Chameleon Field theory 20140076 KIMMUNSIK Physics. Dep INDEX 1. - - PowerPoint PPT Presentation

Chameleon Field theory

20140076 KIMMUNSIK

• Physics. Dep

INDEX

• 1. Introduction – Accelerating expansion of the Universe
• 2. Cosmology constant and its problem
• 3. Quintessence and Chameleon Mechanism
• 4. How to find it?
• 5. Conclusion

Chameleon?

Expansion of the Universe

Hubble’s Law Expanding Universe model Possible model (1) Constant expansion (2) Accelerating expansion (3) Decelerating expansion (4) Vibration model ………

Einstein Field Equation

• Einstein equation
• Friedmann equation from Einstein equation

Mass density and radiation pressure should be positive, the acceleration term should be negative, deceleration model expected.

Acceleration Model

1998, High-z SN Search team and Supernova Cosmology Project

• Accelerating expansion of the universe model is correct.
• Corrected Einstein equation

Where cosmological constant is added to explain “Acceleration feature of the universe”

Acceleration Model

• Equation of the state : w = #

$

Radiation dominant universe case : w=1/3 Non-relativistic matter dominant universe case : w=0

• However, to describe a positive acceleration requires

w<-1/3

Λ CDM concordance Model

• Standard model in Cosmology
• Cosmological constant

Cosmological constant Problem

Quantum fluctuation from any particle in vacuum state. (QM) Vacuum energy was described like this form (associated with Higgs field fluctuation. (CM)

𝜍 ~

Cosmological constant Problem

Can not find the correspond source of the density of the dark energy

However, quantum fluctuation of vacuum is not matched with the density of the dark energy.

The anthropic explanation suggested by Weinberg(1987), 𝜍+ < 10meV 2

Quintessence

• Dark energy as a dynamical process revealing new physics at

the energy scale 𝜍+ ~ 10meV 2.

• Similar with inflation theory.

Acceleration due to energy density of a scalar field

Comparison Inflation Late acceleration Source inflaton Quintessence

Quintessence

• The theory of the gravitational dynamic of a scalar field

Which is the action for gravity and quintessence field 𝜚 : minimal coupling Lagrangian of the scalar field with a generic potential From the variational principle, we can get Einstein equations.

Quintessence

• Einstein’s equation : the response of the metric to a scalar field

Using variational principle

Einstein equation : relation between Einstein tensor and stress-energy tensor of a scalar field

Where, ,

Quintessence

• In the homogeneous Universe, Robertson-Walker metric
• The 00 component of Einstein’s equation reduces to

‘Friedmann equation’

Quintessence

• Using another variational principle :
• The equation of the state

W becomes a dynamic variable!

Using these relations,

Quintessence

• According to the potential V, different cosmology can be

possible

Model Potential form w Standard massive scalar field Ratra and Peeble model

• 1

Quintessence

• Ratra and Peebles suggest the specific potential to make w=-1

How to find the quintessence field?

• 1. Supernovae survay : exact way to find
• 2. Fifth force : If the quintessence field were coupled to dordinary

matter.

• Dimensionless parameter, fine structure constant
• Equivalent principle violation
• etc

The Chameleon

There is a condition to explain the current universe

• Coupling should be very small, much smaller than the gravity

Equivalence Principle :

the gravitational mass and inertial mass are exactly same. Khoury and Weltman (2004) : Chameleon Mechanism

Dark Energy candidate!

The Chameleon Mechanism

• Lagrange density of the scalar field 𝜚 coupled with a fermion ψ

𝛾, the dimensionless constant, corresponds to the strength of the coupling relative to gravity The effective potential can be written :

The Chameleon Mechanism

The mass density of the fermions 𝜍 , not effect on the potential, but on Effective potential

The Chameleon Mechanism

• Review Klein-Gordon equation : Parabolic potential case

The field generated by Static point source -Yukawa potential form :

• The field mediates an interaction between fermions with a range

1/𝜈 Very massive field case, only valid short range!

The Chameleon Mechanism

• Assume the density is uniform everywhere.
• The effective potential is given minimum :

Patra-Peebles potential case : For small perturbation, approximation : Effective mass for the perturbation of the field :

The Chameleon Mechanism

• Effective mass associate with the curvature of the effective

potential at the minimum

• The mass of the field is density dependent - chameleon
• Ex) the Sun, very high density, the field range very small

>> Can not find the effect of the Chameleon

Near the massive mass, chameleon field is hard to see. Low mass density, chameleon field dominate rather than gravity. Therefore this is the source of the Dark energy.

Experiment for searching Chameleon

• 1. Neutron probing strongly coupled chameleons.
• Using slow neutrons – nanometric range Yukawa force detection.
• Neutron interferometry

It is too hard to experiment because the range of the field is too small. In sample sell, the chameleon bubble exists – it should be in vacuum state. Comparing vacuum and air cases, we can find some different scattering pattern if there is Chameleon field.

Experiment for searching Chameleon

• Using torsion pendulum with exquisite sensitivity
• Rotating attractor disk and a torsion pendulum separate few

millimeter.

• Atomic precision tests in the hydrogen atom :
• fields coupled with protons and electrons
• Detecting the coupling with photons :
• Lagrange density term

Modified gravity

• In general framework of modified gravity, action is modified

by putting a scalar field term.

There are many candidates of Dark energy IS IT REALLY EXIST? I DON’T KNOW

Conclusion

• The Dark energy should be exist to explain acceleration

model

• Chameleon mechanism with Quintessence can explain the

Acceleration of the universe.

• It is really hard to search Chameleon in Solar system region
• Gravity constant, neutron interferrometry, and so on

Thank you