Adiabatic invariants and scalar fields in a de Sitter space-time

Bertoni, Carlo Maria; Finelli⋆, F.; Venturi, G.

doi:10.1016/s0375-9601(97)00707-x

Cited by 49 publications

(79 citation statements)

References 21 publications

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“…it is straightforward to check that the unitarity conditions (34,36,38) are satisfied together with (28). Finally, strong continuity in the auxiliary parameter s follows from (35,37,39), by using the asymptotic expansions given above and the fact that a k (s 0 ) is square summable.…”

Section: B the Gowdy And Schmidt Modelsmentioning

confidence: 98%

“…It is important to point out here that the condition (28) implies that |f (k)| 2 |g(k)| 2 ≥ 1/4 and, hence, the convergence of (36) requires an appropriate fall-off of…”

Section: In This Case the Solution To (32) Is Given Bymentioning

confidence: 99%

“…This shows that the convergence of (36) would require lim |k|→∞ f (k)/g(k) = −2 which is not compatible with (28) and, hence,Ŝ(T, T 0 ) cannot be unitary.…”

Section: B the Gowdy And Schmidt Modelsmentioning

confidence: 99%

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Evolution operators for linearly polarized two-Killing cosmological models

Vergel

Villaseñor

2006

Phys. Rev. D

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Section: B the Gowdy And Schmidt Modelsmentioning

confidence: 98%

“…It is important to point out here that the condition (28) implies that |f (k)| 2 |g(k)| 2 ≥ 1/4 and, hence, the convergence of (36) requires an appropriate fall-off of…”

Section: In This Case the Solution To (32) Is Given Bymentioning

confidence: 99%

See 1 more Smart Citation

Evolution operators for linearly polarized two-Killing cosmological models

Vergel

Villaseñor

2006

Phys. Rev. D

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“…Decomposing the scalar field into a complete set of basis functions denoted by {f k ( x)}, see [19], as in (28) with τ replaced by t or η depending on which coordinates we are woking in, it is easy to see that the basis functions take the form f ( x) ∼ e i k· x . With definition (28), the action for the scalar field can be found from the time integral of the Lagrangian (31).…”

Section: Friedman-robertson-walker Space-timementioning

confidence: 99%

Time-dependent particle production and particle number in cosmological de Sitter space

Greenwood

2015

Int. J. Mod. Phys. D

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In this paper we consider the occupation number of induced quasi-particles which are produced during a time-dependent process using three-different methods: Instantaneous diagonalization, the usual Bogolyubov transformation between two different vacua (more precisely the instantaneous vacuum and the so-called adiabatic vacuum), and the Unruh-de Witt detector methods. Here we consider the Hamiltonian for a time-dependent Harmonic oscillator, where both the mass and frequency are taken to be time-dependent. From the Hamiltonian we derive the occupation number of the induced quasi-particles using the invariant operator method; in deriving the occupation number we also point out and make the connection between the Functional Schrödinger formalism, quantum kinetic equation, and Bogolyubov transformation between two different Fock space basis at equal times and explain the role in which the invariant operator method plays.As a concrete example, we consider particle production in the flat FRW chart of de Sitter spacetime. Here we show that the different methods lead to different results: The instantaneous diagonalization method leads to a power law distribution, while the usual Bogolyubov transformation and Unruh-de Witt detector methods both lead to thermal distributions (however the dimensionality of the results are not consistent with the dimensionality of the problem; the usual Bogolyubov transformation method implies that the dimensionality is 3D while the Unruh-de Witt detector method implies that the dimensionality is 7D/2). It is shown that the source of the descrepency between the instantaneous diagonalization and usual Bogolyubov methods is the fact that there is no notion of well-defined particles in the out vacuum due to a divergent term. In the usual Bogolyubov method, this divergent term cancels leading to the thermal distribution, while in the instantaneous diagonalization method there is no such cancelation leading to the power law distribution. However, to obtain the thermal distribution in the usual Bogolyubov method, one must use the large mass limit. On physical grounds, one should expect that only the modes which have been allowed to sample the horizon would be thermal, thus in the large mass limit these modes are well within the horizon and, even though they do grow, they remain well within the horizon due to the mass. Thus one should not expect a thermal distribution since the modes won't have a chance to thermalize.

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“…This is important since the production of particles can be inferred only after we choose some vacuum to compare with our physical solution. A natural choice is the Bunch-Davies vacuum, which is the adiabatic vacuum at early times (t → −∞) [20]. For this adiabatic vacuum at early times A = B = π/2H and ρ becomes ρ = (Hη)…”

Section: Quantization Of the Scalar Field With Emarkov Approachmentioning

confidence: 99%

Quantum scalar field in D-dimensional de Sitter spacetimes

Alencar¹,

Guedes²,

Landim³

et al. 2012

EPL

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In this work we investigate the quantum theory of scalar fields propagating in a D−dimensional de Sitter spacetime. The method of dynamic invariants is used to obtain the solution of the time-dependent Schrödinger equation. The quantum behavior of the scalar field in this background is analyzed, and the results generalize previous ones found in the literature. We point that the Bunch-Davies thermal bath depends on the choice of D and the conformal parameter ξ. This is important in extra dimension physics, as in the Randall-Sundrum model.

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Adiabatic invariants and scalar fields in a de Sitter space-time

Cited by 49 publications

References 21 publications

Evolution operators for linearly polarized two-Killing cosmological models

Evolution operators for linearly polarized two-Killing cosmological models

Time-dependent particle production and particle number in cosmological de Sitter space

Quantum scalar field in D-dimensional de Sitter spacetimes

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