Dark Energy & High-Energy Physics

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





[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]









Possibility 1:The observations are not correct, e.g. the SNIa are not standard candels (dust, evolution etc …)





Possibility 2: Gravity is modified

New “large” characteristic scale

There is a missing component or the stress-energy tensor is not “correct”





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 …






Possibility 3:

The new fluid must have a negative pressure






Possibility 3:








Possibility 3:








Possibility 3:








Possibility 3:


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






Possibility 3:








Possibility 3:



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


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


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


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



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


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


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


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


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


The basic assumption is that Q and the inflaton belong to different sectors of the theory. This means that

Inflation Quintessence


To go further, a model for (chaotic) inflation is needed. One takes

N.B.:

Ratra-Peebles/SUGRA

N.B.:


absolute minimum


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


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 :


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


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


• The confidence region enlarges with the power index

• A “small” number of total e-foldings is favored

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Dark Energy & High-Energy Physics

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