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Dark Energy & High-Energy
Physics
Jérôme Martin
Institut d’Astrophysique de Paris
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. Lett. B, 40 (1999), astro-ph/9905040
• P. Brax & J. Martin, Phys. Rev. D 61, 103502 (2000), astro-ph/9912046
• P. Brax , J. Martin & A. Riazuelo, Phys. Rev. D 62, 103505 (2000), astro-ph/0005428
• P. Brax , J. Martin & A. Riazuelo, Phys. Rev. D 64, 083505 (2001), hep-ph/0104240
• J. Martin & M. Musso, Phys. Rev. D, to appear, astro-ph/0410190
• P. Brax & J. Martin, Phys. Rev. D 71, 063530 (2005), astro-ph/0502069
Measuring the expansion with the SNIa
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
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]
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
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
Possibility 1:
The observations are not correct,
e.g. the SNIa are not standard
candels (dust, evolution etc …)
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
Consequences & Remarks
This is a pure kinematical
measurement (no dynamics)
of the luminosity distance
Possibility 3: There is a missing
component or the stress-energy
tensor is not “correct”
The Universe is accelerating
Possible candidates include …
• Cosmological constant
The Friedmann equation
with pressureless matter
does not describe correctly
the observations
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc …
Consequences & Remarks
This is a pure kinematical
measurement (no dynamics)
of the luminosity distance
Possibility 3: There is a missing
component or the stress-energy
tensor is not “correct”
The Universe is accelerating
The Friedmann equation
with pressureless matter
does not describe correctly
the observations
The new fluid must have a
negative pressure
Consequences & Remarks
This is a pure kinematical
measurement (no dynamics)
of the luminosity distance
Possibility 3: There is a missing
component or the stress-energy
tensor is not “correct”
The Universe is accelerating
Possible candidates include …
• Cosmological constant
The Friedmann equation
with pressureless matter
does not describe correctly
the observations
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc …
Consequences & Remarks
This is a pure kinematical
measurement (no dynamics)
of the luminosity distance
Possibility 3: There is a missing
component or the stress-energy
tensor is not “correct”
The Universe is accelerating
Possible candidates include …
• Cosmological constant
The Friedmann equation
with pressureless matter
does not describe correctly
the observations
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc …
Consequences & Remarks
This is a pure kinematical
measurement (no dynamics)
of the luminosity distance
Possibility 3: There is a missing
component or the stress-energy
tensor is not “correct”
The Universe is accelerating
Possible candidates include …
• Cosmological constant
The Friedmann equation
with pressureless matter
does not describe correctly
the observations
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc …
Consequences & Remarks
This is a pure kinematical
measurement (no dynamics)
of the luminosity distance
Possibility 3: There is a missing
component or the stress-energy
tensor is not “correct”
The Universe is accelerating
Possible candidates include …
• Cosmological constant
The Friedmann equation
with pressureless matter
does not describe correctly
the observations
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc …
Consequences & Remarks
This is a pure kinematical
measurement (no dynamics)
of the luminosity distance
Possibility 3: There is a missing
component or the stress-energy
tensor is not “correct”
The Universe is accelerating
Possible candidates include …
• Cosmological constant
The Friedmann equation
with pressureless matter
does not describe correctly
the observations
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc …
Consequences & Remarks
This is a pure kinematical
measurement (no dynamics)
of the luminosity distance
Possibility 3: There is a missing
component or the stress-energy
tensor is not “correct”
The Universe is accelerating
Possible candidates include …
• Cosmological constant
The Friedmann equation
with pressureless matter
does not describe correctly
the observations
• Scalar field (quintessence)
• Extented quintessence
• K-essence
• Chaplygin gas-Quartessence
• Bulk viscosity
• Super-horizon modes
• Quantum cosmological effect
• etc …
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
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
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
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
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
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
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
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, p>1
no direct coupling between X and Q,
otherwise the matrix is not diagonal
High energy physics & Quintessence
After straightforward calculations, the potential reads
SUGRA correction
This simple estimate leads to different problems
But how to control terms like
In some sense, the fine tuning reappears …
with
?
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 
Measuring the (constant) equation of state
WMAP1+CBI+ACBAR
SUGRA
WMAP1+CBI+ACBAR+2dF
SNIa 2004
High energy physics & Quintessence
mSUGRA
Inflaton
Gravity mediated
SUSY
Hidden sector
Observable sector
Fifth force test, equivalence
principle test etc …
Quintessence sector
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
Coupling the inflaton to quintessence
The basic assumption is that Q and the inflaton belong to different
sectors of the theory. This means that
Inflation
Quintessence
Coupling the inflaton to quintessence
To go further, a model for (chaotic) inflation is needed. One takes
N.B.:
Ratra-Peebles/SUGRA
N.B.:
Coupling the inflaton to quintessence
absolute minimum
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
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
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.
Quantum effects during inflation
The quantum effects in curved space-time can be computed with the
formalism of “ stochastic inflation”.
Window function
Coarse-grained field,
averaged over a Hubble patch:
contains long-wavelength modes
Only contains short wavelength modes
because of the window function
The window function does
not vanish if :
“Hubble patch”
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
“Classical drift”
“quantum noise”, sourced by
the short wavelength modes
For the free case, one can check that one recovers the standard result :
Brownian motion
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
Quantum effects during inflation
• The confidence region enlarges with the power index 
• A “small” number of total e-foldings is favored