From The Big Bang to Dark Energy
- I - From Daily life to the Big Bang
- II - Birth of Elements and Higgs Boson

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.

Table of Contents

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

1.3 - Why Elliptic ?

1.4 - Why does everything fall the same way ?

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

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

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

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

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

1.10 - Cosmic expansion

II - Birth of Elements and Higgs Boson

2.1 - Birth of Elements 1

2.2 - Birth of Elements 2

2.3 - Birth of Elements 3

2.4 - Birth of Elements 4

2.5 - Birth of Elements 5

2.6 - Higgs Boson frozen into the universe 1

2.7 - Higgs Boson frozen into the universe 2

2.8 - Higgs Boson frozen into the universe 3

2.9 - Higgs Boson frozen into the universe 4