In Friedmann's first model of the universe time, like space, is finite. A simple representation of this model is a line with two ends, or boundaries. Like this finite line, time has a beginning and an end. If we introduce in Einstein's equations the amount of matter known to exist today in the universe, they show that about 13.7 E10+9 years ago all the mass of the universe was concentrated in one point. All the cosmology theories assume that space-time is smooth and nearly flat. It was obviously not the case at that time when the theories break down.
All three so-called Friedmann's possible universes assume that some 10 to 20 10E+9 years ago all the masses were concentrated in one point of infinite density. At that time the curvature of the space-time was also infinite. This was lately called the BIG BANG. As mathematics cannot deal with infinite numbers, the general theory of relativity, on which Friedmann's theory is based, does not work at such a point (that the mathematicians call a singularity). What happened after, or before the big bang, cannot be either forecasted or deduced from the conditions at the big bang. This means that if we knew the parameters of some events before the big bang, they could not be used to predict what happened after. Due to this singularity, although we know what happened after the big bang, these information cannot be used to find what happened before. As a result nothing can be known about what happened before the big bang and we must admit that, for all purposes, time began then.
When the universe had zero size, the temperature was also infinite but it soon decreased after the big bang. However, when the temperature was still very high, so were the energy and the speed of the particles in the universe. In these conditions the particles moved so fast that they escaped the attraction due to the nuclear and electromagnetic forces. Luckily for us the temperature continued decreasing and, at lower temperatures, particles regrouped together.
Some scientists suggested that there is no need for a big bang. The best-known alternative proposed by these scientists is the "Steady State Theory". According to this theory, as galaxies move away from each other, new galaxies from new matter created all the time replace them. If this was true, then the universe would look the same all the time and the amount of mass should be the same in all point of space. By analysing radio wave sources from faraway in space as well as those closer to us, scientists found that there were many more weak sources -the more distant- than strong ones from nearer. This could only mean that there were more wave sources in the past that is at the time when these radio waves started their journey towards us, that there are now. This contradicts the Steady State Theory. This was confirmed later when microwave radiation discovered in space showed that the mass density in the universe was greater in the past that it is now. As a result, it is now believed that the universe most probably had a singularity at the beginning, as the general theory of relativity shows. However this is not yet a definite proof that the universe began with a big bang.
In 1965, Roger Penrose, a British mathematician and physicist, showed that if one takes into consideration the behaviour of the light cones in general relativity and the always attractive gravity, it results that a star collapsing under its gravity is finally trapped and reduced to a single point in the space. The star matter is therefore compressed to such an extent that its density becomes infinite and, in this region, the curvature of the space-time also becomes infinite. This singularity within a space-time region is known as a black hole.
Stephen Hawking, after becoming aware of Penrose's theory that any body collapsing under its gravity forms a singularity, went one step further as often happens in science. By reversing the direction of time in Penrose's theory, that is by assuming that instead of a collapse we have an expansion, the theory is still valid if the universe was similar to a Friedmann model at the time. In conclusion, as Penrose's theory showed that a collapsing body must lead to a singularity, conversely an expanding Friedman universe must have began with a singularity that is, a BIG BANG. In a second time Hawking showed that to have a singularity at the beginning of time the universe must be infinite, and the rate of expansion must be above the critical velocity to avoid a new collapse. In 1970 Penrose and Hawking proved that there must have been a big bang singularity at the beginning of time if the general theory of relativity is right and if the universe contains at least as much matter as we know there is.
The origin of the universe
Einstein's theory of relativity shows that space-time started with a big
bang singularity and would:
- Collapse totally in a big crunch singularity, if the whole universe collapsed
in the future.
- Collapse locally at a singularity inside a black hole if a celestial body
such as a star collapses on itself.
As we have seen, any matter falling in a black hole would be annihilated in this singularity and only the gravitational effect of its mass could still be fell outside it.
Quantum mechanics, on the other hand, seems to show that the mass or energy of the matter falling in a black hole would finally be returned into the universes, and the black hole and its singularity(ies) would disappear. Quantum mechanics cannot be ignored at the big bang, as the gravitational field at that time was extremely high.
The theory of the origin of the universe generally accepted these days
states that it started with a big bang. This assumes that the universe described
by a Friedmann model represents what happened right from the very beginning.
As the universe expanded, its matter or radiation got cooler, the energy
and the speed of the particles decreased and this had an important effect
on the matter in it. When the temperature was very high the particles could
avoid being attracted towards each other by the electromagnetic and nuclear
forces but, when the temperature decreased enough, these forces of attraction
made the particles stick together. The types of particles that existed in
this universe depend on the temperature (when the universe double in size,
the temperature falls by half):
- At very high temperature, the energy of the particles was such that when
they collided pairs of particles and antiparticles were created. Some of
these particles and antiparticles hit each other and were annihilated, but
their speed of production was so high that many escaped annihilation.
- At lower temperature, the particles had lower energy, and the particle
and antiparticle pairs were produced at a lower rate and annihilation became
faster that production.
At the big bang the universe is believed to have had a zero size and an infinite temperature. But as it expanded it soon cooled down.
After a second the temperature was probably down to 10E+10 degrees Celsius (10E+3 the temperature of the sun). Such temperatures are created in an H-bomb explosion. At that time the universe contained mainly light particles such as photons, electrons and neutrinos -and their antiparticles- together with some protons and neutrons. When they collided, they produced many different particle/antiparticle pairs. For instance colliding photons of above a certain minimum energy could have produced electrons and their antiparticles known as positrons. As photons have no mass, to produce protons and neutrons that have a definite mass, they must have had an energy higher that the equivalent (according to Einstein's law, E=mc²) of the mass of these two particles. Some of these particles annihilated after colliding with their antiparticles.
As the expansion continued, the temperature and the energy of the photons dropped and the rate of production of electrons and anti-electrons became smaller that their annihilation rate. As a consequence most electrons and positrons were destroyed by annihilation producing more photons and leaving few electrons. However many neutrinos and antineutrinos would still be there as they interact only weakly with each other and other particles. They must still exist today and, if we could detect them, it would confirm the theory, but their energy -and temperature- would now be too low for us to detect them directly. If they have a mass, however small, we could perhaps detect them indirectly. Being a "dark matter" with gravitational attraction they should try to stop the expansion of the universe or, perhaps, make it collapse.
One hundred seconds after the big bang the temperature would have been around 10E+9 degrees (this is the temperature inside the hottest stars). The protons and neutrons would not have anymore enough energy to escape the attraction of the nuclear force, and would combine to produce nuclei of deuterium (heavy hydrogen made of one proton and one neutron). Deuterium would then combine with more protons and neutrons to produce helium (containing two protons, two neutrons), lithium and beryllium. About 25% of the protons and neutrons would be converted in helium nuclei together with some small amount of deuterium and heavier elements. The remaining neutrons would decay in protons, the nuclei of ordinary hydrogen.
This theory was developed in 1948 by George Gamow together with Ralph Alpher and, partly, by Hans Bethe. They predicted that radiation -photons- from the very hot early universe are still around today but with a very low temperature (a few degrees above the zero absolute, -273ºC). Penzias and Wilson detected this radiation in 1965.
A few hours after the big bang, no more helium or other elements were produced
and the universe went on expanding without anything special happening for
a few million years.
The temperature continued to decrease and when it went down to a few thousand
degrees, electrons and nuclei had not enough energy to escape the electromagnetic
attraction between them, and they started to combine into atoms.
The universe continued expanding and cooling but, in some denser parts,
the expansion was first slowed down by gravitational attraction, and then
completely stopped. This caused the matter in these regions to start collapsing.
The gravitational forces from outside the regions made the collapsing matter
rotate slowly, then faster and faster as the collapsing regions got smaller.
When the regions became small enough, the spinning effect balanced the gravity
and disk-like rotating galaxies were born.
Other collapsing regions that did not start spinning became oval-shaped elliptical galaxies. In these cases, the regions stopped collapsing because parts of these galaxies went in orbit around their centres of gravity.
With time, the hydrogen and helium gas in the galaxies gathered in small
clouds that collapsed under their own gravity. As a consequence of this
contraction, the atoms collided with each other and the temperature of the
gas increased until it was hot enough to cause nuclear fusion reactions.
These reactions transformed more hydrogen into helium releasing energy and
increasing the temperature that lead to a further increase in gas pressure;
later on the clouds stopped collapsing, and they remained stable for a long
period of time. This is the case of the stars like the sun that go on burning
hydrogen into helium and radiating energy as heat and light.
Bigger stars than the sun need to get hotter to balance their strong gravitational
attraction. The nuclear fusion process inside these big stars went on much
faster and their hydrogen was used in as little as 10E+8 years. They then
contracted a little more and became even hotter. At that point helium started
to convert into heavier elements like carbon and oxygen. As little energy
was released at that stage, the centre of the stars collapsed to a very
dense state -creating neutron stars or black holes- while their outer parts
possibly got blown off by terrible explosions called Supernova. Some of
the heavy elements produced at the end of the star's life are thrown back
into the galaxies' gas providing the base for the next generation of stars.
The sun contents about 2% of these heavier elements because it is a second
or third generation star formed about 5*10E+9 years ago out of a cloud of
rotating gas containing the remains of previous supernovas. Most of the
gas in that cloud formed the sun and the rest was blown away; but a small
quantity of heavier elements gathered together to form the sun's planets,
including the earth.
Initially the earth was very hot and without atmosphere. As it cooled down the gas emission from the rocks created a certain atmosphere. It was different of the present one as it contained no oxygen but, instead, many gas poisonous to us such as hydrogen sulphide. Some primitive forms of life were however able to develop in these conditions, possibly in the oceans where the combination of atoms formed large macromolecules that were able to reproduce themselves and multiply. These were at the base of the evolution, as described by Darwin, that finally led to us, human beings after the atmosphere changed to what it is today.
As it seems likely that the universe started with infinite density at the big bang singularity, the general theory of relativity, and all the other physical laws, break down at that point and we cannot predict what came out of the big bang. In consequence, the big bang, and all possible events occurring before it, must be kept out of the theory. For us, space-time has a boundary, or a beginning, at the big bang. On the other hand we have some laws that, within the limits of the uncertainty principle, allow the scientists to predict how the universe changed with time if we know its state at a given moment after the big bang. But still this does not tell us how the universe began, and why! Was it God who chose the initial state of the universe and its laws? If it is the case, He did not intervene anymore later on, He let the universe run on its own? Or is there a logical explanation that scientists have not yet thought about?
One attempt to do just that is called the "Chaotic Boundary conditions". This theory assumes that the universe is infinite, or that there are an infinite number of universes. From this one deduces that the probability of finding a specific spatial region in one configuration is the same in all configurations. The initial state of the universe is chosen at random, and it must have been very chaotic and irregular because there are many more such chaotic and disordered configurations that there are smooth and ordered ones. But it is difficult to imagine how such a smooth and ordered universe as the one we know could have come from such a chaotic start. We must assume that in these chaotic initial conditions there were some regions that started in a smooth and uniform way, and this could be what happened in ours.
The anthropic principle could be a way to solve the problem of the universe. This principle can be explained simply like this: "We see the universe the way it is because we exist".
The antropic principle is very important and there are two versions:
- The weak "Anthropic Principle" says that in a large or infinite
space/time universe the conditions necessary for the development of intelligent
beings is limited to specific regions in space and time. It explains why
the big bang occurred when it occurred (10E+10 years ago): it takes that
long for intelligent beings to evolve. The first generation of stars converted
part of their hydrogen and helium into heavier elements like carbon and
oxygen (required to make human being, plants, animals, fish,…). These
stars exploded as supernovas, and their components went on forming other
stars and planets (such as the solar system that is about 5*10E+9 years
old). The earth was too hot during the first or even the second 10E+9 years
for any development of complicated molecules but, afterwards, for 3*10E+9
years, the conditions were such that evolution took place, and we are the
latest result of this process. Are we the last? Who knows?
- The strong version of the "Anthropic Principle" states that
there are either many different universes or many different regions in a
single universe, each with its own configuration and, perhaps, its own physical
laws. Only a few of these many universes or regions are right for the development
of life and intelligent beings.
The validity and utility of the weak anthropy principle is generally well accepted but this is not the case of the strong one. If there are different universes separated from each other what happens in another universe cannot be seen, and has no effect on ours, and we should cut them out of our theories. But if there are different regions in a given universe, the laws of science would have to be the same in all regions because, if not, we could not move from one region to another. The only difference between regions would be their initial configuration, and the strong anthropic principle would be reduced to the weak one.
Sciences are based on many fundamental numbers: electric charge of electrons,
the mass of protons in relation to the mass of electrons, etc. These numbers
cannot be derived from known theories, they are experimental data. However,
it could be that one day a more general theory will allow us to confirm
theoretically their values. But it is also possible that their values are
different in each universe or, perhaps, inside different parts of the same
universe. In addition it is a fact that their values, as we know them, were
required to allow the development of life. For instance, if the electrical
charge of the electrons had been even slightly different, stars would not
have been able to burn their hydrogen and helium, or would not have exploded.