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There is a persistent state of confusion regarding the account of the quantum origin of the seeds of cosmological structure during inflation.
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Section 10.4, page 364 of “ Structure Formation in the Universe”, T. Padmanabhan (Cambridge University Press, 1993)
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For reviews abut the various approaches to the measurement problem in quantum mechanics see for instance the classical reference “Philosophy of quantum mechanics. The interpretations of quantum mechanics in historical perspective” M. Jammer, (John Wiley and Sons, New York 1974); “The Interpretation of Quantum Mechanics” R. Omnes, ( Princeton University Press 1994), and the more specific critiques “ Why Decoherence has not Solved the Measurement Problem: A Response to P. W. Anderson” - S. L. Adler Stud. Hist. Philos. Mod. Phys
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“Why Decoherence has not Solved the Measurement Problem: A Response to P.W. Anderson”, S. L. Adler, Stud. Hist. Philos. Mod. Phys
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Sec 2.7 of “Quantum Theory Concepts and Methods”, A. Peres (Kluwer Academic Publishers 1993)
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For further discussion of the issue and other points of view see for instance: “Against Many Worlds Interpretations”, A. Kent, Int. J. Mod. Phys
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“Semiclassicality and decoherence of Cosmological perturbations”, D. Polarski and A. A. Starobinsky, Class. Quant. Grav
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Consistent interpretation of quantum mechanics using quantum trajectories. R. B. Griffiths, Phys. Rev. Lett
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Page 348 of “Physical Foundations of Cosmology”, V. Mukhanov (Cambridge University Press, 2005)
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“On the Quantum Origin of the Seeds of Cosmic Structure” A. Perez, H. Sahlmann, and D. Sudarsky, Classical and Quantum Gravity
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“Roots and fruits of Decoherence ”, H. D. Zeh, in Proceedings of the Seminarire Poincaré
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“The Road to Reality”, R. Penrose (Alfred A. Kopf- New York, 2006)
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“Spin Squeezing and Light Entanglement in Coherent Population Trapping” A. Dantan, J. Cviklinski, E. Giacobino, and M. Pinard Phys. Rev. Lett
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“The Seeds Of Cosmic Structure as a Door To New Physics”, proceedings of the conference ”Recent Developments in Gravity NEB XII ”, Napflio Greece, June 2006. J. Phys. Conf. Ser
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“The Seeds of Cosmic structure as a door to New Physics” D. Sudarsky, J. Phys. Conf. Ser
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“Quantum Physics and Human Language” J. B. Hartle, J. Phys. A
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Page 476 “Cosmology”, S. Weinberg (Oxford University Press, 2008)
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“The seeds of cosmic structure: A phenomenological approach” A. De Unanue & D. Sudarsky, Phys. Rev. D 78
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“Generalizing quantum mechanics for quantum space-time” J. B. Hartle,Contributed to 23rd Solvay Conference in Physics: The Quantum Structure of Space and Time, Brussel, Belgium, 1-3 Dec 2005. Published in *Brussels 2005, The quantum structure of space and time* 21-43 e-Print: gr-qc/0602013; “Generalizing quantum mechanics for quantum gravity” J. B. Hartle, Int. J. Theor. Phys
2008
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‘Time Translation of Quantum Properties” R. Laura & L. Vanni, Foundations of Physics
2009
Closest in time.
“ Inflationary Cosmology as a Probe of Primordial Quantum Mechanics” A. Valentini, Phys. Rev. D
2010
Closest in time.