Dark Energy & High-Energy Dark Energy & High-Energy PhysicsPhysics
Jérôme Jérôme MartinMartin
Institut d’Astrophysique de ParisInstitut d’Astrophysique de Paris
OutlineOutline
• 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
• 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
Measuring the expansion with the SNIaMeasuring the expansion with the SNIa
Consequences & Remarks 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 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
[J. L. Tonry et al., Astrophys. J 594, 1 (2003), astro-ph/0305008]
[W. Freedman & M. Turner, Rev. Mod. Phys. 75, 1433 (2003), astro-ph/0308418]
Consequences & Remarks 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 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 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 2: Gravity is modified
New “large” characteristic scale
There is a missing component or the stress-energy tensor is not “correct”
Consequences & Remarks 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 3:
Possible candidates include …
• Cosmological constant• Scalar field (quintessence)• Extented quintessence • K-essence • Chaplygin gas-Quartessence • Bulk viscosity • Super-horizon modes• Quantum cosmological effect • etc …
There is a missing component or the stress-energy tensor is not “correct”
Consequences & Remarks 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 3:
The new fluid must have a negative pressure
There is a missing component or the stress-energy tensor is not “correct”
Consequences & Remarks 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 3:
Possible candidates include …
• Cosmological constant• Scalar field (quintessence)• Extented quintessence • K-essence • Chaplygin gas-Quartessence • Bulk viscosity • Super-horizon modes• Quantum cosmological effect • etc …
There is a missing component or the stress-energy tensor is not “correct”
Consequences & Remarks 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 3:
Possible candidates include …
• Cosmological constant• Scalar field (quintessence)• Extented quintessence • K-essence • Chaplygin gas-Quartessence • Bulk viscosity • Super-horizon modes• Quantum cosmological effect • etc …
There is a missing component or the stress-energy tensor is not “correct”
Consequences & Remarks 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 3:
Possible candidates include …
• Cosmological constant• Scalar field (quintessence)• Extented quintessence • K-essence • Chaplygin gas-Quartessence • Bulk viscosity • Super-horizon modes• Quantum cosmological effect • etc …
There is a missing component or the stress-energy tensor is not “correct”
Consequences & Remarks 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 3:
Possible candidates include …
• Cosmological constant• Scalar field (quintessence)• Extented quintessence • K-essence • Chaplygin gas-Quartessence • Bulk viscosity • Super-horizon modes • Quantum cosmological effect • etc …
There is a missing component or the stress-energy tensor is not “correct”
Consequences & Remarks 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 3:
Possible candidates include …
• Cosmological constant• Scalar field (quintessence)• Extented quintessence • K-essence • Chaplygin gas-Quartessence • Bulk viscosity • Super-horizon modes• Quantum cosmological effect • etc …
There is a missing component or the stress-energy tensor is not “correct”
Consequences & Remarks 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 3:
Possible candidates include …
• Cosmological constant• Scalar field (quintessence)• Extented quintessence • K-essence • Chaplygin gas-Quartessence • Bulk viscosity • Super-horizon modes• Quantum cosmological effect • etc …
QuintessenceQuintessence
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
QuintessenceQuintessence
When the field starts dominating the matter content of the Universe, it leaves the particular solution. This one can be written as
The mass of the field (defined as the second derivative of the potential) is
This happens for
QuintessenceQuintessence
The particular solution is an attractor and is joined for a huge range of initial conditions
The coincidence problem is solved: the acceleration starts recently
radiation
quintessence
matter
The attractor is joined
The attractor is joined
QuintessenceQuintessence
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
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
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
Electroweak scale
QuintessenceQuintessence
QuintessenceQuintessence
The evolution of the small inhomogeneities is controlled by the perturbed Klein-Gordon equation
Clustering of quintessence only on scales of the order of the Hubble radius
WMAP 1 data
High energy physics & QuintessenceHigh 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 & QuintessenceHigh 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
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
can be justified if the charges of X, Y and Q under U(1) are 1, -2 and 0
High energy physics & QuintessenceHigh 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 …
?But how to control terms like with
High energy physics & QuintessenceHigh energy physics & Quintessence
What are the effects of the SUGRA corrections?
2- The exponential corrections pushes the equation of state towards -1 at small redshifts
1- The attractor solution still exists since, for large redshifts, the vev of Q is small in comparison with the Planck mass
3- The present value of the equation of state becomes “universal”, i.e. does not depend on
Measuring the (constant) equation of stateMeasuring the (constant) equation of state
SNIa 2004
WMAP1+CBI+ACBAR
WMAP1+CBI+ACBAR+2dF
SUGRA
High energy physics & QuintessenceHigh energy physics & Quintessence
Observable sector
Quintessence sector
Hidden sector
SUSYGravity mediatedmSUGRA
Inflaton
Fifth force test, equivalence principle test etc …
Coupling the inflaton to quintessenceCoupling 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 quintessenceCoupling 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 quintessenceCoupling 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 quintessenceCoupling the inflaton to quintessence
absolute minimum
Coupling the inflaton to quintessenceCoupling 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 quintessenceCoupling 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
ConclusionsConclusions
• 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 inflationQuantum effects during inflation
The quantum effects in curved space-time can be computed with the formalism of “ stochastic inflation”.
Coarse-grained field, averaged over a Hubble patch:contains long-wavelength modes
Window function Only contains short wavelength modesbecause of the window function
“Hubble patch”
The window function does not vanish if :
Quantum effects during inflationQuantum effects during inflation
The evolution of the coarse-grained field is controlled by the Langevin equation
“Classical drift” “quantum noise”, sourced by the short wavelength modes
For the free case, one can check that one recovers the standard result :
The coarse-grained field becomes a stochastic process
Brownian motion
Quantum effects during inflationQuantum 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 inflationQuantum effects during inflation
• The confidence region enlarges with the power index
• A “small” number of total e-foldings is favored