A General Analytic Formula for the Spectral Index of the Density Perturbations Produced during Inflation
Open accessAbstract
The standard calculation of the spectrum of density perturbations produced during inflation assumes that there is only one real dynamical degree of freedom during inflation. However, there is no reason to believe that this is actually the case. In this paper we derive general analytic formulae for the spectrum and spectral index of the density perturbations produced during inflation.
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The first term on the right hand side of Eq. (26) is momentum dependent and comes from the three-point correlation functions of the fields, computed by quantizing the perturbations inside the Hubble radius during inflation.
“The first term on the right hand side of Eq. (26) is momentum dependent and comes from the three-point correlation functions of the fields, Eq. (21), computed by quantizing the perturbations inside the Hubble radius during inflation [35, 37].”
From Non-Gaussianities in two-field inflation (2006) · cites this paper as [35]
The Introduction (p. 2) describes scalar-field vacuum fluctuations on scales smaller than the Hubble radius, and §4 (p. 6) discusses the momentum dependence of the perturbation spectrum. Our copy does not connect either point to a three-point correlation function or show that such a function produces the cited first term. (LLM, conf=0.82)
Experimental — accuracy not yet measuredScalar fields need not only couple through the potential but may also couple kinetically.
“Generally, the scalar fields need not only couple through the potential, but may also couple kinetically [44, 45, 46, 47].”
From Conditions for large non-Gaussianity in two-field slow-roll inflation (2008) · cites this paper as [45]
During slow-roll inflation, the field three-point correlation functions do not vanish.
“However, Seery and Lidsey [35] have found that during slow-roll inflation the field three-point correlation functions do not vanish and read”
From Non-Gaussianities in two-field inflation (2006) · cites this paper as [35]
Section 4 (p. 6) discusses scalar-field perturbations and the spectral index under slow-roll conditions, but does not address whether field three-point correlations vanish. Searches for three-point correlations and the bispectrum found no passage supporting the claim. The citing sentence names Seery and Lidsey, but that does not establish a source from this paper's text. (LLM, conf=0.76)
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Research works printed but not linked: 4
- [1][1] A. D. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic, Switzerland, 1990); E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, New York, 1990). -
- [15][15] A. A. Starobinsky and J. Yokoyama, gr-qc/9502002. - · arXiv
- [17][17] J. Garc´ ıa-Bellido and D. Wands, gr-qc/9506050. - · arXiv
- [18][18] D. S. Salopek, astro-ph/9506146. - · arXiv
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Lehners, J.-L. (2008) · Physics Reports · doi:10.1016/j.physrep.2008.06.001 · Cited by 381 · see citing works
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Choi, K.-Y., Hall, L. M. H., & Bruck, C. V. D. (2007) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2007/02/029 · Cited by 98 · see citing works
- Authors
- Sasaki, M., & Stewart, E. D.
- Affiliations
- The University of Osaka (JP)
- Lancaster University (GB)
- ORCID
- Sasaki, M.
- Venue
- Progress of Theoretical Physics
- Publisher
- Oxford University Press (OUP)
- Published
- 1996-01-01
- Volume
- 95
- Issue
- 1
- Pages
- 71-78
- ISSN
- 0033-068X (ISSN-L)
- 1347-4081
- OpenAlex
- W2101586960
- Cited by
- 982
- References
- 0
- Citations by year
- 2026: 32 · 2025: 43 · 2024: 41 · 2023: 39 · 2022: 36 · 2021: 35 · 2020: 24 · 2019: 21 · 2018: 37 · 2017: 26 · 2016: 47 · 2015: 44 · 2014: 51 · 2013: 62 · 2012: 64
- FWCI
- 8.26
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Progress of Theoretical Physics (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Keywords
- cosmic inflation, density perturbations, spectral index, power spectrum, closed-form expressions, scalar field dynamics, primordial perturbations
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