Introduction to Mathematical Physics/N body problem and matter description/Origin of matter

\index{matter (origin of)}\index{origin of matter} The problem of the creation of the Universe is an open problem. Experimental facts show that Universe is in expansion[1] Inverting the time arrow, this leads to a Universe that has explosive concentration. In 1948, an ingenious physicist named Gamow, proposed a model known as, Big Bang model\index{Big Bang model}, for the creation of the Universe. When it was proposed the model didn't receive much attention, but in 1965 two engineers from AT\&T, Penzias and Wilson[2] , trying to improve communication between earth and a satellite, detected by accident a radiation foreseen by Gamow and his theory: the 3K cosmic background radiation \index{cosmic background radiation}. In 1992, the COBE satellite (COsmic Background Explorer) recorded the fluctuations in the radiation (see figure figcobe), which should be at the origin of the galaxy formation as we will see now.

figcobe

The Big Bang model states that the history of the Universe obeys to the following chronology[3]:

• During the first period (from $t=0$ to $t=10^{-6}$ s), universe density is huge (much greater than the nucleons density)[4] It's behaviour is like a black hole. Quarks may exist independantly.
• The hadronic epoch[5], (from $t=10^{-6}$, $T=1$GeV (or $T=10^{13}$K) to $t=10^{-4}$ s, $T=100$ MeV), the black hole radiation creates hadrons (particle undergoing strong interaction like proton, neutrons), leptons (particle that undergo weak interaction like electrons and neutrinos[6]) and photons. The temperature is such that strong interaction can express itself by assembling quarks into hadrons. During this period no quark can be observe independantly.
• During the leptonic epoch, (from $t=10^{-4}$ s, $T=100$ MeV to $t=10$ s, $T=1$MeV) hadrons can no more be created, but leptons can still be created by photons (reaction $\gamma \leftrightarrow e^+ + e^-$). The temperature is such that strong interaction can express itself by assembling hadrons into nuclei. Thus indepandant hadrons tend to disappear, and typically the state is compound by: leptons, photons, nuclei[7].
• From $t=10$ s, $T=1$MeV to $t=400,000$ years, $T=1$eV (or $T=3,000$K), density and temperature decrease and Universe enter the photonic epoch (or radiative epoch). At such temperature, leptons (as electrons) can no more be created. They thus tend to disappear as independant particles, reactionning with nuclei to give atoms (Hydrogen and helium) and molecules[8] (H$_2$). The interaction involed here is the electromagnetic interaction (cohesion of electrons and nuclei is purely electromagnetic). Typically the state is compound by: photons, atoms, molecules and electrons. The radiative epoch ends by definition when there are no more free electrons. Light and matter are thus decoupled. This is the origin of the cosmic background radiation. Universe becomes "transparent" (to photons). Photons does no more colide with electrons.
• From $t=400,000$ years, $T=1$eV (or $T=3,000$K) untill today ($t=1.5 10^{10}$ years, $T=3$K), Universe enters the stellar epoch. This is now the kingdom of the gravitation. Because of (unexplained) fluctuations in the gas density, particles (atoms and molecules) begin to gather under gravitation to form prostars and stars.

Let us now summerize the stellar evolution and see how heavier atoms can be created within stars. The stellar\index{star} evolution can be summerized as follows:

• Protostar : As the primordial gas cloud starts to collapse under gravity, local regions begin to form protostars, the precursors to stars. Gravitational energy which is released in the contraction begins to heat up the centre of the protostar.
• Main sequence star: gravitational energy leads the hydrogen fusion to be possible. This is a very stable phase. Then two evolutions are possible:
• If the mass of the star is less that $1.4$ (the Chandrasekhar[9] limit)\index{Chandrasekhar limit} the mass of the sun,
• The main sequence star evolves to a red giant star . \index{red giant star} The core is now composed mostly of helium nuclei and electrons, and begins to collapse, driving up the core temperature, and increasing the rate at which the remaining hydrogen is consumed. The outer portions of the star expand and cool.
• the helium in the core fuses to form carbon in a violent event know as the helium flash \index{helium flash}, lasting as little as only a few seconds. The star gradually blows away its outer atmosphere into an expanding shell of gas known as a planetary nebula \index{planetary nebula}.
• The remnant portion is known as a white dwarf \index{white dwarf}. Further contraction is no more possible since the whole star is supported by electron degeneracy. No more fusion occurs since temperature is not sufficient. This star progressively cooles and evolves towards a black dwarf star .
• If the mass of the star is greater that $1.4$ the mass of the sun,
• When the core of massive star becomes depleted of hydrogen, the gravitational collapse is capable of generating sufficient energy that the core can begin to fuse helium nuclei to form carbon. In this stage it has expanded to become a red giant, but brighter. It is known as a supergiant \index{supergiant star}. Following depletion of the helium, the core can successively burn carbon, neon, etc, until it finally has a core of iron, the last element which can be formed by fusion without the input of energy.
• Once the silicon has been used the iron core then collapses violently, in a fraction of a second. Eventually neutron degeneracy prevents the core from ultimate collapse, and the surface rebounds, blowing out as fast as it collpased down. As the surface collides with the outer portions of the star an explosion occurs and the star is destroyed in a bright flash. The material blown out from the star is dispersed into space as a nebula. The remnants of the core becomes
• If the mass of the star is less than $3$ sun's mass, star becomes a neutron star \index{neutron star}. The core collapses further, pressing the protons and electrons together to form neutrons, until neutron degeneracy stablilises it against further collapse. Neutron stars have been detected because of their strange emission characteristics. From the Earth, we see then a pulse of light, which gives the neutron star its other name, a pulsar \index{pulsar}.
• If the mass of the star is greater than $3$ sun's mass, star becomes a black hole \index{black hole}. When stars of very large mass explode in a supernova, they leave behind a core which is so massive (greater than about 3 solar masses) that it cannot be stabilized against gravitational collapse by an known means, not even neutron degeneracy. Such a core is detined to collapse indefinitely until it forms a black hole, and object so dense that nothing can escape its gravitational pull, ot even light.

Let us now start the listing of matter forms observed at a super nuclear scale (scale larger than the nuclear scale).

1. The red-shift phenomenon was summerized by Hubble in 1929. The Hubble's law states that the shift in the light received from a galaxy is proportional to the distance from the observer point to the galaxy.
2. They received the physics Nobel price in 1978
3. Time origin corresponds to Universe creation time
4. Describing waht compounds Universe at during this period is a challenge to human imagination.
5. Modern particle accelerators reach such energies. The cosmology, posterior to $t=10^{-4}$ s is called "standard" and is rather well trusted. On the contrary, cosmology before the hadronic period is much more speculative.
6. Neutrinos are particles without electric charge and with a very small mass so that on the contrary to electrons they don't undergo electrostatic interaction.
7. Note that heavy nuclei are not created during this period, as it was believed some years at the beginning of the statement of the Big band model. Indeed, the helium nucleus is very stable and prevents heavier nuclei to appear. Heavier nuclei will be created in the stellar phase by fusion in the kernel of the stars.
8. As for the nuclei, not all the atoms and molecules can be created. Indeed, the only reactive atoms, the hydrogen atom (the helium atom is not chemically reactive) gives only the H$_2$ molecule which is very stable.
9. The Indian physicist Subrehmanyan Chandrasekhar received the physics Nobel price in 1983 for his theoretical studies of the structure and evolution of stars.