1. Formation of universe, blackhole and 1st order phase transition

2. Idea
Last time I focused on the relation between particle production, phase transition and black hole
To understand dark energy I studied cosmology, then studied inflation, black hole and bubble nucleation.

3. Key idea Key idea particle production ~ universe formation
~ black hole formation ~ first order phase transition (bubble nucleation)
Further key words
surface tension , cosmological constant , entropy , pressure

4. Particles, Black hole and phase transition
Particle production – Phase transition
- Higgs mechanism can be described as a phase transition.
Particle – Black hole
- Black hole can only have three own properties; Mass, angular momentum and charge (which is same with indistinguishable quantum particle)
- In QFT, particle considered as a point particle. If a energy concentrated on a point, it should be a black hole.
- Recent AdS/CFT says that black hole in bulk Ads space can correspond to gauge field particle at boundary
Black hole –phase transition
- Black hole have thermodynamic properties. It’s formation can also be described with phase transition

5. Bubble nucleation and 1st order phase transition

6. Bubble nucleation and 1st order phase transition
Metastable, false vaccum
Thermal fluctuation,
Energy fluctuation,
Quantum fluctuation

7. Surface tension of bubble

8. Energy of a bubble Shrink Grow releasing latent heat
The probability of a bubble
to appear spontaneously in the heat bath in equilibrium at temperature T

9. Inflation

10. Expanding Universe model
Robertson-Walker Metric
Conformal time
- Hubble parameter

11. Friedmann Equation
Continuity Equation
Friedmann Equation

12. Components of universe

13. First order phase transition, inflation and inflaton
Inflation of universe can be explained with a 1-nd order phase transition
(Why not 2-nd order phase transition?
Phase translate smoothly => no bubble, no boudary
Inflaton : The inflaton field is a hypothetical scalar field that is theorized to drive cosmic inflation in the very early universe.

14. The stress-energy tensor of the scalar field
Friedmann equation

15. Parameters of Inflation
Slow-roll approximation

16. Reheating Reheating Inflaton decay.
- Inflation ends when the potential steepens and the inflaton field picks up kinetic energy. The energy in the inflaton sector then has to be transferred to the particles of the Standard Model. This process is called reheating and starts the Hot Big Bang.
Inflaton decay.
- To avoid that the universe ends up empty, the inflaton has to couple to Standard Model fields. The energy stored in the inflaton field will then be transferred into ordinary particles.

17. Higgs field as a inflaton
Can Higgs field potential can be inflaton potential?
Original version of Higgs potential can not be a inflaton, because it correspond to second order phase transition potential.
There several modification Higgs potential as a inflaton. -> if it lagrangian have odd orders of field, or if there are other scalar field, first order phase trasition possible.

18. Do we live in a black hole?

19. Do we live in a black hole?
There several papers guessing that we might be in a black hole. (We are live in a black hole, or our universe is a black hole)
Original black hole have a mass sigurarity at the center, and vaccuum at the all of other spacetime position. (If some mass density is higher than some point, it collapes to a sigularity)
However if there is a negative pressure that defence collapsing to sigularity, black hole can have finite density.
Or other way, in a black hole role of space coordinate and time coordinate changes. Singularity can be interpreted as a time singularity like big bang.

20. Black hole formation and bubble nucleation
How does the black hole forms? What is the mechanism of increasing of black hole?
There are possibility that black hole formation also can be described using bubble nucleation

21. Surface tension of Black hole
If we regard black as a vacuum bubble, we might think that the surface tension of it. (Originally, black hole only have a surface gravity)
Relation between surface tension and difference of pressure

22. Surface tension and black hole
Surface tension ~ Surface gravity ~ Black hole Entropy ?
There also some papers that make a relation surface tension and cosmological constant.
It can be interpreted that it is related to kind of entropic force.

23. Black hole increasing speed
Increasing black hole in vacuum is similar to increasing universe by vacuum energy.

24. Some ideas
Density of black hole which have 100millions mass is similar to density of water.
The bigger the black hole is, the lower the density is.
A super massive black hole is a source of dark matter?

25. Black hole radius = Hubble radius
Data analytical fact
Schwartschilds radius with universe mass
= Hubble radius of universe
-> our universe is a black hole?
If we assume that our universe is a black hole, flatness problem can be solved.

26. Universe Black hole and flatness problem
known fact
If we assume that the universe is a black hole,
=> Flatness problem can be solved

27. Universe Mass = Black hole Mass
If we assume that our universe is a black hole,

28. Multiverse and bubble like universe

30. Meaning of Lagrangian

31. Meaning of Lagrangian Dimension of Unit
=> [Lagrangian density]=[Energy density]=[Pressure]
In fluid mechanics,
Pressure for ‘Incompressible fluid’
= Hydrostatic Pressure + Hydrodynamic Pressure
Hydrostatic Pressure = Pressure for maintaining that state
Hydrodynamic Pressure = Pressure for making kinetic flow

32. Claim
Potential Energy = Compressed energy (by external force) => Force(Pressure) for getting out that state
(or the resistance to the outside when viewed from the inside of the system.)
(-Potential Energy) = Force to prevent particles from escaping out of the system. (Pressure for keeping)
Lagrangian = Resistance or pressure which particle receiving.
For example, pressing and moving your finger with the rubber plate increases the resistance (pressure) felt on your finger. That is, pressing pressure correspond to potential energy, and moving pressure correspond the kinetic energy.

33. Thank you

34. Consideration
When the rate of change of x is proportional to –x

36. Thank you