Roles of boundary and equation-of-motion terms in cosmological correlation functions
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arXiv
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| Format: | Preprint |
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2024
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| author | Kawaguchi, Ryodai Tsujikawa, Shinji Yamada, Yusuke |
| author_facet | Kawaguchi, Ryodai Tsujikawa, Shinji Yamada, Yusuke |
| contents | We revisit the properties of total time-derivative terms as well as terms proportional to the free equation of motion (EOM) in a Schwinger-Keldysh formalism. They are relevant to the correct calculation of correlation functions of curvature perturbations in the context of inflationary Universe. We show that these two contributions to the action play different roles in the operator or the path-integral formalism, but they give the same correlation functions as each other. As a concrete example, we confirm that the Maldacena's consistency relations for the three-point correlation function in the slow-roll inflationary scenario driven by a minimally coupled canonical scalar field hold in both the operator and path-integral formalisms. We also give some comments on loop calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16022 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Roles of boundary and equation-of-motion terms in cosmological correlation functions Kawaguchi, Ryodai Tsujikawa, Shinji Yamada, Yusuke High Energy Physics - Theory Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology We revisit the properties of total time-derivative terms as well as terms proportional to the free equation of motion (EOM) in a Schwinger-Keldysh formalism. They are relevant to the correct calculation of correlation functions of curvature perturbations in the context of inflationary Universe. We show that these two contributions to the action play different roles in the operator or the path-integral formalism, but they give the same correlation functions as each other. As a concrete example, we confirm that the Maldacena's consistency relations for the three-point correlation function in the slow-roll inflationary scenario driven by a minimally coupled canonical scalar field hold in both the operator and path-integral formalisms. We also give some comments on loop calculations. |
| title | Roles of boundary and equation-of-motion terms in cosmological correlation functions |
| topic | High Energy Physics - Theory Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2403.16022 |