Shifted Riccati Procedure: Application to Conformal Barotropic FRW Cosmologies
In the case of barotropic FRW cosmologies, the Hubble parameter in conformal time is the solution of a simple Riccati equation of constant coefficients. We consider these cosmologies in the framework of nonrelativistic supersymmetry that has been effective in the area of supersymmetric quantum mecha...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146789 |
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| Zitieren: | Shifted Riccati Procedure: Application to Conformal Barotropic FRW Cosmologies / H.C. Rosu, K.V. Khmelnytskaya // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862709856764428288 |
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| author | Rosu, H.C. Khmelnytskaya, K.V. |
| author_facet | Rosu, H.C. Khmelnytskaya, K.V. |
| citation_txt | Shifted Riccati Procedure: Application to Conformal Barotropic FRW Cosmologies / H.C. Rosu, K.V. Khmelnytskaya // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In the case of barotropic FRW cosmologies, the Hubble parameter in conformal time is the solution of a simple Riccati equation of constant coefficients. We consider these cosmologies in the framework of nonrelativistic supersymmetry that has been effective in the area of supersymmetric quantum mechanics. Recalling that Faraoni [Amer. J. Phys. 67 (1999), 732-734] showed how to reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations, we set the latter equations in the supersymmetric approach and divide their solutions into two classes of 'bosonic' (nonsingular) and 'fermionic' (singular) cosmological zero-mode solutions. The fermionic equations can be considered as representing cosmologies of Stephani type, i.e., inhomogeneous and curvature-changing in the conformal time. We next apply the so-called shifted Riccati procedure by introducing a constant additive parameter, denoted by S, in the common Riccati solution of these supersymmetric partner cosmologies. This leads to barotropic Stephani cosmologies with periodic singularities in their spatial curvature indices that we call U and V cosmologies, the first being of bosonic type and the latter of fermionic type. We solve completely these cyclic singular cosmologies at the level of their zero modes showing that an acceptable shift parameter should be purely imaginary, which in turn introduces a parity-time (PT) property of the partner curvature indices.
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| id | nasplib_isofts_kiev_ua-123456789-146789 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:20:48Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
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| spelling | Rosu, H.C. Khmelnytskaya, K.V. 2019-02-11T15:16:03Z 2019-02-11T15:16:03Z 2011 Shifted Riccati Procedure: Application to Conformal Barotropic FRW Cosmologies / H.C. Rosu, K.V. Khmelnytskaya // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81Q60 DOI:10.3842/SIGMA.2011.013 https://nasplib.isofts.kiev.ua/handle/123456789/146789 In the case of barotropic FRW cosmologies, the Hubble parameter in conformal time is the solution of a simple Riccati equation of constant coefficients. We consider these cosmologies in the framework of nonrelativistic supersymmetry that has been effective in the area of supersymmetric quantum mechanics. Recalling that Faraoni [Amer. J. Phys. 67 (1999), 732-734] showed how to reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations, we set the latter equations in the supersymmetric approach and divide their solutions into two classes of 'bosonic' (nonsingular) and 'fermionic' (singular) cosmological zero-mode solutions. The fermionic equations can be considered as representing cosmologies of Stephani type, i.e., inhomogeneous and curvature-changing in the conformal time. We next apply the so-called shifted Riccati procedure by introducing a constant additive parameter, denoted by S, in the common Riccati solution of these supersymmetric partner cosmologies. This leads to barotropic Stephani cosmologies with periodic singularities in their spatial curvature indices that we call U and V cosmologies, the first being of bosonic type and the latter of fermionic type. We solve completely these cyclic singular cosmologies at the level of their zero modes showing that an acceptable shift parameter should be purely imaginary, which in turn introduces a parity-time (PT) property of the partner curvature indices. This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
 One of the authors (HCR) thanks the Organizing Committee for the kind invitation and the
 administration of the Benasque Center for their warm hospitality. We also thank the referees for their valuable comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Shifted Riccati Procedure: Application to Conformal Barotropic FRW Cosmologies Article published earlier |
| spellingShingle | Shifted Riccati Procedure: Application to Conformal Barotropic FRW Cosmologies Rosu, H.C. Khmelnytskaya, K.V. |
| title | Shifted Riccati Procedure: Application to Conformal Barotropic FRW Cosmologies |
| title_full | Shifted Riccati Procedure: Application to Conformal Barotropic FRW Cosmologies |
| title_fullStr | Shifted Riccati Procedure: Application to Conformal Barotropic FRW Cosmologies |
| title_full_unstemmed | Shifted Riccati Procedure: Application to Conformal Barotropic FRW Cosmologies |
| title_short | Shifted Riccati Procedure: Application to Conformal Barotropic FRW Cosmologies |
| title_sort | shifted riccati procedure: application to conformal barotropic frw cosmologies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146789 |
| work_keys_str_mv | AT rosuhc shiftedriccatiprocedureapplicationtoconformalbarotropicfrwcosmologies AT khmelnytskayakv shiftedriccatiprocedureapplicationtoconformalbarotropicfrwcosmologies |