====== From The Big Bang to Dark Energy ======

===== I - From Daily life to the Big Bang =====

==== 1.1 - Night and Day and Four seasons ====

==== 1.2 - Revolution of the Earth ====

  * A good physicall theory should:
    * Agree with observations/experiments.
    * Provide an unified description.
    * Be simple.

==== 1.3 - Why Elliptic ? ====

  * Universal gravitation formula from Newton: \(F = G \frac{M \cdot m}{r^2} \).
  * We also have \(F=m \cdot \vec{a}\)
  * When combining those two equations we can fully explain the elliptical motion of the planets.
  * Earth revolves around the sun at 30km/s.

  * If we consider a circular orbit approximation (which is actually not too bad), then, we have:
    * \(F = -G \frac{M \cdot m}{r^2} \)
    * The centrifuge force gives us: \(F = \frac{m \cdot v^2}{r} \).
    * When combining these we get the approximate orbital speed: \( v = \sqrt{\frac{GM}{r}} \).
    * So outer planets are moving more slowly.


==== 1.4 - Why does everything fall the same way ? ====

  * On the surface of the earth the acceleration is: \(a = -G\frac{M}{R^2}\).
  * In general relativity the mass doesn't really matter because is important part is rather on the curvation of space: eg. gravity seems to be an **illusion** from that perspective.
  * When trying to compute the escape velocity for a black hole we get the result: \(c^2 = \frac{2GM_{BH}}{R} \).
  * For the mass of the sun we find that the limit radius as described above would be R=2.95km.

==== 1.5 - Beginning of the universe, Look far into the past 1 ====

  * Earth-Moon distance is 380000km (eg. 1.3 light seconds)
  * Earth-Sun distance is 8.3 light minutes (eg. 1.5 10^8 km).
  * Voyager is at 16 light hours (it left the solar system already).
  * Our solar system is moving at 220Km/s around the center of the galaxy.
  * The black hole at the center of our galaxy is 4 million times bigger than our sun.

==== 1.6 - Beginning of the universe, Look far into the past 2 ====

  * All the **rotation curves** of galaxies that we have measured so far all look pretty flat: eg the speed of revolution doesn't decrease with the distance from the center of the galaxy.
  * It would seem that galaxies are surrounded by dark matter.

==== 1.7 - Beginning of the universe, Look far into the past 3 ====

  * See: Sloan Digital Sky Survey
  * **Dark ages** is when we observe the universe at 13.6 billion light years : universe was too young to create a star at that time, so, there is no star at all.


==== 1.8 - Beginning of the universe, Look far into the past 4 ====

==== 1.9 - Beginning of the universe, Look far into the past 5 ====

  * The background noise left from the big bang is actually due to light "stretched" to radio lengths. (eg. microwaves)
  * This is called the **cosmic microwave background** (CMB).
  * Age of the universe: 13.8B lyrs.
  * The initials of Stephen Hawkings are written into the picture of the universe.

==== 1.10 - Cosmic expansion ====

===== II - Birth of Elements and Higgs Boson =====

==== 2.1 - Birth of Elements 1 ====

==== 2.2 - Birth of Elements 2 ====

  * The sun is getting lighter by 4 million tons every second. (Because of E=mc2 equation).
  * The Sun will take 4 protons, and produce one helium atom (2 protons + 2 neutrons) with 2 positrons and also 2 neutrino and 25 MeV of energy.
  * The Helium atom and the 2 positrons weight less that the initial 4 protons (so part of the initial mass is converted into energy in the process).
  * A hundred trillion neutrinos are going through our body every second.

==== 2.3 - Birth of Elements 3 ====

  * By capturing neutrinos we can take a "picture" of the center of the sun. (from some tank buried under a mountain in japan !).
  * More info can be found at: http://www-sk.icrr.u-tokyo.ac.jp/sk/detector/detail-e.html
  * The sun is actually going to last 4.5 billion years.

==== 2.4 - Birth of Elements 4 ====

  * In a supernovae, 99% of the energy is released as neutrinos.

==== 2.5 - Birth of Elements 5 ====

  * Our sun is probably a third generation star.
  * Betelgeuse in the orion constallation weights about 20x the mass of our sun and it is about to explode soon...
  * There is a ratio of 3:1 for Hydrogen / Helium produced at the big bang.
  * Heavier elements than iron might have been created during supernovae (but this is not sure at all).

==== 2.6 - Higgs Boson frozen into the universe 1 ====

  * The Higgs Boson was discovered lately in the **Large Hadron Collider** (LHC).

==== 2.7 - Higgs Boson frozen into the universe 2 ====

  * To claim for an evidence we only require "\(3\sigma\)" of precision (eg. 99.7%).
  * To claim for a **discovery** we require "\(5\sigma\)" of precision (eg. 99.99994%). (based on normal distribution)
  * The kinetic energy of the quarks is what we are measuring as the mass of a proton.

==== 2.8 - Higgs Boson frozen into the universe 3 ====

  * The electromagnetic force and the weak force are very similar: there was a symetry between them, but somehow, the symetry got lost (spontanous symetry breaking) and thus is not valid anymore in the current universe.
  * The higgs boson froze in the universe at about 4 quadrillion degrees.

==== 2.9 - Higgs Boson frozen into the universe 4 ====