was ultimately a theory about gravity and its impact on space-time. He had been working on this momentous theory since the publishing of his ground breaking Special Theory of Relativity in 1905. He was working on it all the time Leavitt and Slipher were conducting their own research.
 
 
 
 
Albert Einstein
 
Einstein field equations (EFE) are a set of ten coupled, non-linear partial differential equations that define the basis of general relativity theory. Unfortunately, by the very nature of their tensor mathematics, they were horrendously complex and difficult to solve. Not for the faint hearted. One core equation is:
 
Gab = (8πG/c4)Tab
 
where Gab is the Einstein tensor,  c is the speed of light in a vacuum and G is the gravitational constant, which comes from Newton's law of gravity, and stress-energy tensor Tab.
 
His theory, when applied to the universe at large, could accommodate either an expanding or contracting universe, but significantly, not a static one. Now Einstein had been assured by contemporary astronomers that the universe was static. (Remember, Einstein was a physicist, not an astronomer.) So, although he thought it made his equations messier, tainting their much cherished elegance, he added an extra term with the Cosmological Constant in it, to make his model of the universe static. (Note: This only had any effect on large scales, not local relativity effects. Hence ‘cosmological’.) This expanded the above field equation to:
 
Gab + Λgab = (8πG/c4)Tab.  Λ(lambda) is the Cosmological Constant.
 
This Cosmological Constant would play a major role in future cosmology theories as we will see later, but not before encountering a few bumps along the road.
 
Sir Arthur Eddington.
A few years later after Einstein published his General Relativity Theory, (Sir) Arthur Stanley Eddington, a great English astronomer of his time, thought Slipher’s red shifts might be a vital clue to a new cosmology based on General Relativity. Eddington, at the time, was one of the world’s few astronomers having the mathematical skills to understand General Relativity. He was such a champion of the theory that he led an expedition to observe the solar eclipse on the 29th May 1919 and, by measuring the bending of the light from a star close to the Sun’s edge, provided strong supporting evidence to the theory.
 
 
 
Sir Arthur Eddington 
 
He included Slipher’s red shifts in his 1923 textbook Mathematical Theory of General Relativity. By this act, Eddington was later shown to be a man of perception. Though we won’t hear more of him in this article, Eddington’s contribution to future cosmological debates, particularly with respect to the Cosmological Constant, is not to be underestimated.
 
 
The Friedman Models.
 
General solutions to the Einstein Field Equations for the dynamics of expanding universe models of General Relativity were discovered by the Russian Alexander Friedman in the years 1922 to 1924. 
 
 
  
Alexander Friedman 
 
Friedman’s solutions were derived as a ‘simplification’ of the Friedman-Lemaître-Robertson-Walker (FLRW) metric which was a quantum level higher in complexity. If you want to see horrendously complex mathematics that beggars your senses, google FLRW etc and stand back. Friedman’s simplified model (even its simplified mathematics is daunting for mere mortals) enables us to at least grasp a concept of the issue at play with the expanding universe.
 
The Friedman equations start with the simplifying assumption that the universe is spatially homogeneous (uniform density) and isotropic (appears the same in all directions). This is known as the Cosmological Principle. While obviously not applicable to our local region of the universe, it is justified on scales larger than ~100 Mpc (megaparsecs) as the 2dF and Sloane galaxy surveys show us. That is, it is a fair representation of the universe on a large scale.
 
What they basically tell us is how the rate of expansion of the universe changes with time. Keep in mind this was all theoretical as at that time it was thought the universe was static, with no expansion or contraction. The Friedman model describes a competition between the uniform expansion of the universe and the force of gravity to prevent this from happening. Now with the field equations of general relativity, this is hugely complicated. But, happily, it turns out that when solved and simplified, they equate to a very simple Newtonian physics model which our minds can grasp, as shown in the following diagram:
 
 
  
 
 
This model translates neatly into the question: “What is the deceleration due to gravity of a galaxy located at the surface of a uniformly expanding sphere which has a density equal to the average density of the universe?” The average density of the universe is called ??(rho).
 
Solutions to this question produced three Friedman models, for three different values of Density Parameter.
 
If we call Ω (the Density Parameter) = ρ/ρcrit, where ρcrit  = the average density that gives a value of Ω = 1 (called the Critical Density), then for:
 
Ω > 1 (that is the universe has a high density, greater than the critical density), the gravitational deceleration is high enough to halt the Universe’s expansion, causing it to reverse and collapse to a Big Crunch;
 
Ω  = 1, the Universe expands to infinity, then stops (This is the Einstein – de Sitter model);
 
Ω  < 1 ( that is the universe has a low density, less than the critical density), there is insufficient mass to prevent matter expanding to infinity and to keep going, never stopping. 
 
The three models are shown on the three curves in the following chart, with the spacial expansion of the universe (the Scale Factor) on the vertical axis and time moving to the right on the horizontal axis. The chart sets values of Ω  = 2 ( which is > 1) and  Ω  = 0 (an extreme example of  Ω  < 1).  
 
 
 
 
This model by Friedman would form the basis for future theories of a Big Bang. In fact, some argue that Friedman was the father of the Big Bang theory. More about that later on.
 
This concept of the Universe’s Density Parameter Ω will be very important later when we look more deeply into some other big cosmological questions, including the very shape of the universe. Is it ‘flat’, ‘spherical’ or ‘hyperbolic’? Do the angles of cosmic sized triangles add up to more, less or equal than 180°? The value of Ω has a direct influence on that, as shown here:
 
 
 
 
A measurement of the value of the universe’s density parameter Ω was to become another ‘holy grail’ for cosmologists. 
 
Edwin Hubble and the expanding universe.
 
It was after this in 1924 that Edwin Hubble used the giant 100” Mount Wilson telescope to identify Cepheid Variable stars in the Andromeda ‘spiral nebula’ and calculate their distances. The earlier work of Henrietta Leavitt’s is finally utilised to great effect.
 
 
        
 Edwin Hubble
 
Hubble calculated that the Andromeda ‘nebula’ was over a million light years away, clearly outside our own and a galaxy in its own right. (Hubble got the distance wrong initially – from a calibration error of Cepheid brightness – but when corrected gave the distance of about 2 million light years. We now know it is further than that, around 2.5 million light years.)
 
This showed that those wispy ‘spiral nebulae’ were not solar systems in formation (as hinted by Slipher) or just gaseous clouds but immense stellar systems outside our own Milky Way. Thus the existence of remote galaxies, just like ours, was established. 
 
The universe had experienced its first major paradigm shift. The Milky Way was no longer the whole Universe.
 
(Personal aside: It’s difficult for some people now to imagine how huge a shift in thinking that would have been to astronomers of the time. Would it have been a similar shock to that experienced by 17th century astronomers realising, post-Copernicus and Kepler, that the Earth was not the centre of the universe as taught by Ptolemy’s Almagest, but ‘just’ one of six planets orbiting the Sun?
 
I remember while studying at Sydney University browsing through the ‘stacks’ at Fisher Library and finding a very old astronomy text, published ca 1920. I was taken aback when I saw B&W images of what I knew then in 1964 to be spiral galaxies but the book described as filmy nebulae, clearly within and part of the Milky Way. I had no idea until then that astronomers had once held that view.)
 
Hubble’s ‘discovery’ should not have come as a total surprise to astronomers as this had been a subject of speculation and debate for quite some time. 18th and 19th century astronomers and philosophers had speculated about ‘island universes’ but there was no observational evidence so it remained speculation. It actually became a major controversy when on 26th April 1920 there occurred what is now called ‘The Great Debate’ between two astronomical heavyweights Harlow Shapley and Heber Curtis held in the Baird auditorium of the Smithsonian Museum of Natural History. The debate focused on two related questions: What is the physical size of the Milky Way (‘The Galaxy’)? and; Are the ‘spiral nebulae’ extra-galactic systems or do they belong to the Milky Way? The debate did not resolve the issue. That was left to Hubble.
 
Hubble had applied himself to measuring the spectra of many distant galaxies (following the earlier work of Slipher and using some of his red shift data). He found that, apart from the obvious closer ones which were ‘blue shifted’ (moving towards us), all the others were red shifted, indicating they were receding from us.
 
By 1929, he had measured the red shifts and distances to a large sample of galaxies and got an amazing result. The more distant the galaxy, the greater the measured red shift and, therefore, the faster it was moving away from us. In fact, after doing what all scientists love to do – plot their data on a chart - he showed: The speed away from us was directly proportional to its distance.
 
This became known as HUBBLE’S LAW, and the constant Ho in the formula was called Hubble’s Constant. (It has been suggested it was extremely immodest for Hubble to give the constant his own initial, H. However, in fairness he actually initially designated it with a ‘K’ for constant (he couldn’t use ‘C’). Somehow, it morphed to H and has stayed as such.)
 
 
 
 
An accurate measurement of the value of Ho has been a Holy Grail of cosmologists since then. The unit of H is km/s/Mpc. That is: kilometres per second per megaparsec, where a megaparsec is 3.26 million light years. Its measured value has gone up and down (in the early days due to uncertainties) from 100 to 50 km/s/Mpc but has settled down these days. The accepted current value of Ho is 72.0 km/s/mpc. It is important to remember, however, that that value is for Ho, the current value in our time for the nearby universe. This is important when we consider issues later in this article.
 
Hubble’s data suggested something very special and a new idea: The Universe was expanding. That is, all the galaxies are receding from us, and the further away, the faster it is receding. 
 
This was the next paradigm shift in cosmology. But it was not really such a new idea – Friedman had indicated its possibility in his General Relativity solutions and modelling in 1924 as we previously saw. Hubble’s work effectively corroborated it with observational evidence.
 
A caution and explanation is necessary here. Some who hear about Hubble’s discovery for the first time leap to the conclusion that all the galaxies are all racing away from our galaxy and therefore it must be at the centre of the universe. Nothing could be more incorrect. In fact, from any of the 100 billion odd galaxies in the universe, all the galaxies would be seen to be racing away from it. In that sense, everywhere is the centre of the universe. The fact is, the whole universe is expanding and all galaxies are moving away from each other at a speed proportional to their distance. Hubble’s Law! 
 
Although this discovery certainly brought light to the vast majority of astronomers and cosmologists in the world, it could be said it brought a sense of gloom to at least one person – the great Albert Einstein.
 
Einstein’s greatest mistake:
 
There is a well known story of Einstein, on learning of Hubble’s discovery of the expanding universe, rueing his insertion of the cosmological constant Λ into his Field Equations.
 
 Gab + Λgab = (8πG/c4)Tab.   
 
As reported by George Gamow in his ‘My World Line’ (1970): “Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder of his life.”
 
This has morphed into the folklore of modern physics. But why did he put the cosmological constant in? In simple terms, he put it into his field equations in 1917, as a last resort, to make his equations result in a static universe, which he had been led to believe was the case. Ironically, his original equations were telling him that the universe wasn’t static, that is was either expanding or contracting, but his blinkered view of the universe caused him to amend the equations, resulting in him losing an opportunity to make one of the most stupendous predictions in science. And irony poured onto irony. Even when he stuck to his ‘static universe’ paradigm, a little further analysis on his part would have revealed the inherent instability of that state. The most infinitesimal disturbance to that state would have led to an unstoppable expansion or contraction.
 
So it was that when Hubble proved the universe was expanding, Einstein kicked his cosmological constant out.
 
 
 
 
Further readings of Einstein’s rationale for including the cosmological constant reveal various philosophical viewpoints and recognition of the alternative possibilities resulting from his equations. But the over-riding motivating influence was his belief, based on contemporary astronomical observations, of the effectively ‘non-moving’ status of the stars. Hence his aim to have his equations predict a static universe.
 
As we will see later, Einstein was to have the last laugh, if only posthumously. His cosmological constant was to return with a vengeance, not to cause a static universe, but a much more dramatic outcome.
 
So in 1929 Hubble had shown that the universe was expanding. All the galaxies were moving away from each other at a speed determined by their distance and in keeping with Hubble’s Law: V = H0 x D. Why was this so?
 
DUELLING THEORIES:
 
 
 
 
In the following two decades astronomers developed two major theories to explain the expanding universe. The theories could not have been more different in concept and description of the dynamics of the universe. There was no room for compromise. It had to be one or the other. No serious third contender arose.
 
 
THE BIG BANG THEORY.  
 
In 1927, Abbe Georges Lemaitre,  applying the Second law of Thermodynamics as a starting point, theorised that the Universe had a definite beginning in time when all matter and energy was concentrated at a small point, which exploded and everything has been expanding since, resulting in an ongoing increase in the disorder (entropy) of the system (the universe).  This could explain what we see as receding galaxies, what Friedman had postulated in his expanding universe solution to Einstein’s General Relativity.
 
On May 9, 1931, Lemaître published his theory of the universe in the journal Nature and it was met with a fair degree of scepticism.
 
 
  
 
Abbe Georges Lemaitre
 
However, applying recent discoveries in quantum theory, George Gamow further developed Lemaitre’s work, calculating the resulting energies and temperatures of the theorised universe, what temperatures the necessary fusion reactions would occur at to provide the particles and elements needed to make the observed universe. The theory was a ‘work in progress’, not universally accepted by any means, but worked on by more and more reputable physicists. One initial flaw in Gamow’s model was his hypothesis that all the elements now seen in the universe were created in the original fireball. This was later shown to be mathematically unsupportable. However, continuing calculations on high temperature particle physics and fusion processes helped the model gain momentum until, ultimately, a credible alternative cosmological model appeared.
 
It is of interest that the name of Lemaitre and Gamow’s theory – The Big Bang Theory – was not suggested by its proponents but by its opponents. Fred Hoyle, when giving a radio interview about his own theory, gently derided his competitors’ theory, call it ‘that big bang’, and the name stuck.
 
THE STEADY STATE THEORY.  
 
20 years later (around 1950), a completely alternative idea was presented by British astronomer Fred Hoyle and associates Thomas Gold and Hermann Bondi. Folklore has it that in 1946 these scientists watched a movie called ‘Dead of Night’. 
 
The plot line of this movie was such that the ending returned to the beginning, in a continuous loop. This kindled the idea of a continuous universe in their heads. Gold and Bondi went on to develop the theory based on the perfect cosmological principal, with Hoyle joining the collaboration later with the mathematics to make the necessary mechanism happen.
 
(
 
 
Their theory proposed that the universe was the same in all places (homogeneous) and in all directions (isotropic) and – and this was the nub – at all times. This is consistent with the ‘perfect cosmological principle’. A logical consequence of this was that it had no beginning and no end and was infinite in extent.  But Hubble showed that the galaxies are all rushing away from each other. How could this be?
 
This model had significant support in its day, for both scientific reasons but also philosophical and religious reasons. Hoyle, Gold and Bondi maintained that the universe was infinitely old, remained in a steady state and yet was also expanding. How did these ideas coexist?
 
The ‘cleverness’ of the so-called Steady State Theory (also known as the Infinite Universe theory or Continuous Creation theory) was that the observed expansion was the result of new matter being spontaneously created, pushing the existing matter away. This was actually supportable by the theoretical quantum physics of the day. To explain this, Hoyle proposed that a field existed in space which he dubbed “the C-field”, the “C” standing for creation. (This is not as strange an idea as it may seem, when you consider the now discovered Higgs boson which generates the theoretical “Higgs field” which causes all the particles to have mass.) The C-field has the property of negative pressure, enabling it to drive the steady expansion of the cosmos, whilst also creating new matter.
 
The model went basically like this: The average density of the universe had to remain constant. This was achieved by new matter being created in the new areas resulting from the expansion of space. How much matter was needed to meet this requirement? Amazingly little. Every billion years, one hydrogen atom for each cubic metre of space. As insignificant as that sounds, it translates to roughly one new galaxy per year in the entire observable universe of about a hundred billion galaxies. Such a rate of introduction of new matter would be totally undetectable which is why it could not be contradicted by direct observations.
 
THE  PROOF OF A THEORY IS IN ITS PREDICTIONS:
 
There was much hot debate between cosmologists at that time between these two theories.  It is important to note that Friedman’s work on Einstein’s field equations supported both models so it was a very interesting time in the history of cosmology and cosmologists tended to fall into one camp or the other.
 
An idea of the difference between these two models is given by the following diagram:
 
 
 
 
Like all good theories, both the Big Bang and Steady State made predictions that should be verifiable from observations. As telescopes grew in size and radio astronomy technology improved, while the Big Bang had its setbacks, the Steady State model began to seriously wobble.
 
One initial setback for the Big Bang theory was that, using contemporary ‘measured’ values of the Hubble Constant, the approximate age of the universe was only 2 billion years. That was a problem, as the age of the Earth was confidently established at about 4.6 billion years, and there were stars whose ages had been determined to be over 10 billion years. How could the universe be younger? Obviously, this was a huge incentive to determine a more accurate value of the Hubble Constant.
 
The first wobble in the Steady State theory occurred in the 1950s when radio galaxies and quasars were discovered at great distances. These showed that evolving galaxies were very active billions of years ago, as predicted by the Big Bang theory. The wobble became extremely worrying when, in the 1960s, an extensive survey was done of the distribution of quasars and radio galaxies in both the near and far distant cosmos. According to the Steady State theory, there should be no difference in these distributions, whereas observations clearly showed they existed in far greater numbers in the past compared to much fewer numbers in the present epoch, as predicted by the Big Bang.
 
Still, the Steady State Theory held on.
 
WHAT SETTLED THE DISPUTE?
 
George Gamow had been a major contributor to the development of the mechanisms associated with post Big Bang eras, along with his associates Alpher and Herman.
 
 
          
They analysed what would have happened after the Big Bang and proposed that some of the chemical elements observed today were created in the first few minutes after the birth of the universe.  After initial errors in suggesting all the current elements were made by the Big Bang, it was eventually realised that it did in fact create all the hydrogen and helium now seen in the universe. (We now know that all the heavier elements were ‘cooked’ in the nuclear furnaces of supernovae once stars were formed from the primordial hydrogen and helium.) Also it was initially hot and dense and it cooled as it expanded. 
 
In 1948 they published a paper in which they argued that the post-Big Bang universe would go through stages of domination, first by radiation (the Radiation Era) in the form of a raging sea of energy. As this continued to expand, the energy would be largely converted to matter (the Matter Era). There would still be a remnant of energy (as radiation) which would permeate all of the universe. Alpher and Herman made a bold prediction: That this initial 4,000 degree Kelvin radiation would cool as the universe continued to expand and by this present era, would have very low energies, with a predicted temperature around 5 degrees Kelvin. The Steady State Theory made no such prediction. Obviously, the search was on to find this fossil radiation, called the Cosmic Microwave Background (CMB).
 
DISCOVERY OF THE COSMIC MICROWAVE BACKGROUND.
 
The CMB was found in 1965, by Arno Penzias and Robert Wilson, purely by serendipity (that is, a happy accident) while researching an unrelated radio astronomy problem. Accident or not, it won them the Nobel Prize for Physics.
 
 
 
 
Arno Penzias and Robert Wilson
 
Despite meticulous cleaning and checking of their horn antenna, they could not ‘get rid’ of this pesky and ubiquitous signal. Ubiquitous because it was detected equally from every point in the sky. It was indeed the ancient signal from the final radiation of the early universe after the Big Bang. It is seen in every direction in space and has travelled to us since 380,000 years after the Big Bang. Its measured value is now more accurately measured as 2.725°K +/- 0.001°K.
 
 
 
All sky map of the Cosmic Microwave Background
 
This was the final nail in the coffin of the Steady State Theory as it most specifically had no room for such a radiation in its ‘continuous creation’ model. The Steady State Theory quietly faded into the sunset while the Big Bang Theory, with its ‘smoking gun’ CMB evidence became the Theory de jour. And has remained so to this day.
 
[As a side note, there is some irony in the fact that certain aspects of Hoyle’s now defunct “C-Field” bear a striking similarity to aspects of modern cosmological models. For example, it is similar to the so-called ‘inflaton field’ employed in the Inflationary Theory of the Big Bang to explain a sudden exponential expansion of the early universe. More about the Inflation Theory later. It also provided a ‘negative pressure’ to expand the universe, which is the very similar to the effect of the resurrected cosmological constant proposed as a cause of the recently discovered acceleration of the universe’s expansion. Ironic indeed.]
 
The Big Bang is currently the generally accepted model of how the universe developed from the initial highly dense superhot ‘singularity’. It should be noted that physicists and cosmologists do not claim to know what happened before that sudden expansion nor what the trigger for it was. But they are confident in their explanation of what followed after the first 10-43 seconds.
 
 
WHAT IS THE BIG BANG THEORY?
 
The details are very complex and an article of this length cannot hope to give a comprehensive description. After all, this is a history of cosmology, not a text book on the subject. However, here is a simplified explanation of the theory that cosmologists developed.
 
The Universe started as an extremely small speck of matter (smaller than a grain of salt). But it was unimaginably dense and hot at it had to contain all the matter and energy of the universe as we know it now.
 
Then, for reasons no one knows (and cosmologists don’t pretend to know), it suddenly ‘exploded’ (or more precisely, unfolded time and matter) and the Universe started expanding at a furious rate while extremely hot but cooling as it expanded. In a trillionth of a trillionth of a trillionth of a second, it doubled in size at least 100 times (a size increase factor of 1043). This aspect of the theory is called The Inflation Model which was developed at a later stage – more of that in a moment. This resulted in a super-hot super dense mixture of matter and energy.
 
After Inflation, it continued to expand but at a much slower rate, the universe cooled and became less dense. A very brief timeline of that expansion and cooling is:
 
* 1 second after ‘Big Bang’ (t = 1 second), the cosmic temperature was approx 10 billion degrees Kelvin.
* At t = 3 seconds, the Universe was a scorching plasma of photons (radiation) and quarks (subatomic particles) smashing together to form protons and neutrons. They call this the Quark-Gluon Plasma.
* There was a furious process of creation, then collision and annihilation of matter and anti-matter, causing huge amounts of radiation and heat.
* After t = 3 minutes, all the hydrogen and helium nuclei of the universe had been created, but ionised as it was too hot to retain electrons. Apart from a negligible trace of Lithium, there were no other chemical elements existing.
* This went on for about 380,000 years, the Radiation Era. At the end of this time, the Universe had cooled to 4,000 degrees Kelvin and the hydrogen and helium nuclei were able to capture and hold free electrons, forming electrically neutral atoms of hydrogen and helium. The cosmos became transparent and astronomers can ‘see’ what was happening. This was the ‘Matter Era’.
* It was this final 4,000 degrees that, red shifted over the distance and time since then was observed as the cold 2.725°K CMB. That is part of the hiss of static on your radio or TV between stations.
 
Since then, the universe continued to expand and went through the long process of gravitationally collecting the hydrogen and helium gas to form galaxy clusters, then galaxies and stars, leading ultimately to the universe we see today in our telescopes.
 
 
 
 
 
WHAT IS THE INFLATION THEORY?
 
The original Big Bang theory was plagued by some difficult conundrums which the then ‘Hot Big Bang Theory’ could not explain. These were: 
 
The Horizon problem: Why is the universe, in all directions, the same temperature, homogenous and isotropic  when in the time of the age of the universe the opposite extremes could not possibly have ‘communicated’ with each other at the speed of light to reach an equilibrium state?
 
The Flatness/Fine Tuning problem: Why is the Universe ‘Flat’ (as they believed) with such small curvature? It hadn’t had time to reach that state of low curvature, or flatness.
 
The magnetic monopole (or lack of them) problem: A complex issue I won’t go into here. However, the Hot Big Bang Theory predicted if the early universe was very hot, a large number of very heavy, stable magnetic monopoles would be produced. These simply have not been found. Why?
 
The origin of density fluctuations (that led to clumping for galaxies). From the CMB it was seen that density fluctuations across the entire 380,000 year old universe are incredibly small (in the order of 1 in 100,000). How could they have been smoothed out so effectively?
 
These problems weighed heavily on the Big Bang Theory, undermining some confidence in it. This was soon to change.
 
In 1979, 32 years old Alan Guth, an American theoretical physicist and cosmologist was researching particle physics on the particular issue of magnetic dipoles. 
 
 
 
Alan Guth 
 
On the night of December 6th, he had a sudden inspiration that was to change the theory of cosmology. What if, he thought, after the very beginning of the Big Bang, starting at t = 10-34 seconds and through to 10-32 seconds, all the dimensions in the universe increased exponentially by a factor of e100, or about 1043? Thus was born the concept of cosmic inflation, leading finally to the ‘Hot Inflationary Big Bang Theory’, now the Standard Model. A comparison of the rate of cosmic expansion and Scale factor for the original and Inflationary Big Bang models is shown below:
 
 
 Where did the impetus for this inflation come from? Supposedly from some unknown (as then) repulsive force which, incredibly (and thankfully for us), switched itself off after t = 10-32 seconds. This idea may have been laughed out of town if it didn’t overnight solve all of those conundrums listed before. The unbelievably fast and huge expansion of the miniscule and irregular pre 10-34 seconds old universe provided answers to all those questions. The explanations are again too long to include here.
 
So that was the state of understanding of the Universe around the 1970s. Then things took another interesting turn. The universe has a way of continually teaching cosmologists a lesson in humility. 
 
AT THIS STAGE THERE WAS A MAJOR COSMOLOGICAL PROBLEM:
 
I have already mentioned the Density Parameter Ω which is the ratio of the observed average density of the Universe to the ‘critical density’. The critical density is that value which divides ‘expansion forever’ from ‘ultimate contraction’. 
 
Now the Critical Density has a real value. It is 10-26 kg/m3 – extremely small. That is equivalent to 5.9 hydrogen atoms per cubic meter. Compare this to the air we breathe which has 1025 particles/m3. The best vacuum on Earth, inside the beam tube at the Large Hadron Collider, has 1015 atoms/m3.
 
Now from calculations of all the matter in all the galaxies in the observable universe, the total Density Parameter only came to 0.04. That’s a lot less than 1.0. This suggests that the Universe has an open (hyperbolic) geometry, not flat (Euclidean) and will expand without limit.
 
Cosmologists were extremely uncomfortable with that. They were convinced that the universe was flat, for reasons that are too lengthy to cover here.
But where was the extra necessary matter to bring Ω up to 1?
 
THEN SOME MAJOR AND AMAZING DISCOVERIES WERE MADE.
 
 
DARK MATTER
 
In 1933, a very cantankerous astronomer, Fritz Zwicky, pointed out unusual results with his measurements of the mass of the Coma Cluster of galaxies (in the Coma Berenices constellation), using the motion of galaxies at the fringe of the cluster. 
 
 
 
Fritz Zwicky
 
He calculated that it contained 400 more times the mass than expected from what telescopes could see. He concluded that there must be a huge amount of ‘invisible’ matter with enough mass (and therefore gravity) to prevent the cluster from flying apart.
 
He was generally ignored by his peers, whom he famously described as ‘spherical bastards’. That is, “they were bastards from whatever direction you looked at them.” History would show that Zwicky was a genuine astronomy genius, but he clearly lacked people skills.
 
Then in 1975, astronomer Vera Rubin did similar calculations and observations for stars on the outskirts of spiral galaxies. 
 
 
 
Vera Rubin
 
 
 They were moving at the speeds that the visible matter could not account for. She suggested that up to 50% of the mass of the galaxy must be contained in a dark halo enveloping the galaxy. The justified ghost of Zwicky returned.
 
In fact, now astronomers believe that 85% of all the matter that makes up the Universe consists of this invisible Dark Matter. The remaining 15% is the visible stuff, made of protons, neutrons and electrons that we see in galaxies, stars, planets, gas etc.
 
WHAT IS DARK MATTER?
 
No-one knows yet, but there’s a Nobel Prize waiting for the discoverer. There are currently two main streams of thought. One is that it is comprised of ordinary matter (but not stars or dust), dubbed MACHOS for Massive Compact Halo Objects, such as Jupiter sized planets, black holes, brown dwarfs. The other stream is it is some exotic particle from new physics, weakly interacting massive particles, or WIMPS. The jury is very much out on this. There is hope that experiments at the Large Hadron Collider may shed light on Dark Matter.
 
Dark matter, or at least its effects, can be seen directly by what is called Gravitational Lensing. Just like the lenses in our glasses bend the light to help us see better, huge concentrations of Dark Matter can bend the light from objects far behind them to bring them into our view.
 
Here is an example of Gravitational Lensing. 
 
 
 
 
Galaxies beyond an intermediate star cluster, its mass greatly increased by its dark matter, have their images distorted by the cluster’s gravity, appearing as arcs rather than their true galactic shape. This effect is demonstrated by the following diagram.
 
 
 
 So Dark Matter, whatever it is, is real and huge amounts of it surround all the galaxies, including ours.
 
A major benefit of Dark Matter for the cosmology theorists was that it helped with the Flat Universe problem. When the amount of Dark Matter was allowed for in the Matter Density Parameter ΩM, it came to about ΩM  = 0.3. This is much closer to 1 than the 0.04 for visible matter alone. But not close enough. It would still suggest that the universe is NOT FLAT.
 
Cosmologists were still convinced Ω should = 1.  They had a conundrum.
 
Another conundrum: If the Universe was only made of 100% matter (normal and dark), then the universe has been decelerating while expanding. Theory tells astronomers that for a value of ΩM  = 1, computing the age of the universe is given simply by 2/3 x 1/Ho
 
 
 
But for a value of Ho = 72, this gives an age of the universe of 9 billion years. This is much less than the 12 billion years age of the oldest stars in globular clusters. 
 
That’s not good. The baby is older than the mother!
 
That is a good argument for ΩM  < 1, say 0.3, which as the above chart shows, gives and age of 12.5 billion years, very close to what was expected.
But they still need the Ω  = 1   for a Flat universe. An extra 0.7 for Ω  would be nice. Yes, cosmologists wanted the best of both worlds. What to do to solve this conundrum?
 
DARK ENERGY
 
Up till 1998, cosmologists were debating what the ultimate fate of the universe was. Would it:
 
a) Slow its expansion, stop, then contract to a Big Crunch ( or gnaB giB?)
 
b) Slow its expansion to a halt and stay there?
 
c) Slow its rapid expansion but never quite halt, continuing a slow expansion to a Big Cool?
 
It all depended on the total mass of the Universe. The ‘smart money’ was on b) or c).
 
This was completely turned on its head in 1998 when a fourth alternative was discovered.
 
Two independent teams of astronomers published their results of extensive studies of distances to extremely remote Type 1a supernovae. (These supernovae were excellent standard candles of known luminosity. They result from the total annihilation of a white dwarf star when is accumulates enough matter from a binary partner red giant to reach a critical mass of 1.44 solar masses.)  
 
 
 
 
Looking back into the earlier life of the Universe (about 5 billion light years away, or z = 0.7), they were shocked to find that these supernovae were further away than expected. There was only one possible conclusion:
 
The universe now is expanding at a faster speed than it was then. The Hubble Constant now is higher than it was back then. The universe’s expansion is accelerating!
 
There are many proposals as to why this is so. But they generally come under one title: Dark Energy. Some strange energy in the vacuum of space itself, is causing space to expand faster, carrying the galaxies along with it.
 
It’s a very complex question, with varying theories to explain it, but no-one is seriously arguing against the accelerating universe theory.
Ironically, it is behaving exactly as Einstein’s Cosmological Constant said it would, and now it is agreed Einstein should have left that term in his field equations. This Dark Energy now has the symbol Λ (Lambda) for that reason.
 
The amazing thing is that the supernova study teams were able to find Type 1a supernovae even further back in time, as far as 8 billion years (or z = 1.2). To their relief, they found that these were closer than they would have been if the universe was accelerating at that era. It meant that the initial expansion of the universe was decelerating (as always originally thought), then Dark Energy started to battle gravity and the universe expansion coasted, then after about 8 billion years after the Big Bang, the Dark Energy dominated gravity and the universe’s expansion  started to accelerate. This is shown by the red ‘S’ curve in the following diagram. It shows that at the present era, the coasting has stopped and acceleration is underway. The other curves (with their colour keys) show the expansion rates for the other possible values of ΩM and ΩΛ
 
 
 
The shape of the Scale Curve allows cosmologists to measure the amount of Dark Energy and its mass equivalence in the Density Parameter equation. Remember that, with E = Mc2, the Dark Energy can be counted in the mass-energy Density Parameter. And the ΩΛ works out to be ~ 0.7.
 
That is, ΩTot = ΩM (0.3) + ΩΛ (0.7) = 1.
 
This, happily, solves the cosmologists’ conundrum.
 
This keeps the universe FLAT. Also, applying the shape of the S curve and the measured values of the Hubble constant along it, gives a very confident age of the Universe of 13.7 +/- 0.1 billion years. The ‘coasting’ and acceleration has moved the age up from the previous 9.2 billion years for deceleration only.
 
By pure coincidence, for ΩM = 0.3 and ΩΛ =0.7, the slowing down and then speeding up about balance out and the time elapsed from the Big Bang to now works out the same as simply taking 1/Ho for Ho = 72 km/s/mpc.  13.7 billion years. Fluke?
 
More accurate measurements have since been done, giving the whole universe’s matter/energy budget to be made up of: 
 
 
 
 
73% Dark Energy, 23% Dark matter and a mere 4% of ‘normal’ matter.
 
That is all the bits of the Universe that we can actually see makes up only 4% of the whole Universe. The rest is DARK. That is very humbling.
 
Since then, independent measurements based on the CMB were able to measure the geometry of larger scale universe and arrived at Ωtotal = 1.0 +/- 0.04.  
i.e  Ω= 1.
 
This independently validated the existence of Dark Energy, Flatness of the Universe, and Inflation after Big Bang.
 
The cosmological pieces were falling into place like the final pieces of a jig-saw.
 
SO, WHAT DOES THAT MEAN IN TERMS OF THE FATE OF THE UNIVERSE?
 
A new scenario d) is: The universe will continue to expand faster and faster (gravity unable to counteract the repulsive force of Dark Energy) and, many hundreds of billions of years from now, galaxies will drift so far apart they will lose sight of each other. 
 
Ultimately, in hundreds of billions of years, due to lack of new star births, all the stars will fade or be consumed by black holes and the Universe will be a very dark place.
 
But who knows what new discovery will turn that scenario on its head? In other words, what will the next 100 years of cosmology reveal?
As a distinguished cosmologist famously said: 
 
 
 
 
 
 
 
 

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