Can we constrain models from the string theory by Non- gaussianity ?

1. Can we constrain models from the string theory by Non-gaussianity ? APCTP-IEU Focus Program Cosmology and Fundamental Physics June 11, 2011 Kyung Kiu Kim (IEU) With Chanju Kim and FredericoArroja

2. Outline • Motivation • Large volume scenario • Non-gaussianity in Multi-field Inflation (C. Peterson and M. Tegmark) • Possible way to produce large Non-gaussianity in some model from Large volume scenario • Evolution of non-gaussianity with the adiabaticity assumption. • Summary

3. Motivation • I’m in the IEU. • I would like to know whether my main tool, string theory, can explain our universe or not. • The string theory is a consistent theory and has good properties mathematically. • So many string theorists hope that string theory plays a role of TOE. • But the string theory looks so far from observations or experiments, because the energy scale is so high (gravity scale).

4. Motivation • In cosmology, the inflation model was proposed and gives good agreement or fitting to observations. • It provides many nice explanations for our universe. • If it is the right model for our universe and the sting theory is the theory of the universe, then the string theory should contain the inflation model. • Recently, Human beings paid really big money for taking photos and we are waiting for the results.

5. Motivation • One of the results is the non-gaussianity of the universe. • This could give very important information for our early universe. • If we assume the string theory explains the inflation, we need to calculatethe non-gaussianity in string theory models and compare it to the observation.

6. The models from the string theory • Since we don’t want inconsistency in string theory, there is many obstacles and difficulties in construction of models in string theory. • The models for non-gaussianity in string theory- The large volume scenarios from flux compactification(eta problem)- DBI inflation models(movement of D brane, Fred’s talk)- Axionmonodromy models(eta problem)- …. • We are devoted to the large volume scenarios.

7. The large volume Scenario • String theory is defined in 10 dimensional spacetime. • One of way to obtain 4 dimensional model is compactifiying 6 dimension in type IIB string theory. • This gives a 4 dimensional N=1 Supergravity action.

8. The large volume Scenario • However, the supergravityhas a fine tuning problem, eta problem. • Without fine-tuning, we cannot produce small eta during the inflation. • In order to solve the problem, we may take some assumption. • The resulting scenario is the large volume scenarios.

9. The large volume Scenario • Details of the construction can be found in the Prof. Nam’s talk. • I gives a very short introduction here. • N=1 SUGRA action given by the Kahler potential K and the holomorphicsuperpotential W. • V_uplift is effect of the supersymmetry-breaking from other sectors of the theory.( We know physical origin.)

10. The large volume Scenario • From flux compactification of Type IIB string theory, These K and W are given by

11. The large volume Scenario 4 cycle volume + i (axionic partner) Origin was known(instantonor gaugino condensation,…).

12. The large volume Scenario • Dimensionless classical volume • D_iis a harmonic 2 form in M. • t^i is an area of 2 cycle in M

13. The large volume Scenario • Because of G_3, complex structure moduli and axion have string scale masses and they are decoupled. • The low energy theory • Taking large volume scenario, • Alpha and lambda are from the intersection number.

14. The large volume Scenario • The model is up to with

15. The large volume Scenario • In order to make the metric canonical, one can introducethen the metric on field space becomes canonical type.

16. The large volume Scenario • One may introduce a simple model(an example in 1010.3261) • Two light fields play role of inflatons. • The model is boiled down to

17. Non-gaussianity in Multi field inflation • Single field slow roll inflation model which has canonical kinetic term gives small non-gaussianity. • Easiest way to avoid small non-gaussianity is introducing multi-field which could produce large Non-gaussianity. • In string theory, many fields situations are very common because there are many scalar fields. • As we explained, after flux compactification, it is very natural to obtain many scalar field with canonical type of kinetic term.

18. Non-gaussianity in Multi field inflation • The local type non-gaussianityhas beengiven by WMAP data. • The Planck will give more exact value of NG. • For simplicity and insight, we first consider two field case with delta N formalism(Ki-young’s talk). • Starting with action

19. Non-gaussianity in Multi field inflation(C peterson and M Tegmark) • The number of e-folds N is given by • We can express time derivative with e-folds numbers • The background eom becomes

20. Non-gaussianity in Multi field inflation • With the slow-roll parameters • The field velocity • Define some vectors

21. Non-gaussianity in Multi field inflation • Slow-roll approximation in this conventionand • This means low field-speed and slowly changing speed.

22. Non-gaussianity in Multi field inflation • We have many fields, one may choose another direction and take slowly changing limit • Slow turn limit • In the SRST limit, the evolution equation is • The speed-up rate and turn-rate are approximated by • Give by potential V

23. Non-gaussianity in Multi field inflation • The hessian • The perturbation equation in Fourier space. In SRST limit

24. Non-gaussianity in Multi field inflation • The evolution of is approximated by • The curvature mode and the iso-curvature mode • This evolution is expressed by a transfer matrix

25. Non-gaussianity in Multi field inflation • Alpha and beta are given by in SRST limit • Related to two point function • Three kinds of spectrum (curvature, cross and iso-curvature )

26. Non-gaussianity in Multi field inflation • The curvature spectral indexwhere, tensor spectral index was usedThe gradient of NCorrelation angle

27. Non-gaussianity in Multi field inflation • Curvature iso-curvature correlation • Tensor to scalar ratio • f_NL and power spectrum in the delta N formalismthen

28. Non-gaussianity in Multi field inflation • One can find • f_NL becomes simpler form • With a little algebra

29. Non-gaussianity in Multi field inflation • Most important term is • Condition for large f_NL1. The total amount of sourcing of curvature modes by iso-curvature modes (TRS) must be extremely sensitive to a change in the initial conditions perpendicular to the inflaton trajectory. In other words, two neighboring trajectories must experience dramatically different amounts of sourcing.2. The total amount of sourcing must be non-zero. Usually, the amount of sourcing must also be moderate, to avoid having

30. Non-gaussianity in Multi field inflation • Fine tuning for Non-gaussianity 1 vs 100

31. Possible way to produce large Non-gaussianity in some model from Large volume scenario • One model from string flux compactification.

32. Evolution of non-gaussianity with the adiabaticity assumption • 1011.4934 (J. Meyers and N. Sivanandam) • The adiabaticity assumption • The non-gaussianity is decreasing exponentially.

33. Evolution of non-gaussianity with the adiabaticity assumption • If the adiabaticity assumption is considered, we cannot expect local type large non-gaussianity. • So it could be difficult to produce large NG in all the multi field case. • However, this assumption is not so strong.

34. Summary • Flux compactification of type IIB string theory can give multi-field inflation model(Large volume scenario). • In the multi- field case, the large NG requires fine tuning in the field trajectories. • In the string theory, we can generate the model which can produce large NG. • With the adiabaticity assumption, large NG is very difficult produce. • In order to constrain string theory models, we have to understand how the fine-tuning constrains the parameter space of the models.