Possible role of Berry phase in inflationary cosmological perturbations

Pal, Barun Kumar; Pal, Supratik; Basu, B.

doi:10.1088/1742-6596/405/1/012025

Cited by 2 publications

(2 citation statements)

References 12 publications

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“…Hannay's angle is the classical counterpart of the additional quantum phase known as Berry's phase [12][13][14][15]. Among the many areas in which Hannay's angle and Berry's phase play important roles, cosmology [6,8,[16][17][18][19][20][21][22][23] and celestial mechanics [24,25] have been actively investigated so far in connection with them. Hannay's angle (or Berry's phase) can be applied in extracting useful information associated with the theoretical interpretation of observational aspects of inflation-ary perturbations, such as the dynamical evolution of the quantum fluctuations [16], vacuum instability [17], the symmetry breaking of cosmological time [18], and energy conservation in a gravity-scalar system [19].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay’s angle

Bouguerra¹,

Maamache²,

Choi³

2017

Chinese Phys. C

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Hannay's angle is a classical analogue of the "geometrical phase factor" found by Berry in his research on the quantum adiabatic theorem. This classical analogue is defined if closed curves of constant action variables return to the same curves in phase space after an adaibatic evolution. Adiabatic evolution of Yang-Mills cosmology, which is described by a time-dependent quartic oscillator, is investigated. Phase properties of the Yang-Mills fields are analyzed and the corresponding Hannay's angle is derived from a rigorous evaluation. The obtained Hannay's angle shift is represented in terms of several observable parameters associated with such an angle shift. The time evolution of Hannay's angle in Yang-Mills cosmology is examined from an illustration plotted on the basis of numerical evaluation, and its physical nature is addressed. Hannay's angle, together with its quantum counterpart Berry's phase, plays a pivotal role in conceptual understanding of several cosmological problems and indeed can be used as a supplementary probe for cosmic inflation.

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Section: Introductionmentioning

confidence: 99%

Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay’s angle

Bouguerra¹,

Maamache²,

Choi³

2017

Chinese Phys. C

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“…Aharonov-Bohm 1959 [10] QED Topological Abelian anyons 1977 [23] Condensed Matter Topological 1982 [23] 1984 [23] Berry 1984 [2] Quantum Mechanics Adiabatic 2013 [ 20,21] Cosmology 2021 Cosmology with Bell's inequality violation (present work)…”

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confidence: 99%

C${\cal C}$osmological G${\cal G}$eometric P${\cal P}$hase F${\cal F}$rom P${\cal P}$ure Q${\cal Q}$uantum S${\cal S}$tates: A Study without/ with having Bell's Inequality Violation

Choudhury

2022

Fortschritte der Physik

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In this paper, using the concept of Lewis Riesenfeld invariant quantum operator method for finding continuous eigenvalues of quantum mechanical wave functions we derive the analytical expressions for the cosmological geometric phase, which is commonly identified to be the Pancharatnam Berry phase from primordial cosmological perturbation scenario. We compute this cosmological geometric phase from two possible physical situations, (1) In the absence of Bell's inequality violation and (2) In the presence of Bell's inequality violation having the contributions in the sub Hubble region (−kτ≫1$-k\tau \gg 1$), super Hubble region (−kτ≪1$-k\tau \ll 1$) and at the horizon crossing point (−kτ=1$-k\tau = 1$) for massless field (m/scriptH≪1$m/{\cal H}\ll 1$), partially massless field (m/scriptH∼1$m/{\cal H}\sim 1$) and massive/heavy field (m/scriptH≫1$m/{\cal H}\gg 1$), in the background of quantum field theory of spatially flat quasi De Sitter geometry. The prime motivation for this work is to investigate the various unknown quantum mechanical features of primordial universe. To give the realistic interpretation of the derived theoretical results we express everything initially in terms of slowly varying conformal time dependent parameters, and then to connect with cosmological observation we further express the results in terms of cosmological observables, which are spectral index/tilt of scalar mode power spectrum (nζ$n_{\zeta }$) and tensor‐to‐scalar ratio (r). Finally, this identification helps us to provide the stringent numerical constraints on the Pancharatnam Berry phase, which confronts well with recent cosmological observation.

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Possible role of Berry phase in inflationary cosmological perturbations

Cited by 2 publications

References 12 publications

Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay’s angle

Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay’s angle

C${\cal C}$osmological G${\cal G}$eometric P${\cal P}$hase F${\cal F}$rom P${\cal P}$ure Q${\cal Q}$uantum S${\cal S}$tates: A Study without/ with having Bell's Inequality Violation

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