Berry phase of primordial scalar and tensor perturbations in single-field inflationary models

Balajany, Hamideh; Mehrafarin, Mohammad

doi:10.1016/j.physleta.2018.04.026

Cited by 2 publications

(3 citation statements)

References 34 publications

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“…obtained [31,32] by using the same approach as for the time-independent harmonic oscillator, as explained in appendix E. Plugging those states into eq. ( 5.21) gives rise to the following phases:…”

Section: Jcap02(2020)022mentioning

confidence: 99%

“…(6.39) reduces to u k + k 2 u k = 0 in that case, i.e. simply 32 For small arguments and real ν, the behaviour of the Hankel functions is given by [47] H (1) ν (z)…”

Section: Jcap02(2020)022mentioning

confidence: 99%

“…They define a Fock space, and in this appendix we elaborate on the results of refs. [31,32] and derive the wavefunctions for the n-particles states (Fock states, see appendix E.1) and for the eigenstates of the annihilation operator (quasiclassical states, see appendix E.2).…”

Section: Jcap02(2020)022mentioning

confidence: 99%

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Canonical transformations and squeezing formalism in cosmology

Grain

Vennin

2020

J. Cosmol. Astropart. Phys.

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Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part of this work we study the symplectic structure associated with linear canonical transformations. After reviewing salient mathematical properties of the symplectic group in a pedagogical way, we introduce the squeezing formalism, and show how any linear dynamics can be cast in terms of an invariant representation. In the second part, we apply these results to the case of cosmological perturbations, and focus on scalar field fluctuations during inflation. We show that different canonical variables select out different vacuum states, and that this leaves an ambiguity in observational predictions if initial conditions are set at a finite time in the past. We also discuss how the effectiveness of the quantum-to-classical transition of cosmological perturbations depends on the set of canonical variables used to describe them.

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Section: Jcap02(2020)022mentioning

confidence: 99%

“…(6.39) reduces to u k + k 2 u k = 0 in that case, i.e. simply 32 For small arguments and real ν, the behaviour of the Hankel functions is given by [47] H (1) ν (z)…”

Section: Jcap02(2020)022mentioning

confidence: 99%

See 1 more Smart Citation

Canonical transformations and squeezing formalism in cosmology

Grain

Vennin

2020

J. Cosmol. Astropart. Phys.

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Geometric phase of cosmological scalar and tensor perturbations in f(R) gravity

Balajany

Mehrafarin

2018

Mod. Phys. Lett. A

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By using the conformal equivalence of f(R) gravity in vacuum and the usual Einstein theory with scalar-field matter, we derive the Hamiltonian of the linear cosmological scalar and tensor perturbations in f(R) gravity in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes as a Lewis–Riesenfeld phase.

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Berry phase of primordial scalar and tensor perturbations in single-field inflationary models

Cited by 2 publications

References 34 publications

Canonical transformations and squeezing formalism in cosmology

Canonical transformations and squeezing formalism in cosmology

Geometric phase of cosmological scalar and tensor perturbations in f(R) gravity

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