Diapositive%201

1


The Quintessence Field during Inflation
Jérôme Martin
Institut dAstrophysique de Paris
2
Quintessence
Quintessence scalar field dominating the
todays 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.
Tracking behavior
SUGRA
P. Brax J. Martin (1999)
3
Quintessence
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?
4
Quintessence 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
However
Stochastic effects are important
From high energy considerations, the inflaton and
the quintessence field must interact
5
Quantum effects
Stochastic inflation regime
Stochastic quintessence regime
Chaotic inflation
The field undergoes quantum jump H/2? every
Hubble time
Quantum effects are important for quintessence!
M. Malquarti A. Liddle (2002) J. Martin M.
Musso (2004)
6
Quantum 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)
7
High energy physics Quintessence
mSUGRA
SUSY
Gravity mediated
Inflaton
Hidden sector
Observable sector
Fifth force test, equivalence principle test etc
Quintessence sector
8
Coupling the inflaton to quintessence
Time-dependent trajectory of the quintessence
minimum
P. Brax J. Martin (2005)
absolute minimum
9
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
10
Conclusions
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??
11
Inflation 25 A conference to celebrate the
25th anniversary of inflationary cosmology
Institut dAstrophysique 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
12
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
13
Coupling the inflaton to quintessence
Another basic assumption is that Q and the
inflaton belongs to different sectors of the
theory. This means that
14
Coupling the inflaton to quintessence
To go further, a model for (chaotic) inflation is
needed. One takes
N.B.
Ratra-Peebles/SUGRA
N.B.