Testing multifield inflation: A geometric approach
We develop an approach for linking the power spectra, bispectrum, and trispectrum to the geometric and kinematical features of multifield inflationary Lagrangians. Our geometric approach can also be useful in determining when a complicated multifield model can be well approximated by a model with on...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2013
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| Online Access: | http://hdl.handle.net/1721.1/80795 https://orcid.org/0000-0001-7670-7190 |
| _version_ | 1826207938403893248 |
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| 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 develop an approach for linking the power spectra, bispectrum, and trispectrum to the geometric and kinematical features of multifield inflationary Lagrangians. Our geometric approach can also be useful in determining when a complicated multifield model can be well approximated by a model with one, two, or a handful of fields. To arrive at these results, we focus on the mode interactions in the kinematical basis, starting with the case of no sourcing and showing that there is a series of mode conservation laws analogous to the conservation law for the adiabatic mode in single-field inflation. We then treat the special case of a quadratic potential with canonical kinetic terms, showing that it produces a series of mode sourcing relations identical in form to that for the adiabatic mode. We build on this result to show that the mode sourcing relations for general multifield inflation are an extension of this special case but contain higher-order covariant derivatives of the potential and corrections from the field metric. In parallel, we show how the mode interactions depend on the geometry of the inflationary Lagrangian and on the kinematics of the associated field trajectory. Finally, we consider how the mode interactions and effective number of fields active during inflation are reflected in the spectra and introduce a multifield consistency relation, as well as a multifield observable β[subscript 2] that can potentially distinguish two-field scenarios from scenarios involving three or more effective fields. |
| first_indexed | 2024-09-23T13:57:19Z |
| format | Article |
| id | mit-1721.1/80795 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:57:19Z |
| publishDate | 2013 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/807952022-09-28T17:21:51Z Testing multifield inflation: A geometric approach Peterson, Courtney M. Tegmark, Max Erik Massachusetts Institute of Technology. Department of Physics MIT Kavli Institute for Astrophysics and Space Research Tegmark, Max Erik We develop an approach for linking the power spectra, bispectrum, and trispectrum to the geometric and kinematical features of multifield inflationary Lagrangians. Our geometric approach can also be useful in determining when a complicated multifield model can be well approximated by a model with one, two, or a handful of fields. To arrive at these results, we focus on the mode interactions in the kinematical basis, starting with the case of no sourcing and showing that there is a series of mode conservation laws analogous to the conservation law for the adiabatic mode in single-field inflation. We then treat the special case of a quadratic potential with canonical kinetic terms, showing that it produces a series of mode sourcing relations identical in form to that for the adiabatic mode. We build on this result to show that the mode sourcing relations for general multifield inflation are an extension of this special case but contain higher-order covariant derivatives of the potential and corrections from the field metric. In parallel, we show how the mode interactions depend on the geometry of the inflationary Lagrangian and on the kinematics of the associated field trajectory. Finally, we consider how the mode interactions and effective number of fields active during inflation are reflected in the spectra and introduce a multifield consistency relation, as well as a multifield observable β[subscript 2] that can potentially distinguish two-field scenarios from scenarios involving three or more effective fields. National Science Foundation (U.S.) (Grant AST-0708534) National Science Foundation (U.S.) (Grant AST-0908848) David & Lucile Packard Foundation 2013-09-18T15:32:55Z 2013-09-18T15:32:55Z 2013-05 2012-11 Article http://purl.org/eprint/type/JournalArticle 1550-7998 1550-2368 http://hdl.handle.net/1721.1/80795 Peterson, Courtney M., and Max Tegmark. “Testing multifield inflation: A geometric approach.” Physical Review D 87, no. 10 (May 2013). © 2013 American Physical Society https://orcid.org/0000-0001-7670-7190 en_US http://dx.doi.org/10.1103/PhysRevD.87.103507 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 Testing multifield inflation: A geometric approach |
| title | Testing multifield inflation: A geometric approach |
| title_full | Testing multifield inflation: A geometric approach |
| title_fullStr | Testing multifield inflation: A geometric approach |
| title_full_unstemmed | Testing multifield inflation: A geometric approach |
| title_short | Testing multifield inflation: A geometric approach |
| title_sort | testing multifield inflation a geometric approach |
| url | http://hdl.handle.net/1721.1/80795 https://orcid.org/0000-0001-7670-7190 |
| work_keys_str_mv | AT petersoncourtneym testingmultifieldinflationageometricapproach AT tegmarkmaxerik testingmultifieldinflationageometricapproach |