1. Trispectrum Estimator of Primordial Perturbation in Equilateral Type Non-Gaussian Models Ｋｅｉｓｕｋｅ Ｉｚｕｍｉ （泉 圭介） Collaboration with Shuntaro Mizuno Kazuya Koyama

2. Inflation The problem of Big Bang cosmology Flatness problem Horizon problem Inflation can solve these problems by the exponentially expansion. Additional advantage of inflation Primordial fluctuations are created quantum mechanically. These fluctuations become the seed of the structure of Universe. However, there are O(100) inflation models. Identification of inflation model is one of important tasks. How? More accurate observation of primordial fluctuations (CMB) Observation of gravitational wave (tensor fluctuations)

3. Cosmic Microwave Background (CMB) What we observe? In early universe, the energy density is high and photon can not propagate freely. Last scattering surface Since universe expands, at some time photon can propagate freely. We see this surface and measure the temperature. http://map.gsfc.nasa.gov/ WMAP 7year The perturbation produced in inflation era Almost the same temperature about 3000K (2.7K now) There is small fluctuation ΔT/T ～ 10^-5 Gravitational perturbation Temperature perturbation

4. Statistics of CMB fluctuation Origin is quantum fluctuation in inflation era. (Almost) Gaussian Almost de Sitter expansion. (Almost) scale invariant interaction Non-Gaussianity 3-point function -> bispectrum 4-point function -> trispectrum Scale dependence Other direction WMAP polarization

5. Bispectrum Definition of bispectrum of curvature perturbation Because of isotropy and homogeneity, depends only on amplitude of momenta Assuming scale invariance, depends on two parameters Shape of Bispectrum local 0 10.5 1 equilateralorthogonal

6. Local shape 0 1 0.5 1 Small scale Large scale Definition of local shape Maximum Large scale Local limit of bispectrum can be interpreted as powerspectrum on background modulated by large scale perturbation Derivation of local shape

7. Equilateral and orthogonal shape 0 10.5 1 Definition of equilateral shape Maximum: equilateral shape 0 1 Definition of orthogonal shape In single field inflation model, all bispectra can be written as linear combination of local, equilateral and orthogonal shapes.

8. Non-Gaussianity Bispectrum :Leading order non-Gaussianity WMAP PLANCK If, it can be observed. advantage Ease of calculation and data analysis. disadvantage Only see a part of full information For instance, it is difficult to distinguish between DBI inflation and ghost inflation. Trispectrum :Next order non-Gaussianity advantage Complication of calculation and data analysis. disadvantage More informations In Trispectrum, can we see difference between DBI inflation and ghost inflation? 6 parameters WMAP PLANCK If, it can be observed. Defining inner product of Trispectrum shapes, we quantify similarity between two shapes. Komatsu et al. 2010 Regan et al. 2010 Kogo, Komatsu 2006 PLANCK homepage http://www.sciops.esa.int/index.php?project=PLANCK

9. Inner Product and correlator Definition of bispectrum of curvature perturbation depends on 6 parameters Shape function Inner product correlator Non-gaussianity parameter

10. Result correlator Highly correlated Low correlation Some models can be discriminated by trispectrum

11. Summary Analysis of non-Gaussianity of primordial perturbation is one of way to discriminate inflation models. We can distinguish some of models by trispectrum. We also see non-gaussianity parameter in some models. Thank you for your attention.