Abstract
On the largest scales there is evidence of discrete structure, examples of this are superclusters and voids and also by redshift taking discrete values. In this paper it is proposed that discrete redshift can be explained by using the spherical harmonic integer l; this occurs both in the metric or density perturbations and also in the solution of wave equations in Robertson-Walker spacetime. It is argued that the near conservation of energy implies that l varies regularly for wave equations in Robertson-Walker spacetime, whereas for density perturbations l cannot vary regularly. Once this is assumed then perhaps the observed value of discrete redshift provides the only observational or experimental data that directly requires an explanation using both gravitational and quantum theory. In principle a model using this data could predict the scale factor R (or equivalently the deceleration parameter q). Solutions of the Klein-Gordon equation in Robertson-Walker spacetimes are used to devise models which have redshift taking discrete values, but they predict a microscopic value for R. A model in which the stress of the Klein-Gordon equation induces a metrical perturbation of Robertson-Walker spacetime is devised. Calculations based upon this model predict that the Universe is closed with 2 q0 - 1=10-4.
Similar content being viewed by others
References
Agnese, A.G.: 1984, A Naive Approach to the Quantization of the Microscopic and Macroscopic World, Lett. Nuovo Cim. 40, 111-114.
Agnese, A.G. and Testa, R.: 1997, Clues to Discretization on the Cosmic Scale, Phys. Lett. A227, 165-171.
Allen, C.W.: 1973, Astrophysical Quantities, Athlone Press, p. 163.
Alvarez, E.: 1989, Quantum Gravity: an introduction to some recent results, Rev. Mod. Phys. 6, 561-604.
Arp, Halton: 1996, The 37.5 Km s-1 Redshift Periodicity of Galaxies as the Machion Frequency, Phys. Lett. B387, 48-50.
Arp, H., Bi, H.G., Chu. Y. and Zhu, X.: 1990, Periodicity of quasar redshifts, Astron. Astrophys. 239, 33-49.
Arp, H. and Sulentic, J.W.: 1983, Analysis of Groups of Galaxies with Accurate Redshifts, Astrophys. J. 291, 88-111.
Barrow, J.D. and Matzner, R.A.: 1980, Size of a bouncing mixmaster universe, Phys. Rev. D21, 336-340.
Barut, A.O., Budinich, P., Niederle, J. and Raczka, R.: 1994, Conformal Space-times-The Arenas of Physics and Cosmology, Found. Phys. 24, 1461-1494.
Barut, A.O. and Duru, I.H.: 1987, Exact Solution of the Dirac Equation in spacially flat Robertson-Walker spacetimes, Phys. Rev. D36, 3705-3711.
Budinich, P.: 1995, Conformal Compactificatied Homogeneous Spaces, Possible Observable Consequences, Found. Phys. 25, 969-993.
Budinich, P., Nurowski, P., Racza, R. and Ramella, M.: 1995, The Spontaneous Violation of the Cosmological Principle and the Possible Wave Structures of the Universe, Astrophys. J. 451, 10-23.
Broadhurst, T.J., Ellis, R.S., Koo, D.C. and Szalay, A.S.: 1990, Large-scale Distribution of Galaxies at the Galactic Poles, Nature 343, 726-728.
Buitrago, J.: 1988, A Different Approach to the Cosmological Quantized Redshift Problem, Astrophys. Lett. 27, 1-4.
Burbidge, G.R. and O'Dell, S.L.: 1972, The distribution of redshifts of quasi-stellar objects and related emission-line objects, Astrophys. J. 178, 583-605.
Capozziello, S., Feoli, A. and Lambiase, G.: 1998, Oscillating Universes as Eigensolutions of [a] Cosmological Schrödinger Equation, gr-qc/9808010.
Carneiro, S.: 1998, The Large Number Hypothesis and Quantum Mechanics, gr-qc/9712014, Found. Phys. Lett. 11, 95.
Carvalho, J.C.: 1985, On Large Scale Quantization, Lett. Nuovo Cim. 44, 337-342.
Carvalho, J.C.: 1997, The Periodic Distribution of Redshifts, Astrophys. Space Sci. 249, 227-234.
Cocke, W.J.: 1983, A Theoretical Framework for Quantized Redshift and Uncertainty in Cosmology, Astrophys. Lett. 23, 239-249.
Cocke, W.J.: 1985, Theory and Interpretation of Quantized Extragalactic Red Shifts, Astrophys. J. 288, 22-28.
Cocke, W.J. and Tifft, W.G.: 1983, Redshift Quantization in Compact-groups of Galaxies, Astrophys. J. 268, 56-59.
Cohen, J.: 1999, Clustering in the Caltech Faint Galaxy Redshift Survey, astro-ph/9910242.
Cowan, C.L.: 1969, Periodic Clustering of Red-shifts in the Spectra of Quasi-stellar and other Unusual Objects, Nature 224, 665-656.
Crittenden, R.G. and Steinhart, P.J.: 1992, New Constraints and Improvements on Oscillating Physics, Astrophys. J. 395, 3600-365.
Crousdale, M.R.: 1989, Periodicity in Galaxy Redshifts, Astrophys. J. 345, 72-83.
Dekel, A., Blumenthal, G.R., Primack, J.R. and Stanhill, D.: 1992, Large-scale Periodicity and Gaussian fluctuations, Mon. Not. R. Astron. Soc. 257, 715-730.
DerSarkissian, M.: 1984, Does Wave-Particle Duality Apply to Galaxies, Lett. Nuovo Cim. 40, 390-394.
DerSarkissian, M.: 1985, New Consequences of Cosmic Quantum-mechanics, Lett. Nuovo Cim. 43, 274-276.
Dirac, P.A.M.: 1937, The Cosmological Constants, Nature 139, 323-323.
Dwari, D., DasGupta, P. and Narlikar, J.V.: 1996, Peaks and Periodicities in the Redshift Distribution of Quasi-Stellar Objects, IAU Symp. 168, 555.
Edelen, D.G.B.: 1994, Space-Time Defect Solutions of the Einstein Field Equations, Int. J. Theor. Phys. 33, 1315-1334.
Ehlers, J.: 1971, General Relativity and Kinetic Theory, in: R.K. Sachs (ed.), Rendiconti della Scuola Internazional di fisica Enrico Fermi 47, 1-70.
Einasto, J., Einasto, M., Gottlöber, S., Múller, V., Sarr, V., Starobinsky, A.A., Tago, E., Tucker, D., Andernach, H. and Frisch, P.: 1997, A 120-Mpc periodicity in the three-dimensional distribution of galaxy superclusters, Nature 385, 139.
Ellis, G.F.R.: 1971, Relativistic Cosmology, in: R.K. Sachs (ed.), Rendiconti della Scuola Internazional di fisica Enrico Fermi 47, 104-182.
Farhi, E., Graham, N., Haagensen, P.E., Jaffe, R.L.: 1998, Finite Quantum Fluctuations About Static Field Configurations, hep-th/9802015.
Faroni, V.: 1997, The Redshift Periodicity of Galaxies as a Probe of the Correctness of General Relativity, gr-qc/9608067, Gen. Relativ. Gravitation 29, 251-257.
Fischer, J.R. and Tully, R.B.: 1981, Neural Hydrogen Observations of a Large Sample of Galaxies, Astrophys. J. Suppl. 47, 139-200.
Ford, L.H.: 1976, Quantum Vacuum Energy in a Closed Universe, Phys. Rev. D14, 3304-3313.
Freedman, W.L.: 1999, The Hubble Constant and the Expansion age of the Universe, astroph/ 9909076. David Schramm Memorial Volume, Physics Reports, Elsevier, 2000, in press.
Green, R.F. and Richstone, D.O.: 1976, On the Reality of Periodicities in the Redshift Distribution of Emission-line Objects, Astrophys. J. 208, 639-645.
Greenberger, D.M.: 1983, Quantization in the Large, Found. Phys. 13, 903-951.
Grishchuk, L.P.: 1997, Signatures of Quantum Gravity in the Large-Scale Universe, gr-qc/9708070.
Guthrie, B.N.G. and Napier, W.M.: 1991, Evidence for Redshift Periodicity in Nearby Field Galaxies, Mon. Not. R. Astron. Soc. 253, 533-544.
Guthrie, B.N.G. and Napier, W.M.: 1996, Redshift Periodicity in the Local Supercluster, Astron. Astrophys. 310, 353-370.
Haynes, M.P.: 1981, Neutral Hydrogen Streams in Groups of Galaxies. 1. Observations, Astron. J. 86, 1126.
Helou, G., Salpeter, E.E. and Terzian, Y.: 1982, Neutral Hydrogen in Binary and Multiple galaxies, Astron. J. 87, 1443.
Hill, C.T., Steinhardt, P.J. and Turner, M.S.: 1990, Can Oscillating Physics Explain an Apparently Periodic Universe?, Phys. Lett. B252, 343-348.
Hill, C.T., Steinhardt, P.J. and Turner, M.S.: 1991, Coherent Peculiar Velocities and Periodic Redshifts, Astrophys. J. 366, L57-L60.
Holba, Á., Horváth, I., Lukács, B. and Paál, G.: 1994, Once More on Quasar Periodicities, Astrophys. Space Sci. 222, 65-83.
Ikeuchi, S. and Turner, E.L.: 1991, Quasi-periodic Structures in the Large-scale Galaxy Distribution and Three-dimensional Voroni Tessellations, Mon. Not. R. Astron. Soc. 250, 519-522.
Karlsson, K.G.: 1971, Possible Discretization of Quasar Redshifts, Astron. Astrophys. 13, 333-335.
Khodyachikh, M.F.: 1996, Cosmological Periodicity in the Distribution of Quasars, Astron. Rep. 40, 6.
Kiefer, C.: 1999, Conceptual Issues in Quantum Cosmology, Proceedings of the Karpacz Winter School on From Cosmology to Quantum Gravity, gr-qc/9906100, in press.
Klainerman, S. and Sarnak, P.: 1981, Ann. Inst. H. Poincare 35, 253.
Kortenkamp, S.J. and Dermott, S.E.: 1998, A 100 000 Year Periodicity in the Accretion Rate of Interplanetary Dust, Science 280, 874-876.
Kruogovenko, A.A. and Orlov, V.V.: 1992, The Peaks and Gaps in the Redshift Distribution of Active Galactic Nuclei and Quasars, Astrophys. Space Sci. 193, 303-307.
Lamb, D.J., Capri, A.Z. and Kobaski, M.: 1994, Discrete Spectral Shift in an Anisotropic Universe, hep-th/9411237, Mod. Phys. Lett. A9, 2945-2952.
Larson, E.E. and Birkland, P.W.: 1982, Putnam's Geology, 4th Edition, Oxford University Press.
Lifshitz, E.M.: 1946, J. Phys. U.S.S.R. 10, 116.
Lifshitz, E.M. and Khalatnikov, I.M.: 1963, Investigations in Relativistic Cosmology, Translated by J.L. Beeby, Adv. Phys. 12, 185-249.
Loll, R.: 1998, Discrete Approaches to Quantum Gravity in Four Dimensions, gr-qc/9805049, Living Reviews in Relativity 13.
Lui, Y.-Z. and Hu, F.-X.: 1998, Periodicity Revealed by Statistics of the Absorption-line Redshifts of Quasars, Astron. Astrophys. 329, 821-826.
Malin, D.F. and Carter, D.: 1980, Giant Shells around Normal Elliptical Galaxies, Nature 285, 643-645.
Mashhoon, B.: 1973, Electromagnetic Waves in an Expanding Universe, Phys. Rev. D8, 4297-4302.
Mirzoyan, L.V. and Vardanyan, R.A.: 1993, A Possible Explanation for the Discretization of the Redshifts of Quasars, Astrophysics [Tr. Astrofyika] 35, 372.
Modanese, G.: 2000, Large ‘Dipolar’ Vacuum Fluctuations in Quantum Gravity, gr-qc/0005009.
Monnet, G. and Deharveny, J.M.: 1977, Experimental Evidence against Discrete States of Redshift in Galaxies, Astron. Astrophys. 58, L1-L3.
Morikawa, M.: 1991, Universe with oscillating expansion rate, Astrophys. J. 369, 20-29.
Müller, P.O.: 1939, Phys. Zeit. 40, 366.
Naidu, P.D. and Malmgren, B.A.: 1995, A 2 200 Year Periodicity in the Asian Monsoon System, Geophys. Res. Lett. 22, 2361-2364.
Narlikar, J.V.: 1992, The Mystery of Redshift Periodicities, Indian Inst. Sci. J. 72, 273-278.
Narlikar, J.V. and Burbidge, G.R.: 1981, An Empirical Approach to Cosmology, Astrophys. Space Sci. 74, 111-129.
Newman, W.I., Haynes, M.P. and Terzian, Y.: 1989, Double Galaxy Redshifts and the Statistics of Small Numbers, Astrophys. J. 344, 111-114.
Newman, W.I., Haynes, M.P. and Terzian, Y.: 1994, Redshift Data and Statistical Inference, Astrophys. J. 431, 147-155.
Newman, W.I. and Terzain, Y.: 1996, Power Spectrum Analysis and Redshift Data, Astrophys. Space Sci. 244, 127-141.
Nieto, M.M.: 1986, Relative Realization of a Proposed Model of Quantized Redshifts, Astrophys. Lett. 25, 45-50.
North, J.D.: 1965, The Measure of the Universe, Clarendon Press, Oxford.
Peterson, S.D.: 1979, Double Galaxies. 1. Observational Data on a well-define sample, Astrophys. J. Suppl. 40, 527-575.
Pitucco, A.P., Tifft, W.G., DeVito, C.L. and Cocke, W.G.: 1996, Joint International conference on Mathematical Models of Time and Their Application to Physics and Cosmology, Astrophys. Space Sci. 244, 1-6.
Roberts, M.D.: 1991, Galactic Rotation Curves and Quadratic Lagrangians, Mon. Not. R. Astron. Soc. 249, 32-42.
Roberts, M.D.: 1993, The World Function in Robertson-Walker Spacetime, gr-qc/9905005, Astrophys. Lett. Commun. 28, 349-357.
Rosen, N.: 1993, Quantum Mechanics of a Mini universe, Int. J. Theor. Phys. 32, 1435-1440.
Sachs, R.K. and Wolfe, A.M.: 1967, Perturbations of a Cosmological Model and Angular Variations of the Microscopic Background, Astrophys. J. 147, 73-90.
Salgado, M., Sudarsky, D. and Quevedo, H.: 1996, Galactic Periodicity and the Oscillating G Model, Phys. Rev. D53, 6771-6783.
Saunders, W., Frenck, C., Rowan-Robinson, M., Efstathiou, G., Lawrence, A., Kaiser, N., Ellis, R., Crawford, J., Xiao-Yang, X. and Parr, I.: 1991, The Density Field of the Local Universe, Nature 349, 32-38.
Schiff, L.I.: 1949, Quantum Mechanics, McGraw-Hill, Singapore, 34.
Schrödinger, E.: 1938, Commentationes Pontificae Acad. Sci. 2, 321.
Schrödinger, E.: 1939, The Proper Vibrations of the Expanding Universe, Physica 6, 899-912.
Schrödinger, E.: 1940, Proc. Roy. Irish Acad. A46, 9.
Schrödinger, E.: 1956, Expanding Universes, Math. Rev. 17, 1015, Cambridge University Press.
Scott, D.: 1991, Against the Δ ln (1+ z) ≃ 0.205 periodicity in Quasar Redshifts, Astron. Astrophys. 242, 1-12.
Sharp, N.A.: 1984, Double Galaxy Redshifts and Dynamical Analysis, Astrophys. J. 286, 437-444.
Sidharth, B.G.: 1999, Large Scale Structure in the Universe, gr-qc/9903053.
Silva, P.R.: 1997, Microcosmos and Macrocosmos-A Look at These Two Universes in a Unified Way, Int. J. Mod. Phys. A12, 1373-1384.
Sudarsky, D.: 1992, Bounds on Oscillating Physics from Solar System Experiments, Phys. Lett. B281, 98-99.
Tifft, W.G.: 1976, Discrete States of Redshift and Galaxy Dynamics. 1. Internal motions in a single galaxy, Astrophys. J. 206, 38-56.
Tifft, W.G.: 1977a, Discrete States of Redshift and Galaxy Dynamics. 2. Systems of Galaxies, Astrophys. J. 211, 31-46.
Tifft, W.G.: 1977b, Discrete States of Redshift and Galaxy Dynamics. 3. Abnormal Galaxies and Stars, Astrophys. J. 211, 377-391.
Tifft, W.G.: 1978a, Discrete Redshift and Asymmetry in H1 profiles, Astrophys. J. 221, 449-455.
Tifft, W.G.: 1978b, Absolute Solar Motion and Discrete Redshift, Astrophys. J. 221, 756-775.
Tifft, W.G.: 1980, Periodicity in the Redshift Interval for Double Galaxies, Astrophys. J. 236, 70-74.
Tifft, W.G.: 1982a, Quantum Effects in the Redshift Intervals for Double Galaxies, Astrophys. J. 257, 442-449.
Tifft, W.G.: 1982b, Double Galaxy Investigations. 2. The Redshift Periodicity in Optically Observed Pairs, Astrophys. J. 262, 44-47.
Tifft, W.G.: 1996, Global Redshift Periodicities and Periodic Structure, Astrophys. J. 468, 491-518.
Tifft, W.G.: 1997, Global Redshift Periodicities and Variability, Astrophys. J. 485, 465-483.
Tifft, W.G. and Cocke, W.J.: 1984, Global Redshift Quantization, Astrophys. J. 287, 492-502.
Tipler, F.J.: 1986, Interpreting the Wave Function of the Universe, Math.Rev.87g:83161, Phys. Rep. C137, 231-275.
Trees, R.E.: 1956, Application of the Rayleigh-Schrödinger Perturbation Theory to the Hydrogen Atom, Phys. Rev. 102, 1553-1556.
Tytler, David, Sandoval, John and Fan, Xiao-Ming: 1993, Upper Limit on Periodicity in the Three-dimensional Large-scale distribution of matter, Astrophys. J. 405, 57-93.
Vajk, J.P.: 1968, Exact Robertson-Walker Cosmological Solutions Containing Relativistic Fluids, J. Math. Phys. 10, 1145-1151.
van de Weygaert, R.: 1991, Quasi-periodicity in deep redshift surveys, Mon. Not. R. Astron. Soc. 249, 159-163.
Weinberg, S.: 1972, Gravitation and Cosmology, John Wiley, New York.
Wereide, Th.: 1923, The General Principle of Relativity Applied to the Rutherford-Bohr Atom Model, Phys. Rev. 21, 391-396.
White, S.D.M., Frenck, C.S., Davis, M. and Efstathiou, G.: 1987, Clusters, Filaments, and Voids in a Universe Dominated by Cold Dark Matter, Astrophys. J. 313, 505-516.
Whittaker, E.T. and Watson, G.N.: 1927, Introduction to Analysis, Fourth Edition, Cambridge University Press, 406.
Williams, B.G., Peacock, J.A. and Heavens, A.F.: 1991, Large-scale Periodicity: Problems with Cellular Models, Mon. Not. R. Astron. Soc. 252, L43-L46.
Willmer, L.N.A., Koo, D.C., Szalaz, A.S. and Kurtz, M.J.: 1994, A Medium-Deep Redshift Survey of a Minislice at the North Galactic Pole, Astrophys. J. 437, 560-563.
Yamammoto, K., Sasaki, M., Tanaka, T.: 1996, Quantum fluctuations and CMB Anisotropies in One-bubble Open Inflation Models, astro-ph/9605103, Phys. Rev. D54, 5031-5048.
Yu, J.T. and Peebles, P.J.E.: 1969, Superclusters of Galaxies?, Astrophys. J. 158, 103-113.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Roberts, M.D. Quantum Perturbative Approach to Discrete Redshift. Astrophysics and Space Science 279, 305–342 (2002). https://doi.org/10.1023/A:1015154421825
Issue Date:
DOI: https://doi.org/10.1023/A:1015154421825