Diapositive 1

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Dark Energy High-Energy Physics
Jérôme Martin
Institut dAstrophysique de Paris
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Outline

• Measuring the accelerated expansion
• Quintessence basics
• Implementing Quintessence in high energy physics
• Quintessence and its interaction with the rest
  of the world the
• case of the inflaton field
• Conclusions

References

• P. Brax J. Martin, Phys. Rev. D 71, 063530
  (2005), astro-ph/0502069

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Measuring the expansion with the SNIa
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Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
The Universe is accelerating
The Friedmann equation with pressureless matter
does not describe correctly the observations
5
Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
The Universe is accelerating
J. L. Tonry et al., Astrophys. J 594, 1 (2003),
astro-ph/0305008
The Friedmann equation with pressureless matter
does not describe correctly the observations
W. Freedman M. Turner, Rev. Mod. Phys. 75,
1433 (2003), astro-ph/0308418
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Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
The Universe is accelerating
The Friedmann equation with pressureless matter
does not describe correctly the observations
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Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
Possibility 1
The observations are not correct, e.g. the SNIa
are not standard candels (dust, evolution etc )
The Universe is accelerating
The Friedmann equation with pressureless matter
does not describe correctly the observations
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Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
Possibility 2
Gravity is modified
The Universe is accelerating
New large characteristic scale
The Friedmann equation with pressureless matter
does not describe correctly the observations
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Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
There is a missing
component or the stress-energy tensor is not
correct
Possibility 3
The Universe is accelerating
Possible candidates include

• Cosmological constant
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc

The Friedmann equation with pressureless matter
does not describe correctly the observations
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Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
There is a missing
component or the stress-energy tensor is not
correct
Possibility 3
The Universe is accelerating
The Friedmann equation with pressureless matter
does not describe correctly the observations
The new fluid must have a negative pressure
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Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
There is a missing
component or the stress-energy tensor is not
correct
Possibility 3
The Universe is accelerating
Possible candidates include

• Cosmological constant
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc

The Friedmann equation with pressureless matter
does not describe correctly the observations
12
Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
There is a missing
component or the stress-energy tensor is not
correct
Possibility 3
The Universe is accelerating
Possible candidates include

• Cosmological constant
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc

The Friedmann equation with pressureless matter
does not describe correctly the observations
13
Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
There is a missing
component or the stress-energy tensor is not
correct
Possibility 3
The Universe is accelerating
Possible candidates include

• Cosmological constant
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc

The Friedmann equation with pressureless matter
does not describe correctly the observations
14
Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
There is a missing
component or the stress-energy tensor is not
correct
Possibility 3
The Universe is accelerating
Possible candidates include

• Cosmological constant
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc

The Friedmann equation with pressureless matter
does not describe correctly the observations
15
Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
There is a missing
component or the stress-energy tensor is not
correct
Possibility 3
The Universe is accelerating
Possible candidates include

• Cosmological constant
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc

The Friedmann equation with pressureless matter
does not describe correctly the observations
16
Consequences Remarks
This is a pure kinematical measurement (no
dynamics) of the luminosity distance
There is a missing
component or the stress-energy tensor is not
correct
Possibility 3
The Universe is accelerating
Possible candidates include

• Cosmological constant
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc

The Friedmann equation with pressureless matter
does not describe correctly the observations
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Quintessence
One postulates the presence of a scalar field Q
with a runaway potential and ? 0
If the field is subdominant, there exists a
particular solution such that
NB is the equation of state of the
background fluid, i.e. 1/3 or 0
The field tracks the background and eventually
dominates
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Quintessence
When the field starts dominating the matter
content of the Universe, it leaves the particular
solution. This one can be written as
This happens for
The mass of the field (defined as the second
derivative of the potential) is
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Quintessence
The particular solution is an attractor and is
joined for a huge range of initial conditions
radiation
The attractor is joined
matter
quintessence
The coincidence problem is solved the
acceleration starts recently
The attractor is joined
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Quintessence
The equation of state is a time-dependent (or
redshift -dependent) quantity
The present value is negative and different from
-1. Hence it can be distinguished from a
cosmological constant
Of course, the present value of the equation of
state is also independent from the initial
conditions
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Quintessence
The energy scale M of the potential is fixed by
the requirement that the quintessence energy
density today represents 70 of the critical
energy density
Electroweak scale
The index ? is a free quantity. However, ?
cannot be too large otherwise the equation of
state would be too far from -1 even for the
currently available data
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Quintessence
The evolution of the small inhomogeneities is
controlled by the perturbed Klein-Gordon
equation
WMAP 1 data

Clustering of quintessence only on scales of the
order of the Hubble radius
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High energy physics Quintessence
We address the model-building question in the
framework of Super-gravity. The main purpose is
to test what should be done in order to produce
a satisfactory dark energy model
F-term
D-term
The model is invariant under a group which
factorizes as G U(1)
Fayet-Iliopoulos
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High energy physics Quintessence
To go further, one must specify the Kähler and
super - potentials in the quintessence sector
Q, X, Y. A simple expression for W is
can be justified if the charges of X, Y and Q
under U(1) are 1, -2 and 0
Mass scale cut-off of the effective theory used
There are two important ingredients
no quadratic term in Y, pgt1
no direct coupling between X and Q, otherwise
the matrix is not diagonal
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High energy physics Quintessence
After straightforward calculations, the potential
reads
SUGRA correction
This simple estimate leads to different problems
?
In some sense, the fine tuning reappears
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High energy physics Quintessence
What are the effects of the SUGRA corrections?
1- The attractor solution still exists since,
for large redshifts, the vev of Q is small in
comparison with the Planck mass
2- The exponential corrections pushes the
equation of state towards -1 at small redshifts
3- The present value of the equation of state
becomes universal, i.e. does not depend on ?
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Measuring the (constant) equation of state
WMAP1CBIACBAR
SUGRA
WMAP1CBIACBAR2dF
SNIa 2004
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High energy physics Quintessence
mSUGRA
SUSY
Gravity mediated
Inflaton
Observable sector
Hidden sector
Fifth force test, equivalence principle test etc
Quintessence sector
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Coupling the inflaton to quintessence
The basic assumption is that Q is a test field in
a background the evolution of which is
controlled by the inflaton ? with
COBE WMAP
Typically, the quintessence field is frozen
during inflation
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Coupling the inflaton to quintessence
The basic assumption is that Q and the inflaton
belong to different sectors of the theory. This
means that
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Coupling the inflaton to quintessence
To go further, a model for (chaotic) inflation is
needed. One takes
N.B.
Ratra-Peebles/SUGRA
N.B.
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Coupling the inflaton to quintessence
absolute minimum
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Coupling the inflaton to quintessence
If the quintessence field is a test field, then Q
evolves in an effective time-dependent
potential given by
Slow-rolling inflaton field
The effective potential possesses a
time-dependent minimum
N.B. at the minimum, Q is not light
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Coupling the inflaton to quintessence
The evolution of the minimum is adiabatic
The minimum is an attractor
The effect of the interaction term is important
and keeps Q small during inflation
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Conclusions

• Quintessence is a model of dark energy where a
  scalar field is supposed
• to be responsible for the accelerated expansion
  of the Universe. It has
• some nice properties like the ability to solve
  the coincidence problem.
• The Quintessence equation of state now is not -1
  as for the cosmological
• constant and is red-shift dependent.
• Quintessence is not clustered on scales smaller
  than the Hubble radius.
• Implementing Quintessence in high energy physics
  is difficult and no
• fully satisfactory model exists at present.
• The interaction of Quintessence with the rest of
  the world is non trivial
• and can lead to interesting phenomena and/or
  constraints.

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Quantum effects during inflation
The quantum effects in curved space-time can be
computed with the formalism of stochastic
inflation.
Window function
Only contains short wavelength modes because of
the window function
Coarse-grained field, averaged over a Hubble
patch contains long-wavelength modes
The window function does not vanish if
Hubble patch
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Quantum effects during inflation
The evolution of the coarse-grained field is
controlled by the Langevin equation
The coarse-grained field becomes a stochastic
process
quantum noise, sourced by the short wavelength
modes
Classical drift
For the free case, one can check that one
recovers the standard result
Brownian motion
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Quantum effects during inflation
The quintessence field during inflation is also
controlled by a Langevin equation
Quintessence noise
Depends on the inflaton noise
The solution to this equation allows us to
compute the mean value of the Quintessence field
N.B. The inflaton noise does not play an
important role
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Quantum effects during inflation

• The confidence region enlarges with the power
  index ?
• A small number of total e-foldings is favored