Dark Energy

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Dark Energy

• Shinji Tsujikawa (?? ??)
• Tokyo University of Science (??????)

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Dark energy
Observations suggest that more than 70 of the
energy density of the current universe is dark
energy that gives an accelerated expansion.
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The energy components in the present universe
72 Dark Energy Negative pressure
Responsible for cosmic acceleration
23 Dark Matter Pressure-less dust
Responsible for the growth of large-scale
structure
4.6 Atoms
Responsible for our existence!
0.01 Radiation
Remnants of black body radiation
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Equation of state
Energy fraction
Supernova Ia
Cosmic microwave background
Large-scale structure
The current universe is accelerating!
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Negative pressure P of dark energy
pressure
Equation of state
energy density
Friedmann equation
Continuous equation
When w is constant
accelerated expansion

exponential expansion
(Cosmological constant)
is a constant
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Current observational constraints on dark energy
(for constant w)
Komatsu et al (2008)
(95 confidence level)
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Observational evidence for dark energy
The existence of dark energy is supported by

• Supernovae Ia (SN Ia)
• The age of the oldest stars
• Cosmic Microwave background (CMB)
• Baryon oscillations
• Large-scale structure (LSS)
• etc

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Supernovae observations
The luminosity distance
L
The absolute luminosity of a source
s
F observed flux
is used for the distance measure of SN Ia
observations.
Kgt0 closed K0 flat Klt0 open
and
where
For z ltlt 1 we have
In the presence of dark energy with the
luminosity distance gets larger.
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The luminosity distance
Flat universe with dark energy
Open universe without dark energy
Flat universe without dark energy
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Perlmutter et al and Riess et al (1998)
They showed that cosmological constant is present
at the 99 confidence level.
(Perlmutter et al)
The rest is dark energy.
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More data over the past 10 years
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The age of the oldest stars (globular clusters)
Cosmic age
where
In the flat Universe without dark energy we have
Smaller than the age of the oldest stars (Cosmic
age problem)
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Flat universe with cosmological constant
Cosmic age gets larger in the presence of
cosmological constant.
(age problem is solved)
The WMAP bound
for h0.70
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Cosmic Microwave Background (CMB)
Dark energy affects the CMB temperature
anisotropies in two ways

• The change of the position of acoustic peaks
• The Integrated Saches Wolfe (ISW) effect

ISW effect
Larger
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The change of the position of acoustic peaks
The characteristic angle of the first peak is
Sound horizon
Comoving angular diameter distance
The multipole moment that corresponds to this
angle is
(CMB shift parameter)
where
decreases for larger
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Observational bound on
(WMAP 5-yr data)
For w -1 we have
DE
CMB data alone do not provide strong
constraints on dark energy.
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ISW effect on the CMB
Perturbed metric
The l-th multiple moment of the present
temperature anisotropy is
(Hu and Sugiyama, 1995)
_____________________________
ISW contribution
Non-negligible when the gravitational potentials
vary.
Only the large-scale modes with low l contribute
to the ISW effect.
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Baryon acoustic oscillations (BAO)
Before the recombination, baryons are tightly
coupled to photons.
The oscillations of the sound wave are imprinted
in baryon oscillations as well as CMB
anisotropies.
In 2005 Eisenstein et al found baryon
oscillations in the large-scale
correlation function measured from 46, 748
luminous galaxies.
This provides another independent test of dark
energy.
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In the presence of dark energy the gravitational
potentials vary.
Accelerated epoch
ISW effect
However this is not powerful enough to place
constraints on the property of dark energy.
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Percival et al. obtained the following quantity
at two redshifts from the 2dF survey
where
(The redshift at which baryons are released
from photons)
comoving angular diameter distance
The observational constraint is
Useful to constrain the nature of dark energy
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)
The BAO distance ratio
(
The BAO data supports the presence of
cosmological constant.
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Combined analysis of CMB, SNIa and BAO for
constant equation of state of dark energy
(95 confidence level)
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What is the origin of dark energy?
The simplest candidate Cosmological constant
However this suffers from a fine-tuning problem
if it originates from vacuum energy.
Many other dark energy models
Quintessence, k-essence, chaplygin gas, tachyon,
phantom, f (R) gravity, scalar-tensor theories,
Braneworld,
These models generally give the dynamically
changing equation of state w.
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Simplest model of dark energy
Cosmological constant
(Equation of state )
This corresponds to the energy scale
If this originates from vacuum energy in particle
physics,
Huge difference compared to the present value!
Cosmological constant problem
(known even before the discovery of dark energy)
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Many other models of dark energy
There are two approaches to dark energy.
(Einstein equations)

(i) Modified gravity
(ii) Modified matter
f(R) gravity models, Scalar-tensor
models, Braneworlds, ..
Quintessence, K-essence, Tachyon, Chaplygin
gas, ..
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Example of modified matter models
Quintessence (fifth matter)
X matter
Chiba, Sugiyama, Nakamura (1997)
Quintessence
Caldwell, Dave, Steinhardt (1998)
Cosmic acceleration is realized by the potential
energy of a slow-rolling scalar field (like
cosmic inflation)
There are some pioneering works before 1997.
Fujii (1982), Wetterich (1988), Ratra and Peebles
(1988)
They discussed cosmological dynamics in the
presence of a scalar field and matter.
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Quintessence French wine!
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Potential of quintessence
Energy density
Pressure
The equation of state is
phantom
Quintessence
In the slow-roll limit
we have
Cosmic acceleration is realized for a flat
potential.
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Tracking condition
If the quantity
decreases, the energy density
of the scalar field dominates over a background
fluid at late times.
This condition translates into
The exponential potential
gives a border of acceleration and decceleration.
For the potential that is flatter than the
exponential, e.g.,
Tracking occurs at late times and cosmic
acceleration is realized.
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Potential
(Caldwell et al)
The field mass squared
The Hubble parameter
The accelerated stage
(present field)
for
Compatible with the energy scale in particle
physics
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Difficulty of quintessence
To get the present acceleration, most of these
models are based upon scalar fields with a very
light mass

• In super-symmetric theories the flatness of the
  potential is
• easily spoiled by loop corrections to the
  potential.
• (Kolda and Lyth)

• The quintessence field should interact with
  standard model
• particles because of a light mass (Carroll).

It is still a challenge to construct viable
quintessence models in the framework of particle
physics.
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Phantom scalar fields
The observations allow the equation of state
Quintessence does not give rise to this equation
of state.
It is possible to have if the
kinetic energy of the scalar field is negative.
However phantom fields are generally plagued by
severe UV quantum instabilities. The vaccum is
unstable against the chatestrophic production of
ghosts and normal fields.
The negative kinetic energy is problematic !
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Modified gravity models
1. f(R) gravity
2. Scalar-tensor theories

• DGP Braneworld models (a brane embedded in a
• 5-dimensional Minkowski bulk)

In some of these models it is possible to have w
lt -1 without having the instability problem of a
vacuum.
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Modified gravity models can be generally more
strongly constrained compared to modified matter
models.
1. Modifying gravity leads to the change of
Newtons law.
Models are constrained by local gravity tests,
e.g., Solar-system tests and the violation of
equivalence principle.
2.
The evolution of the matter perturbation is also
modified.
___
Modified in f(R) gravity 4/3 times compared to
GR
This leads to changes of the matter power
spectrum as well as the spectrum of weak
lensing.
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Current status of modified gravity
1. f(R) gravity
After the burst of activities over the past 5
years, many forms of f(R) have been excluded.
Viable form
for
2. Scalar-tensor gravity
Fine as long as the scalar-field coupling with
Ricci scalar is not so strong.
3. DGP braneworld
Under strong observational pressure.
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Future prospects for dark energy
Currently all observational data are consistent
with the LCDM model (w-1)
It is important to find some observational
evidence for the deviation from the LCDM model.
where
If observations are accurate enough to measure
the expansion rate H, it is possible to get
precise evolution of w. Also the evolution of
perturbations is important to place constraints
on dark energy.
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Future observations
1. Supernovae Ia
More data will come in high z regime.
2. CMB
Well established, but should be more refined
(Planck etc).
3. BAO
The information coming from the separation of
radial and its orthogonal direction will be
important.
4. Weak lensing
This will provide accurate information of matter
perturbations.
5. Gamma Ray Burst
Still preliminary, but can be very important in
future.
Lets hope to find some evidence for the
deviation from the LCDM model !