The Quintessence Field during Inflation
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Transcript of The Quintessence Field during Inflation
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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.: