Trispectrum Estimator of Primordial Perturbation in Equilateral Type Non-Gaussian Models

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. Additionaladvantageof 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. Since universe expands, at some time photon can propagate freely. We see this surface and measure the temperature. Last scattering surface Almost the same temperature about 3000K (2.7K now) WMAP 7year There is small fluctuation ΔT/T～10^-5 The perturbation produced in inflation era Gravitational perturbation http://map.gsfc.nasa.gov/ Temperature perturbation

4. Statistics of CMB fluctuation Origin is quantum fluctuation in inflation era. (Almost) Gaussian Other direction interaction Almost de Sitter expansion. Non-Gaussianity (Almost) scale invariant 3-point function -> bispectrum 4-point function -> trispectrum Scale dependence 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 equilateral orthogonal 0 1 1 0.5

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

7. Equilateral and orthogonal shape Definition of equilateralshape Maximum: equilateral shape 0 Definition of orthogonal shape 1 In single field inflation model, all bispectra can be written as linear combination of local, equilateral and orthogonal shapes. 0 1 1 0.5

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

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 Highly correlated correlator 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.