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 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 , 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.

The Big Bang model states that the history of the Universe obeys to the following chronology : Let us now summerize the stellar evolution and see how heavier atoms can be created within stars. The stellar\index{star} evolution can be summarized as follows: Let us now start the listing of matter forms observed at a super nuclear scale (scale larger than the nuclear scale).
 * During the first period (from $$t=0$$ to $$t=10^{-6}$$ s), universe density is huge (much greater than the nucleons density) Its behaviour is like a black hole. Quarks may  exist independently.
 * The hadronic epoch, (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 ) 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 independently.
 * 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 independent hadrons tend to disappear, and typically the  state is compound by: leptons, photons, nuclei.
 * 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 independent particles, reacting with nuclei to give  atoms (hydrogen and helium) and molecules (H$$_2$$). The  interaction involved 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) until 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.
 * 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   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 collapsed 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 destined to collapse indefinitely until it  forms a black hole, and object so dense that nothing can escape its  gravitational pull, ot even light.
 * 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 collapsed 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 destined to collapse indefinitely until it  forms a black hole, and object so dense that nothing can escape its  gravitational pull, ot even light.
 * 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 destined to collapse indefinitely until it  forms a black hole, and object so dense that nothing can escape its  gravitational pull, ot even light.
 * 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 destined to collapse indefinitely until it  forms a black hole, and object so dense that nothing can escape its  gravitational pull, ot even light.
 * 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 destined to collapse indefinitely until it  forms a black hole, and object so dense that nothing can escape its  gravitational pull, ot even light.
 * 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 destined to collapse indefinitely until it  forms a black hole, and object so dense that nothing can escape its  gravitational pull, ot even light.