### Abstract

We investigate an estimator to measure the primordial trispectrum in equilateral type non-Gaussian models such as k-inflation, single field DBI inflation and multi-field DBI inflation models from Cosmic Microwave Background (CMB) anisotropies. The shape of the trispectrum whose amplitude is not constrained by the bispectrum in the context of effective theory of inflation and k-inflation is known to admit a separable form of the estimator for CMB anisotropies. We show that this shape is 87% correlated with the full quantum trispectrum in single field DBI inflation, while it is 33% correlated with the one in multi-field DBI inflation when curvature perturbation is originated from purely entropic contribution. This suggests that g^{equil}
_{NL} , the amplitude of this particular shape, provides a reasonable measure of the non-Gaussianity from the trispectrum in equilateral non-Gaussian models. We relate model parameters such as the sound speed, c_{s} and the transfer coefficient from entropy perturbations to the curvature perturbation, T _{RS} with g^{equil}
_{NL} , which enables us to constrain model parameters in these models once g^{equil}
_{NL} is measured in WMAP and Planck.

Original language | English |
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Title of host publication | Proceedings of the 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010 |

Pages | 278-281 |

Number of pages | 4 |

Publication status | Published - 2010 |

Externally published | Yes |

Event | 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010 - Kyoto Duration: 2010 Sep 21 → 2010 Sep 25 |

### Other

Other | 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010 |
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City | Kyoto |

Period | 10/9/21 → 10/9/25 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Proceedings of the 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010*(pp. 278-281)

**Trispectrum estimator in equilateral type non-Gaussian models.** / Mizuno, Shuntaro; Koyama, Kazuya.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010.*pp. 278-281, 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010, Kyoto, 10/9/21.

}

TY - GEN

T1 - Trispectrum estimator in equilateral type non-Gaussian models

AU - Mizuno, Shuntaro

AU - Koyama, Kazuya

PY - 2010

Y1 - 2010

N2 - We investigate an estimator to measure the primordial trispectrum in equilateral type non-Gaussian models such as k-inflation, single field DBI inflation and multi-field DBI inflation models from Cosmic Microwave Background (CMB) anisotropies. The shape of the trispectrum whose amplitude is not constrained by the bispectrum in the context of effective theory of inflation and k-inflation is known to admit a separable form of the estimator for CMB anisotropies. We show that this shape is 87% correlated with the full quantum trispectrum in single field DBI inflation, while it is 33% correlated with the one in multi-field DBI inflation when curvature perturbation is originated from purely entropic contribution. This suggests that gequil NL , the amplitude of this particular shape, provides a reasonable measure of the non-Gaussianity from the trispectrum in equilateral non-Gaussian models. We relate model parameters such as the sound speed, cs and the transfer coefficient from entropy perturbations to the curvature perturbation, T RS with gequil NL , which enables us to constrain model parameters in these models once gequil NL is measured in WMAP and Planck.

AB - We investigate an estimator to measure the primordial trispectrum in equilateral type non-Gaussian models such as k-inflation, single field DBI inflation and multi-field DBI inflation models from Cosmic Microwave Background (CMB) anisotropies. The shape of the trispectrum whose amplitude is not constrained by the bispectrum in the context of effective theory of inflation and k-inflation is known to admit a separable form of the estimator for CMB anisotropies. We show that this shape is 87% correlated with the full quantum trispectrum in single field DBI inflation, while it is 33% correlated with the one in multi-field DBI inflation when curvature perturbation is originated from purely entropic contribution. This suggests that gequil NL , the amplitude of this particular shape, provides a reasonable measure of the non-Gaussianity from the trispectrum in equilateral non-Gaussian models. We relate model parameters such as the sound speed, cs and the transfer coefficient from entropy perturbations to the curvature perturbation, T RS with gequil NL , which enables us to constrain model parameters in these models once gequil NL is measured in WMAP and Planck.

UR - http://www.scopus.com/inward/record.url?scp=84887450158&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887450158&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84887450158

SP - 278

EP - 281

BT - Proceedings of the 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010

ER -