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Contributions to Cosmology: An Overview of Peppe Marmo's Works

This presentation provides insights into Peppe Marmo's significant contributions to cosmology, focusing on topics such as Noether symmetries, Bianchi groups, quantum cosmology, and exact solutions for cosmological models. It also discusses recent developments in inflationary models and observational results. The text showcases key papers on Bianchi groups and the tomographic approach in cosmology, emphasizing the importance of studying quantum cosmology and classical tomograms. The main purposes of the research include formulating new approaches in quantum cosmology, reconstructing initial conditions, and exploring the quantum potential. The text delves into Hartle-Hawking Wigner functions and Wheeler-De Witt equations, highlighting the evolution of tomograms through probability transition functions. Examples of constrained FLRW models with and without cosmological constants are also presented.

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Contributions to Cosmology: An Overview of Peppe Marmo's Works

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  1. Cosmologia è Geometria an overview of the relevantcontributions of Peppe Marmo to Cosmology Cosimo Stornaiolo INFN – sezione di Napoli San Rufo 11-13 July 2016

  2. Contributions to cosmology • Noethersymmetries in cosmology • Bianchi groups • Quantum cosmology in tomographicapproach • Discussions and suggestions

  3. Noethersymmetries • Motivations • Inflation • Slow roll vs exactsolutions

  4. Experimental status of inflationarymodels • Recentobservationalresults (Planckmission) rule out 91% of the slow rollinflationarymodels • Onlythose with a potential with a plateau • Need a similarcheck for exactmodels

  5. see for example

  6. 111 citations! • Elencare i membri principali della scuola (preside, bibliotecario e così via) • Includere un organigramma

  7. The first twoequations are a dynamicsystemassociated to the vector

  8. The potentialis

  9. Constant of motion

  10. We need to consider all the cases after imposing • For the first two cases (with sin and sinh) we have and • For the exp case we have

  11. Solution with power law inflation

  12. Solution with exponentialinflation

  13. New approach to findexactsolutions for cosmologicalmodels with a scalar field. R. de Ritis,G. Marmo, G. Platania, C. Rubano, P. Scudellaro, C. Stornaiolo, Phys.Rev.D 42, 1091-1097 (1990)TOPCITE = 100+ • New exactsolutions of cosmologicalequations with considerationsupon the cosmologicalconstant. R. de Ritis, G. Marmo, G. Platania, C. Rubano, P. Scudellaro, C. Stornaiolo, Phys.Lett.A149, 79-83 (1990) • Scalar field, nonminimalcoupling, and cosmology, M. Demianski, R. de Ritis, G. Marmo, G. Platania, C. Rubano, P. Scudellaro, C. Stornaiolo Phys.Rev.D 44 3136-3146 (1991)

  14. Bianchi groups

  15. Papers • V.I Man’ko, G. Marmo and C.S.‘’Radon Transform of the Wheeler-De Witt equation and tomography of quantum states of the universe’’ Gen. Relativ. Gravit. (2005) 37: 99–114 • V.I Man’ko, G. Marmo and C.S. ‘’Cosmological dynamics in tomographic probability representation’’ Gen.Rel.Grav.37:2003-2014, 2005 • V.I Man’ko, G. Marmo and C.S. ‘‘Tomographic entropy and cosmology’’ Gen.Rel.Grav.40:1449-1465, 2008 • S. Capozziello, V.I Man’ko, G. Marmo and C.S. ‘ • Tomographic Representation of Minisuperspace Quantum Cosmology and Noether Symmetries’’. Gen. Rel. Grav. 40 (2008) 2627-2647 • S. Capozziello, V.I Man’ko, G. Marmo and C.S “A Tomographicdescription for classical and quantum cosmologicalperturbations. ”Phys.Scripta 80 (2009) 045901

  16. Main purposes • New formulation of quantum cosmology • Reconstruction of the initialconditions • Study of the properties of the quantum potential in quantum cosmology • Tomographicformulation of classicalcosmology.

  17. The Hartle-Hawking Wignerfunction

  18. The Hartle-Hawking tomogram

  19. Wheeler-De Witt tomographic equation • Similarlyto Quantum Mechanics , we can define a correspondingequationfor the Wheeler-DeWittequation

  20. ClassicalTomograms Itispossibletodefineclassicaltomograms, asfunctions on phasespace, ifinsteadof the Wignerfunctiononeconsiders the classicalsolutionof the Liouvilleequation. .

  21. Propagators • The evolution of tomograms is described by the following propagatore, i.e. probability transition functions in the following way

  22. The equation for the probability transition function for the harmonic oscillator • The probability transition function Π satisfies the following equation

  23. The homogeneous and isotropic metric • Let us consider the metric • Which, by defining the conformal time takes the form

  24. Examples of constrainedFLRW with and withoutcosmologicalconstant

  25. Tomogram for a constrainedsystem

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