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The Quintessence Field during The Quintessence Field during Inflation Inflation

Jérôme Jérôme MartinMartin

Institut d’Astrophysique de ParisInstitut d’Astrophysique de Paris

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QuintessenceQuintessence

Quintessence: scalar field dominating the today’s energy density budget of the Universe and such that its potential allows insensitivity to the initial conditions (otherwise one-to-one mapping between the equation of state and the shape of the potential) and reasonable model building.

Electroweak scale

Tracking behavior SUGRA

P. Brax & J. Martin (1999)

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QuintessenceQuintessence

radiation

quintessence

matter

The attractor is joined

The attractor is joined

reheating

Inflation

Do we have initial conditions (final conditions from the point of view of inflation) that are compatible with the attractor?What are the initial conditions for the quintessence field at the beginning of inflation?

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Quintessence during inflationQuintessence during inflation

Test Quintessence field in a background the evolution of which is controlled by chaotic inflation:

Typically, the quintessence field is frozen during inflation

Stochastic effects are important

From high energy considerations, the inflaton and the quintessence field must interact

However …

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Quantum effectsQuantum effects

Chaotic inflation

Stochastic inflation regime

The field undergoes quantum jump H/2 every Hubble time

Stochastic quintessence regime

Quantum effects are important for quintessence!M. Malquarti & A. Liddle (2002)J. Martin & M. Musso (2004)

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Quantum effectsQuantum effects

• The confidence region enlarges with the power index

• A “small” number of total e-foldings is favored because otherwise the Quintessence field has too much time to drift away from the allowed range of initial conditions

J. Martin & M. Musso (2004)

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High energy physics & QuintessenceHigh energy physics & Quintessence

Observable sector

Quintessence sector

Hidden sector

SUSYGravity mediatedmSUGRA

Inflaton

Fifth force test, equivalence principle test etc …

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Coupling the inflaton to quintessenceCoupling the inflaton to quintessence

absolute minimum

Time-dependent trajectory of the “quintessence minimum”

P. Brax & J. Martin (2005)

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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

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ConclusionsConclusions

The quintessence field is driven away from the allowed range of initial conditions by the stochastic effects during inflation

On the contrary, its unavoidable interaction with the inflaton field keeps its vev small

What about the quantum effects in presence of interaction?? Technically very complicated, not yet addressed

The interaction between the quintessence and inflaton fields is unavoidable in SUGRA. What about the interaction between the observable sector and the quintessence field?

How does the quintessence behave during reheating??

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Inflation +25Inflation +25

A conference to celebrate the 25th anniversary of inflationary cosmology

Institut d’Astrophysique de Paris

June 26 to 30, 2006

http://www.iap.fr/col2006/

… registration opens end 2005 …

Plenary speakers: Guth, Linde, Kallosh, Mukhanov, Vilenkin, Starobinsky, Lyth, Turok, Wands, Kolb, Durrer, Peiris, Seljak, Prunet, Riotto, Kofmann, Sakalleriadou, Cooray, etc …

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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

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Coupling the inflaton to quintessenceCoupling the inflaton to quintessence

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

Inflation Quintessence

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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.: