Neutrino Model of Dark Energy
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Neutrino Model of Dark Energy
Yong-Yeon Keum
Academia Sinica/Taiwan
Mujuresort, Feb./16-19/2005
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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)
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Experimental Observations(1)Experimental Observations(1)
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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.
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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
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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.)
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(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
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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
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( 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
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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
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( 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
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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
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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
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Interacting dark energy modelInteracting dark energy model
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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
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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
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