The Quintessence Field during Inflation

1. The Quintessence Field during Inflation Jérôme Martin Institut d’Astrophysique de Paris

2. Electroweak scale Quintessence 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. Tracking behavior SUGRA P. Brax & J. Martin (1999)

3. radiation The attractor is joined matter quintessence 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 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 …

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. Inflation Quintessence 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.: