Neutrino Model of Dark Energy

Yong-Yeon Keum

Academia Sinica/Taiwan

Mujuresort, Feb./16-19/2005

ContentsContents

Experimental evidence of accelerating universe

Candidates of Dark Energy

Neutrino Model of Dark Energy

Lesson from FKNW model (An example of interacting dark matter and

dark energy model)

Experimental Observations(1)Experimental Observations(1)

Experimental Observation(2)Experimental Observation(2)

Our universe is flat, accelerating. The dominance of a dark energy component with negative

pressure in the present era is responsible for the universe’s accelerated expansion.

Accelerating UniverseAccelerating Universe

Cosmological Constant Problem: Why is the energy of the vacuum so much small ?

Dark Energy Puzzle: What is the nature of the smoothly-distributed, persistent

energy density which appears to determine the universe.

Coincidence Scandal: Why is the dark energy density approximately equal to

the matter density today

Candidates of Dark EnergyCandidates of Dark Energy

(A) Cosmological Constant (consntant)(B) Dynamical Cosmological Constant

(Time-dependent; Quintessence field)

(C) Modified Gravity (Modified Friedmann Eq.)

(A) Cosmological Constant(A) Cosmological Constant

Typical scale ：

Hence a new energy density scale is too low

from the particle physics point of view.

2 42 20 (10 )H GeV

22 2 40

0 )8 P

N

HM H eV

G

4)particle GeV

8 NG g G T

Cosmological constant problemCosmological constant problem

Many different contributions to vacuum energies:

(a) QCD ~ Digression to particle physics and the vacuum energy

problem

(b) EW physics ~ (c) GUT ~

(d) SUSY ~

All these contributions should conspire to cancel down to . Extreme fine tuning !!!

4(1 )GeV

16 4(10 )GeV3 4(10 )GeV

4 4(10 )GeV

2 4(10 )GeV

( B ) Quintessence( B ) Quintessence

Quintessence = dark energy as a scalar field = dynamical cosmological constant

No evidence for evolving smooth energy, but attractive reasons for dynamical origins !

(a) why small, why not zero, why now ??? (b) suggest the physical cosmological evolution. Canonical quintessence:

2

3(1 )

1, ( )

2( )

3 0, 3 ( ) 0

( 1)

K V

dVH H p

d

p a

Quintessence (2)Quintessence (2)

If potential energy dominates over the kinetic energy

This type of potential is not so easy to stabilize w.r.t.quantum loop corrections.

2 2

0

0 4 40

1 1( ); ( )

2 2

1 ( )

1 1( ) ( ) [ 3(1 ) ]

2 2

(10 )

P

P c

V p V

paccelerating

V V ExpM

M V eV

( C ) Modified Gravity( C ) Modified Gravity Newtonian Cosmology: Gravitational Force law determines the

evolution

Combining the above eqs:

Moreover, E = constant and decelleration !!

2

34

3( )

N

F MR G

m R

M R

R a t r

4( )

3 N

aG t

a

33

2/3

4 1

3

0

E M Ra

a t a

Modified ForceModified Force

For simplicity g=1

(1) Early times t << tc so that

matter domination, no acceleration

(2) Later time, t > tc when

Accelerated expansion !!!

22

2

3

( )

4( ) ,

3

( ) 0

Nc

N c

G MFR m Rg R

m R

R G R m g R R

d a

2 2/34, ~

3N c NG m R G R a t

2 2 2, ~ , ~ 0!!!cm tN c c cG m R m R a e a m

Neutrino Model of Dark EnergyNeutrino Model of Dark Energy

Cosmological constant:

What physics is associated with this small energy scale ?? It is clearly a challenge to understand dynamically how the

small energy scale associated with dark-energy(DE) density aries and how it is connected to particle physics.

33 2 2 40

0

4 4 )

( ) 1

(1.5 0.1) 10 , )

N DE N DE

DE DE

DE P o

G G p p

p

Since H x eV M H eV

E eV

Interacting dark energy modelInteracting dark energy model

FNW scenarioFNW scenario

Fardon, Nelson and Weiner suggested that tracks the energy density in neutrinos

The energy density in the dark sector has two-components:

The neutrinos and the dark-energy are coupled because it is assumed that dark energy density is a function of the mass of the neutrinos:

DE

( )m m n

dark DE

( )DE DE n

Since in the present epoch, neutrinos are non-relativistic (NR),

Assuming dark-energy density is stationary w.r.t. variations in the neutrino mass,

Defining

( )dark DEm n m n m

( )0

3 ( )

dark DE mnm m

H p

,

1

dark

dark

dark dark DE DE

dark DE

p

p p p

m n m n

m n