Non-Gaussianity in two-field inflation
We derive semianalytic formulas for the local bispectrum and trispectrum from general two-field inflation and provide a simple geometric recipe for building observationally allowed models with large non-Gaussianity. We use the δN formalism to express the bispectrum in terms of spectral observables a...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2011
|
| Online Access: | http://hdl.handle.net/1721.1/67346 https://orcid.org/0000-0001-7670-7190 |
| _version_ | 1811087315197493248 |
|---|---|
| author | Peterson, Courtney M. Tegmark, Max Erik |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Peterson, Courtney M. Tegmark, Max Erik |
| author_sort | Peterson, Courtney M. |
| collection | MIT |
| description | We derive semianalytic formulas for the local bispectrum and trispectrum from general two-field inflation and provide a simple geometric recipe for building observationally allowed models with large non-Gaussianity. We use the δN formalism to express the bispectrum in terms of spectral observables and the transfer functions, which encode the superhorizon evolution of modes. Similarly, we calculate the trispectrum and show that the trispectrum parameter τNL can be expressed entirely in terms of spectral observables, which provides a new consistency relation for two-field inflation. To generate observably large non-Gaussianity during inflation, we show that the sourcing of curvature modes by isocurvature modes must be extremely sensitive to a change in the initial conditions orthogonal to the inflaton trajectory and that the amount of sourcing must be nonzero. Under some minimal assumptions, we argue that the first condition is satisfied only when neighboring trajectories in the two-dimensional field space diverge during inflation. Geometrically, this means that the inflaton must roll along a ridge in the potential V for some time during inflation and that its trajectory must turn somewhat in field space. Therefore, it follows that under our assumptions, two-field scenarios with attractor solutions necessarily produce small non-Gaussianity. This explains why it has been so difficult to achieve large non-Gaussianity in two-field inflation and why it has only been achieved in a small fraction of models where the potential and/or the initial conditions are fine-tuned. Some of our conclusions generalize at least qualitatively to multifield inflation and to scenarios where the interplay between curvature and isocurvature modes can be represented by the transfer function formalism. |
| first_indexed | 2024-09-23T13:44:08Z |
| format | Article |
| id | mit-1721.1/67346 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:44:08Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/673462022-09-28T15:48:18Z Non-Gaussianity in two-field inflation Peterson, Courtney M. Tegmark, Max Erik Massachusetts Institute of Technology. Department of Physics MIT Kavli Institute for Astrophysics and Space Research Tegmark, Max Erik Tegmark, Max Erik We derive semianalytic formulas for the local bispectrum and trispectrum from general two-field inflation and provide a simple geometric recipe for building observationally allowed models with large non-Gaussianity. We use the δN formalism to express the bispectrum in terms of spectral observables and the transfer functions, which encode the superhorizon evolution of modes. Similarly, we calculate the trispectrum and show that the trispectrum parameter τNL can be expressed entirely in terms of spectral observables, which provides a new consistency relation for two-field inflation. To generate observably large non-Gaussianity during inflation, we show that the sourcing of curvature modes by isocurvature modes must be extremely sensitive to a change in the initial conditions orthogonal to the inflaton trajectory and that the amount of sourcing must be nonzero. Under some minimal assumptions, we argue that the first condition is satisfied only when neighboring trajectories in the two-dimensional field space diverge during inflation. Geometrically, this means that the inflaton must roll along a ridge in the potential V for some time during inflation and that its trajectory must turn somewhat in field space. Therefore, it follows that under our assumptions, two-field scenarios with attractor solutions necessarily produce small non-Gaussianity. This explains why it has been so difficult to achieve large non-Gaussianity in two-field inflation and why it has only been achieved in a small fraction of models where the potential and/or the initial conditions are fine-tuned. Some of our conclusions generalize at least qualitatively to multifield inflation and to scenarios where the interplay between curvature and isocurvature modes can be represented by the transfer function formalism. National Science Foundation (U.S.) (grant AST-0708534) National Science Foundation (U.S.) (grant AST-0908848) David & Lucile Packard Foundation 2011-12-02T16:36:11Z 2011-12-02T16:36:11Z 2011-07 2010-12 Article http://purl.org/eprint/type/JournalArticle 0556-2813 http://hdl.handle.net/1721.1/67346 Peterson, Courtney, and Max Tegmark. “Non-Gaussianity in Two-field Inflation.” Physical Review D 84.2 (2011) © 2011 American Physical Society https://orcid.org/0000-0001-7670-7190 en_US http://dx.doi.org/10.1103/PhysRevD.84.023520 Physical Review D Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Peterson, Courtney M. Tegmark, Max Erik Non-Gaussianity in two-field inflation |
| title | Non-Gaussianity in two-field inflation |
| title_full | Non-Gaussianity in two-field inflation |
| title_fullStr | Non-Gaussianity in two-field inflation |
| title_full_unstemmed | Non-Gaussianity in two-field inflation |
| title_short | Non-Gaussianity in two-field inflation |
| title_sort | non gaussianity in two field inflation |
| url | http://hdl.handle.net/1721.1/67346 https://orcid.org/0000-0001-7670-7190 |
| work_keys_str_mv | AT petersoncourtneym nongaussianityintwofieldinflation AT tegmarkmaxerik nongaussianityintwofieldinflation |