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

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