The Berry phase in inflationary cosmology

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

doi:10.1088/0264-9381/30/12/125002

Cited by 11 publications

(20 citation statements)

References 53 publications

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“…Now that there is no such discrepency, two interpretation should yield identical results. In [18], we have been able to show that isotropy can be achieved at late times for Bianchi-I.…”

Section: Generalisationmentioning

confidence: 85%

“…The boundary condition(s) can result to a specific energy specturm of the Hamiltonian of the universe, can even set a ground state energy for the universe, which is what happens in Bianchi-I [18].…”

Section: Generalisationmentioning

confidence: 99%

“…However, specifcally commenting on how a particular extension effects a particular model requires solving Wheeler-deWitt equation, which can be tricky for many cases. For Bianchi-I, the extension can be done explicitly for a particular operator ordering [15,18]. In case of Binachi-V, IX, Kantowoski Sachs (KS) model, it is possible to do it explicitly only for some choices of the perfect fluid, for a particular operator ordering [16,17].…”

Section: Generalisationmentioning

confidence: 99%

“…For KS and Bianchi-III, we see the differential equation is not even separable for α = 1 fluid. In spite of these technical difficulties, we can take cue from Bianchi-I studied in [18] to make following remarks: 1. Self-adjoint extension essentially controls the behaviour of wavefunction near singularity when sclae factor shrinks to 0.…”

Section: Generalisationmentioning

confidence: 99%

“…Even when an explicit solution is not found, the existence of a self-adjoint extension for the Hamiltonian can be ascertained [15,16,17]. Furthermore, this is acheieved not at the cost of the anisotropy itself [18]. With a scalar field distribution, Almeida et al discussed the possibility of a self-adjoint extension for the Hamiltonian [19].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Anisotropic models are unitary: A rejuvenation of standard quantum cosmology

Pal

Banerjee

2016

Journal of Mathematical Physics

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The present work proves that the folk-lore of the pathology of non-conservation of probability in quantum anisotropic models is wrong. It is shown in full generality that all operator ordering can lead to a Hamiltonian with a self-adjoint extension as long as it is constructed to be a symmetric operator, thereby making the problem of non-unitarity in context of anisotropic homogeneous model a ghost. Moreover, it is indicated that the selfadjoint extension is not unique and this non-uniqueness is suspected not to be a feature of Anisotropic model only, in the sense that there exists operator orderings such that Hamiltonian for an isotropic homogeneous cosmological model does not have unique selfadjoint extension, albeit for isotropic model, there is a special unique extension associated with quadratic form of Hamiltonian i.e Friedrichs extension. Details of calculations are carried out for a Bianchi III model.

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“…Now that there is no such discrepency, two interpretation should yield identical results. In [18], we have been able to show that isotropy can be achieved at late times for Bianchi-I.…”

Section: Generalisationmentioning

confidence: 85%

Section: Generalisationmentioning

confidence: 99%

Section: Generalisationmentioning

confidence: 99%

Section: Generalisationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Anisotropic models are unitary: A rejuvenation of standard quantum cosmology

Pal

Banerjee

2016

Journal of Mathematical Physics

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

Balajany

Mehrafarin

2018

Physics Letters A

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In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations 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 in terms of the Lewis-Riesenfeld phase. We conclude by discussing the discrepancy in the results of Pal et. al [Class. Quant. Grav. 30, 12 (2013)] for these Berry phases, which is resolved to yield agreement with our results.

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The Berry phase in inflationary cosmology

Cited by 11 publications

References 53 publications

Anisotropic models are unitary: A rejuvenation of standard quantum cosmology

Anisotropic models are unitary: A rejuvenation of standard quantum cosmology

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

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

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