More on the covariant retarded Green’s function for the electromagnetic field in de Sitter spacetime

Higuchi, Atsushi; Cheong, Lee Yen; Nicholas, Jack R.

doi:10.1103/physrevd.80.107502

Cited by 10 publications

(17 citation statements)

References 3 publications

(12 reference statements)

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“…The propagator obtained in this paper can now be used to study the massive vector field theory in de Sitter space. Various calculations have been performed in the massless case using the propagators in the Feynman gauge [21][22][23] as well as the Landau gauge [24][25][26] . Physical results should naturally be independent of ξ (and more generally of any gauge fixing term) if the gauge invariance is correctly incorporated.…”

Section: Discussionmentioning

confidence: 99%

Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space

Fröb

Higuchi

2014

Journal of Mathematical Physics

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We perform canonical quantization of the Stueckelberg Lagrangian for massive vector fields in the conformally flat patch of de Sitter space in the Bunch-Davies vacuum and find their Wightman two-point functions by the mode-sum method. We discuss the zero-mass limit of these two-point functions and their limits where the Stueckelberg parameter ξ tends to zero or infinity. It is shown that our results reproduce the standard flat-space propagator in the appropriate limit. We also point out that the classic work of Allen and Jacobson for the two-point function of the Proca field and a recent work by Tsamis and Woodard for that of the transverse vector field are two limits of our two-point function, one for ξ → ∞ and the other for ξ → 0. Thus, these two works are consistent with each other, contrary to the claim by the latter authors.

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Section: Discussionmentioning

confidence: 99%

Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space

Fröb

Higuchi

2014

Journal of Mathematical Physics

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“…Let us consider the gravitational field h ab coupled to the stress-energy tensor T ab . The field in the future domain of dependence of the Cauchy surface Σ, denoted by D + (Σ), is given in terms of the retarded Green's function as [1,2] h ab = h…”

Section: Gauge Generalization In the Gravitational Fieldmentioning

confidence: 99%

“…This is due to the spacelike nature of past infinity of de Sitter spacetime that casts doubt to the validity of the usage of the covariant retarded Green's function to act as a tool to generate the field causally from a source. This paradox can be resolved by including not only the source term but also the initial data on the Cauchy hypersurface at infinite past when calculating the field configuration using retarded Green's function [1,2,13]. Therefore the field is correctly reproduced to satisfy Gauss's Law at any instance of time over the Cauchy hypersurface.…”

Section: Introductionmentioning

confidence: 99%

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On the covariant gauge α of the linearized gravity in de Sitter spacetime

Cheong¹

2012

AIP Conference Proceedings

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In previous work [1,2], we studied the linearized gravity with covariant gauge β = 2/3 and α = 5/3. It was found that the sum of the source and initial contributions reproduces the correct field configuration over the whole de Sitter spacetime. In this paper, we extend this work to generalizing the linearized gravitational field in an arbitrary value of the gauge parameter α but the gauge parameter β remains the same.

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“…The contribution of the l = 0 term in (3.16) to the function (3.15) corresponds to the correlator in dS spacetime in the absence of the cosmic string (for the two-point functions of vector fields, including the massive ones; see [42][43][44][45][46][47][48]). It is simplified to 20) where | x| 2 = r 2 + r 2 − 2rr cos φ + | z| 2 is the square of the spatial distance between the points x and x and we have defined the dS invariant quantity…”

Section: Two-point Functionsmentioning

confidence: 99%

Electromagnetic vacuum fluctuations around a cosmic string in de Sitter spacetime

2017

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The electromagnetic field correlators are evaluated around a cosmic string in background of (D + 1)-dimensional dS spacetime assuming that the field is prepared in the Bunch-Davies vacuum state. The correlators are presented in the decomposed form where the string-induced topological parts are explicitly extracted. With this decomposition, the renormalization of the local vacuum expectation values (VEVs) in the coincidence limit is reduced to the one for dS spacetime in the absence of the cosmic string. The VEVs of the squared electric and magnetic fields, and of the vacuum energy density are investigated. Near the string they are dominated by the topological contributions and the effects induced by the background gravitational field are small. In this region, the leading terms in the topological contributions are obtained from the corresponding VEVs for a string on the Minkowski bulk multiplying by the conformal factor. At distances from the string larger than the curvature radius of the background geometry, the pure dS parts in the VEVs dominate. In this region, for spatial dimensions D > 3, the influence of the gravitational field on the topological contributions is crucial and the corresponding behavior is essentially different from that for a cosmic string on the Minkowski bulk. There are well-motivated inflationary models which produce cosmic strings. We argue that, as a consequence of the quantum-to-classical transition of super-Hubble electromagnetic fluctuations during inflation, in the post-inflationary era these strings will be surrounded by large-scale stochastic magnetic fields. These fields could be among the distinctive features of the cosmic strings produced during the inflation and also of the corresponding inflationary models.

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More on the covariant retarded Green’s function for the electromagnetic field in de Sitter spacetime

Cited by 10 publications

References 3 publications

Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space

Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space

On the covariant gauge α of the linearized gravity in de Sitter spacetime

Electromagnetic vacuum fluctuations around a cosmic string in de Sitter spacetime

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