Testing the origin of primordial perturbations -Use of bi and tri-spectrum-

1. Testing the origin of primordial perturbations -Use of bi and tri-spectrum- Speaker: TeruakiSuyama (RESCEU, Univ. of Tokyo)

2. What is Primordial fluctuation? Primordial fluctuation 13 billion yrs 300,000yrs (WMAP data) • matterfluctuation = fluctuation of spacetime(=curvature perturbation) • It is a source of the current cosmic structure. • From observations, we already know it does exist.

3. What is the origin of the primordial fluctuation? We don’t know. But, it is becoming possible to clarify/restrict the origin of the primordial fluctuation in the next decade.

4. What is the theory of the primordial fluctuation? Basic paradigm During the inflationary stage, any light scalar field acquires fluctuations that are eventually stretched to cosmological scales (very large length scales). When such a scalar field affects the expansion of the Universe, its fluctuating energy density creates the curvature perturbation through the Einstein equations.

5. What is the theory of the primordial fluctuations? Simplest inflaton scenario In the simplest models, inflaton fluctuations create the curvature perturbations. • Inflaton does all the jobs. • Connection between inflaton fluctuation to zeta is well established. • Good in the sense that it is simple, economical and consistent with all the observations so far. But this is just an assumption rather than a prediction.

6. What is the theory of the primordial fluctuations? Non-inflaton scenario Many other models have been proposed in literature.Notice that all of these models are based on inflation. • Curvaton models • Modulated reheating models • Inhomogeneous end of inflation models • Multi-brid models • Trapped models Reality may be even a mixture of them. Several field fluctuations can contribute to the curvature perturbation.

7. How can we reveal the origin of perturbations? Power spectrum All the models predict nearly scale invariant spectrum. P is not enough to disentangle the degeneracy.

8. How can we reveal the origin of perturbations? Is there another way other than the power spectrum? 3- and 4-point functions could be useful!! Useful in the sense that they can provide us what cannot be probed by means of the power spectrum. Potentially observable in the near future.

9. How can we reveal the origin of perturbations? From now on, I will focus on the so-called local type perturbation; : Gaussian variable Same position This type of zeta is realized if the focused scales are super-horizon at the time of conversion.

10. Non-Gaussianity(non-linearity) parameters 3-point function 4-point function (Byrnes, Sasaki and Wands, 2006) Three non-linearity parameters that are observables.

11. Non-Gaussianity parameters Current observational bounds on the non-linearity parameters (Komatsu et al., 2010) (Smidt et al., 2010) Planck is expected to give us and . (Kogo and Komatsu, 2006) More stringent bound may be obtained by using other cosmological probes. (e.g. Pajer&Zaldarriaga 2012)

12. Non-Gaussianity parameters • Standard canonical inflaton fluctuation (e.g. Komatsu et al. 2009) • Non-inflaton scenarios depending on the model Bispectrum can be useful to disentangle the degeneracy of models. What can we do further if non-vanishing fnl is detected in future?

13. Local-type inequality (TS and M.Yamaguchi, 2008) Detection of fnl>20 means we surely detect taunl as well. This inequality also suggests a possibility that fnl is small but taunlcan be very large.

14. Local-type inequality If the curvature perturbation is sourced by a single field like then we have A ratio is a good indicator to get information of number of fields that contribute to the curvature perturbation.

15. Local-type inequality In which case the ratio can be large? As an example, let’s consider a mixed situation where (Ichikawa et al. 2008) Gaussian Non-Gaussian then we have If the non-gaussian part is subdominant, we get large s.

16. (TS et al. 2010)

17. Basic strategy to test the origin of perturbation Single source Detection of fnl multiple sources observation data Detection of taunl multiple sources Non-detection of fnl Non-detection of taunl Maybe, inflaton scenario

18. What about gnl? This is not directly related to fnl and taunl. Thus, it brings another information specific to each model. Example: self-interacting curvaton (e.g. Engvist&Nurmi 2005) without self-interaction with self-interaction gnl is sesitive to the shape of the field potential.

19. What about gnl? We findgnl is model dependent. But, we can classify the models into three types:

20. Consistency relations among non-linearity parameters (TS et al. 2010)

21. Summary Test of non-gaussianity can be useful to reveal the origin of primordial perturbations. We can obtain information about number of fields contributing to the curvature perturbation by using fnl and taunl. Detection of all the non-linearity parameters greatly helps us constrain the model of the early Universe.