1. Dark Energy In Hybrid Inflation Seongcheol Kim (KAIST) Based on Phys. Rev. D75: 063520(2007)

2. CONTENTS 1. Introduction 2. Idea 3. Model Building 4. SUSY Realization 5. Summary

3. INTRODUCTION * Observations say that the Universe is composed of 70% unknown form energy. We call it “Dark Energy”. * There are many models to explain the Dark Energy. For example ΛCDM, quintessence, anthropic principle... * Our model is based on the quintessence model. * Our model comes from a question. How can we couple the early accelerated expansion, and the current one together?

4. IDEA Scalar field 1. Inflation stage 1 st phase transition 2. End of Inflation and start Standard Cosmology 2 nd phase transition 3. Scalar filed slowly rolls again There are 3 scalar fields and 2 phase transitions How can we combine 3 rd scalar field with the others?

5. IDEA  Combining the onset of present acceleration with the primordial inflation by indirectly coupling the inflaton with the quintessence field.  Inflation lasts for a long enough time without being disturbed by the interaction with the quintessence field.  Directly coupling the quintessence field with some different field which plays no role during the inflaton rolls down its potential and only works to finish inflation. inflaton waterfall field quintessence field

6. MODEL BUILDING 1 st phase transition2 nd phase transition Inflation end of inflation quintessence field all fields are start to roll settled down

7. 1 st Stage : Primordial Inflation And And So is located atSo is located at This process is almost same as hybrid inflation when we assume these. 1. The vacuum density is much larger than the potential energy density of the inflaton field. 2. The vacuum energy V(0,0,0) is dominated by.

8. 2 nd Stage : Phase transition between ф and ψ We assumes that the critical point of waterfall field is earlier than the minimum point of the potential The waterfall field ψ oscillates at the minimum and decays so that the Universe is reheated. Ψ field

9. 2 nd Stage : Phase transition between ф and ψ * Waterfall condition 1. The absolute value of the effective mass square of ψ is much larger than H 2 2. The time scale for ф to roll down from ф c to 0 be much shorter than H -1 * Amplitude of density perturbation

10. 3 rd Stage : Phase transition between ψ and σ * We assumed that the critical point of waterfall field is earlier than the minimum point of the potential * The minimum along σ direction is : * The minimum of the potential when all fields are settled down σ field

11. 3 Kinds of Vacuum 1. positive vacuum 2. zero vacuum 3. negative vacuum density density density Similar to ΛCDM usual quintessential inflation

12. SUSY REALIZATION 1. Hybrid Inflation superpotential : where ψ 1 and ψ 2 are pair of superfields in non-trivial representations of some gauge group under which ф is neutral. the effective potential : By simply adding a mass term which softly breaks supersymmetry, we see that the hybrid inflation scenario is possible.

13. SUSY REALIZATION 2. Our Model D-term contribution The coupled term of ψ and σ has a negative sign. We use ψ and σ oppositely charged under U(1) symmetry. ф and ψ are charged with same sign. The coupled terms but1.We do not consider F-term contribution 2. In globally supersymmetric theories the scalar potential does not allow negative value. 3. A more detailed analysis of our model and associated problems should be addressed in the context of supergravity.

14. Summary  We have investigated a simple model based on hybrid inflation.  The quintessence field σ is coupled to the waterfall field ψ so that ψ rolls toward, σ begins to move along the effective potential.  The true minimum of the effective potential depends on our choice of the parameters, allowing the vacuum state with positive, negative and zero energy.  This model could be realized in supersymmetric theories via D-term contribution, but including F-term parts and supergravity effects makes investigation of our model challenging.