Gauge-invariant perturbations at second order: multiple scalar fields on large scales
Open accessAbstract
We derive the governing equations for multiple scalar fields minimally coupled to gravity in a flat Friedmann–Robertson–Walker background spacetime on large scales. We include scalar perturbations up to second order and write the equations in terms of physically transparent gauge-invariant variables at first and second order. This allows us to write the perturbed Klein–Gordon equation at second order solely in terms of the field fluctuations on flat slices at first and second order.
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According to the δN-formalism, ζ evaluated at some time tc is equivalent, on large scales, to the perturbation of the number of e-foldings N from an initial flat hypersurface at t* to a final comoving or uniform density hypersurface at tc.
“According to the so called δN -formalism [30, 31, 32], ζ , evaluated at some time t = t c , is equivalent, on large scales , to the perturbation of the number of e -foldings N ( t c , t ∗ , x ) from an initial fl at hypersurface at t = t ∗ , to a final comoving - or, equivalently, uniform density - hypersurface at t = t c .”
From Non-Gaussianities in two-field inflation (2006) · cites this paper as [31]
The introduction says the ΔN formalism relates the comoving curvature perturbation to a perturbation in the number of e-foldings. The discussion around Eq. (4.8) says comoving and uniform-density curvature perturbations coincide on large scales. Our copy does not specify the claimed initial flat and final comoving or uniform-density hypersurfaces for that e-folding calculation. (LLM, conf=0.85)
Experimental — accuracy not yet measuredFor multi-field inflation, the scalar spectral index at lowest order in slow-roll is given by Eq. (15).
“For multi-field inflation, the expression for the scalar spectral index has been given, for instance, in [31, 1]. At lowest order in slow-roll one has [2]”
From Non-Gaussianities in two-field inflation (2006) · cites this paper as [31]
The Introduction mentions calculating the spectral index, but gives no expression for it. Section 8 applies slow roll to a two-field model to calculate the second-order curvature perturbation, not the lowest-order scalar spectral index. A search for “spectral index” found no formula in our copy that could verify the attribution to Eq. (15). (LLM, conf=0.76)
Experimental — accuracy not yet measured
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Cited by
Sorted by citations
Non-Gaussianities in two-field inflation
Vernizzi, F., & Wands, D. (2006) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2006/05/019 · Cited by 274 · see citing works
- Authors
- Malik, K. A.
- Affiliations
- Lancaster University (GB)
- Corresponding author
- Malik, Karim A
- ORCID
- Malik, Karim A
- Venue
- Journal of Cosmology and Astroparticle Physics
- Publisher
- IOP Publishing
- Published
- 2005-11-16
- Volume
- 2005
- Issue
- 11
- Pages
- 005-005
- ISSN
- 1475-7508 (ISSN-L)
- 1475-7516
- OpenAlex
- W1972011676
- Cited by
- 72
- References
- 0
- Citations by year
- 2025: 1 · 2023: 1 · 2021: 1 · 2019: 1 · 2018: 1 · 2017: 2 · 2016: 5 · 2015: 4 · 2014: 2 · 2013: 7 · 2012: 3
- FWCI
- 6.40
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Cosmology and Astroparticle Physics (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Lancaster EPrints (Lancaster University) (submittedVersion)
- 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 › Relativity and Gravitational Theory
- Keywords
- gauge-invariant perturbations, second-order perturbation theory, multiple scalar fields, scalar perturbations, Klein-Gordon equation, large-scale structure, FRW cosmology, cosmological perturbation theory
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