Massless scalar field vacuum in de Sitter spacetime

Page, Don N.; Xing, Wu

doi:10.1088/1475-7516/2012/11/051

Cited by 17 publications

(24 citation statements)

References 43 publications

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“…The two sets of eigenvalues are in agreement up to a characteristic "knee" at which the causal set spectrum dips and ceases to obey a power-law with exponent −1. 13 There is a clear convergence of the spectrum with causal set size N except that the knee is pushed to smaller eigenvalues as N increases. Figure 3 shows scatter plots of Re[W SJ ] for pairs of events that are causally and spacelike related; it also shows the binned and averaged plots where the convergence becomes clear.…”

Section: Causal Diamond In 2d Minkowski Spacetimementioning

confidence: 91%

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Studies on the SJ vacuum in de Sitter spacetime

Surya

Nomaan

Yazdi

2019

J. High Energ. Phys.

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In this work we study the Sorkin-Johnston (SJ) vacuum in de Sitter spacetime for free scalar field theory. For the massless theory we find that the SJ vacuum can neither be obtained from the O(4) Fock vacuum of Allen and Folacci nor from the non-Fock de Sitter invariant vacuum of Kirsten and Garriga. Using a causal set discretisation of a slab of 2d and 4d de Sitter spacetime, we find the causal set SJ vacuum for a range of masses m ≥ 0 of the free scalar field. While our simulations are limited to a finite volume slab of global de Sitter spacetime, they show good convergence as the volume is increased. We find that the 4d causal set SJ vacuum shows a significant departure from the continuum Mottola-Allen α-vacua. Moreover, the causal set SJ vacuum is well-defined for both the minimally coupled massless m = 0 and the conformally coupled massless m = m c cases. This is at odds with earlier work on the continuum de Sitter SJ vacuum where it was argued that the continuum SJ vacuum is ill-defined for these masses. Our results hint at an important tension between the discrete and continuum behaviour of the SJ vacuum in de Sitter and suggest that the former cannot in general be identified with the Mottola-Allen α-vacua even for m > 0.

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Section: Causal Diamond In 2d Minkowski Spacetimementioning

confidence: 91%

“…There is also a de Sitter invariant and shift invariant vacuum defined in[13]. In this paper, we do not impose shift invariance.…”

mentioning

confidence: 99%

Studies on the SJ vacuum in de Sitter spacetime

Surya

Nomaan

Yazdi

2019

J. High Energ. Phys.

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“…In this sense, it would be intriguing to discuss a massless field with the exact shift symmetry in the de Sitter space (see also Ref. [91]). …”

Section: The Regularity For the Euclidean Vacuummentioning

confidence: 99%

Loops in inflationary correlation functions

Tanaka

Urakawa

2013

Class. Quantum Grav.

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Abstract. We review the recent progress regarding the loop corrections to the correlation functions in the inflationary universe. A naive perturbation theory predicts that loop corrections generated during inflation suffer from various infrared (IR) pathologies. Introducing an IR cutoff by hand is neither satisfactory nor enough to fix the problem of secular growth, which may ruin the predictive power of inflation models if the inflation lasts sufficiently long. We discuss the origin of the IR divergences and explore the regularity conditions of loop corrections for the adiabatic perturbation, the iso-curvature perturbation, and the tensor perturbation, in turn. These three kinds of perturbations have qualitative differences, but in discussing the IR regularity there is a feature common to all cases, which is the importance of the proper identification of observable quantities. Genuinely observable quantities should respect the gauge invariance from the view point of a local observer. Interestingly, we find that the requirement of the IR regularity restricts the allowed quantum states.

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“…In this work, we revisit the study of a minimally coupled scalar field φ(x) of mass m (which could be zero or non-zero) in a Friedmann universe with a power-law expansion a 2 (η) ∝ η −2q in terms of the conformal time η, with q = 1 representing the de Sitter universe. Though this subject has a literature running to several hundreds of papers (we provide a handful sample which a reader can approach for a quick survey, viz., [11,14,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]), we find that fresh insights and new results are still possible. We summarize these below in order to guide the reader through this, rather lengthy, paper.…”

Section: Introductionmentioning

confidence: 99%

Quantum correlators in Friedmann spacetimes: The omnipresent de Sitter spacetime and the invariant vacuum noise

et al. 2018

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We discuss several aspects of quantum field theory of a scalar field in a Friedmann universe. (i) We begin by showing that it is possible to map the dynamics of a scalar field with a given mass, in a given Friedmann background to another scalar field of a different mass in another Friedmann universe. In particular one can map the dynamics of (1) a massless scalar field in a universe with power-law expansion to (2) a massive scalar field in the de Sitter spacetime. This allows us to understand several features of either system in a simple manner and clarifies several issues related to the massless limit. (ii) We relate the Euclidean Green's function for the de Sitter spacetime to the solution of a hypothetical electrostatic problem in D=5 and obtain, in a very simple manner, a useful integral representation for the Green's function. This integral representation is helpful in the study of several relevant limits, and in recovering some key results which are -though known earlier -not adequately appreciated. One of these results is the fact that, in any Friedmann universe, sourced by a negative pressure fluid, the Wightman function for a massless scalar field is divergent. This shows that the divergence of Wightman function for the massless field in the de Sitter spacetime is just a special, limiting, case of this general phenomenon. (iii) We provide a generally covariant procedure for defining the power spectrum of vacuum fluctuations in terms of the different Killing vectors present in the spacetime. This allows one to study the interplay of the choice of vacuum state and the nature of the power spectrum in different co-ordinate systems, in the de Sitter universe, in a unified manner. (iv) As a specific application of this formalism, we discuss the power spectra of vacuum fluctuations in the static (and Painlevé) vacuum states in the de Sitter spacetime and compare them with the corresponding power spectrum in the Bunch-Davies vacuum. We demonstrate how these power spectra are related to each other in a manner similar to the power spectra detected by the inertial and Rindler observers in flat spacetime. This also gives rise to a notion of an invariant vacuum noise in the corresponding spacetimes which is observer independent. (v) In addition, several conceptual and technical issues regarding quantum fields in general cosmological spacetimes are clarified as a part of this study. * kinjalk@iisermohali.ac.in † karthik@iucaa.in ‡

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Massless scalar field vacuum in de Sitter spacetime

Cited by 17 publications

References 43 publications

Studies on the SJ vacuum in de Sitter spacetime

Studies on the SJ vacuum in de Sitter spacetime

Loops in inflationary correlation functions

Quantum correlators in Friedmann spacetimes: The omnipresent de Sitter spacetime and the invariant vacuum noise

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