Transformation of the Angular Power Spectrum of the Cosmic Microwave Background (CMB) Radiation into Reciprocal Spaces and Consequences of This Approach

Author(s)
Ladislav Červinka

ABSTRACT

A formalism of solid state physics has been applied to provide an additional tool for the research of cosmological problems. It is demonstrated how this new approach could be useful in the analysis of the Cosmic Microwave Background (CMB) data. After a transformation of the anisotropy spectrum of relict radiation into a special two-fold reciprocal space it was possible to propose a simple and general description of the interaction of relict photons with the matter by a “relict radiation factor”. This factor enabled us to process the transformed CMB anisotropy spectrum by a Fourier transform and thus arrive to a radial electron density distribution function (RDF) in a reciprocal space. As a consequence it was possible to estimate distances between Objects of the order of ~10^{2} [m] and the density of the ordinary matter ~10^{-22} [kg.m^{-3}]. Another analysis based on a direct calculation of the CMB radiation spectrum after its transformation into a simple reciprocal space and combined with appropriate structure modelling confirmed the cluster structure. The internal structure of Objects may be formed by Clusters distant ~10 [cm], whereas the internal structure of a Cluster consisted of particles distant ~0.3 [nm]. The work points in favour of clustering processes and to a cluster-like structure of the matter and thus contributes to the understanding of the structure of density fluctuations. As a consequence it may shed more light on the structure of the universe in the moment when the universe became transparent for photons. On the basis of our quantitative considerations it was possible to derive the number of particles (protons, helium nuclei, electrons and other particles) in Objects and Clusters and the number of Clusters in an Object.

A formalism of solid state physics has been applied to provide an additional tool for the research of cosmological problems. It is demonstrated how this new approach could be useful in the analysis of the Cosmic Microwave Background (CMB) data. After a transformation of the anisotropy spectrum of relict radiation into a special two-fold reciprocal space it was possible to propose a simple and general description of the interaction of relict photons with the matter by a “relict radiation factor”. This factor enabled us to process the transformed CMB anisotropy spectrum by a Fourier transform and thus arrive to a radial electron density distribution function (RDF) in a reciprocal space. As a consequence it was possible to estimate distances between Objects of the order of ~10

KEYWORDS

CMB Radiation, Analysis of CMB Spectrum, Radial Distribution Function of Objects, Early Universe Cluster Structure, Density of Ordinary Matter

CMB Radiation, Analysis of CMB Spectrum, Radial Distribution Function of Objects, Early Universe Cluster Structure, Density of Ordinary Matter

Cite this paper

nullL. Červinka, "Transformation of the Angular Power Spectrum of the Cosmic Microwave Background (CMB) Radiation into Reciprocal Spaces and Consequences of This Approach,"*Journal of Modern Physics*, Vol. 2 No. 11, 2011, pp. 1331-1347. doi: 10.4236/jmp.2011.211165.

nullL. Červinka, "Transformation of the Angular Power Spectrum of the Cosmic Microwave Background (CMB) Radiation into Reciprocal Spaces and Consequences of This Approach,"

References

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[1] J. L. Sievers, J. R. Bond, J. K. Cartwright, C. R. Contaldi, B. S. Mason, S. T. Myers, S. Padin, T. J. Pearson, U.-L. Pen, D. Pogosyan, S. Prunet, A. C. S. Readhead, M. C. Shepherd, P. S. Udomprasert, L. Bronfman, W. L. Holzapfel and J. May, “Cosmological Parameters from Cosmic Background Imager Observations and Comparisons with BOOMERANG, DASI, and MAXIMA,” Astrophysics Journal, Vol. 591, No. 2, 2003, pp. 599-622. doi:10.1086/375510

[2] G. Hinshaw, D. N. Spergel, L. Verde, R. S. Hill, S. S. Meyer, C. Barnes, C. L. Bennett, M. Halpern, N. Jarosik, A. Kogut, E. Komatsu, M. Limon, L. Page, G. S. Tucker, J. Weiland, Wollack E. and E. L. Wright, “First-Year Wilkinson Microwave Anisotropy Probe (WMAP) observations: The Angular Power Spectrum,” Astrophysical Journal, Supplement Series, Vol. 148, No. 1, 2003, pp. 135-159. doi:10.1086/377225

[3] L. ?ervinka, “Several Remarks on the Medium-Range Order in Glasses,” Journal of Non-Crystalline Solids, Vol. 1, No.1-3, 1998, pp. 1-17. doi:10.1016/S0022-3093(98)00457-8

[4] L. ?ervinka, J. Bergerová, L. Tichy and F. Rocca, “A Contribution to the Structure of Ge-Se-Ag Glasses,” Physics and Chemistry of Glasses, Vol. 46, No. 4, 2005, pp. 444-450.

[5] W. Hu, D. Scott, N. Sugiyama and M. White, “The Effect of Physical Assumptions on the Calculation of Micro- wave Background Anisotropies,” Physical Review, Vol. D52, 1995, pp. 5498-5515.

[6] J. C. Wilson and E. Price, Editors, “International Tables for Crystallography,” Volume C, Mathematical, Physical and Chemical Tables, Second Edition, Published for International Union of Crystallography, Kluwer Academic Publishers, Dordrecht, 1999.

[7] G. Smoot and K. Davidson, “Wrinkles in Time,” Avon, New York, 1977, p. 158.

[8] J. Silk, “Big Bang,” Freeman & Co. Publishers, New York, 1977, p. 299.

[9] V. Pet?í?ek, M. Du?ek and L. Palatinus, “The Crystallographic Computing System,” Institute of Physics, Praha, 2006, Czech Republic.

[10] K. Brandenburg, “Program DIAMOND, Version 2.1c,” Crystal Impact GbR, Bonn, Germany, 1999.

[11] E. L. Wright, J. C. Mather, D. J. Fixsen, A. Kogut, R. E. Eplee, Jr., R. B. Isaacman, S. M. Read, R. A. Shafer, C. L. Bennett, N. W. Boggess, E. S. Cheng, S. Gulkis, M. G. Hauser, M. Janssen, T. Kelsall, P. M. Lubin, S. H. Moseley, Jr., T. L. Murdock, R. F. Silverberg, G. F. Smoot, R. Weiss and D. T. Wilkinson, “Interpretation of the COBE FIRAS CMBR Spectrum,” Astrophysics Journal, Vol. 420, No. 2, 1994, pp. 450-456. doi:10.1086/173576

[12] M. White, D. Scott and J. Silk, “Anisotropies in the Cosmic Microwave Background,” Annual Review of Astronomy and Astrophysics, Vol. 32, 1994, pp. 319-370. doi:10.1146/annurev.aa.32.090194.001535

[13] R. ?mída, Institute of Physics, Acadamic Science of the Czech Republic, 2010 (Private Communication).

[14] J. C. Mather, E. S. Cheng, D. A. Cottingham, R. E. Eplee, Jr., D. J. Fixen, T. Hewagama, R. B. Isaacman, K .A. Jensen, S. S. Meyer, P. D. Noerdlinger, S. M. Read, L. P. Rosen, R. A. Shafer, E. L. Wright, C. L. Bennett, N. W. Boggess, M. G. Hauser, T. Kelsall, S. H. Moseley Jr., R. F. Silverberg, G. F. Smoot, R. Weiss and D. T. Wilkinson, “Measurement of the Cosmic Microwave Background Spectrum by the COBE FIRAS Instrument,” Astrophysics Journal, Vol. 420, No. 2, 1994, pp. 439-444. doi:10.1086/173574

[15] J. C. Wheeler, “Cosmic Catastrophes,” Cambridge University Press, ISBN 0521857147, 2007, pp. 282.

[16] L. Smolin, “The Trouble with Physics,” Mariner Books, New York, 2007, p. 16.

[17] D. Scott, “The Standard Cosmological Model,” Canadian Journal of Physics, Vol. 84, No. 6-7, 2006, pp. 419-435. doi:10.1139/p06-066

[18] K. Steeb, “Springer Tracts in Modern Physics—Ergeb- nisse der exakten Naturwissenschaften,” Vol. 47, Springer- Verlag, Berlin, 1968, pp. 1-66.

[19] R. Hultgren, N. S. Gingrich and B. E. Warren, “The Atomic Distribution in Red and Black P and the Crystal Structure of Black P,” Journal of Chemical Physics, Vol. 3, 1935, p. 351. doi:10.1063/1.1749671

[20] J. Krogh Moe, “A Method for Converting Experimental X-Ray Intensities to an Absolute Scale,” Acta Crystallographica, Vol. 9, No. 11, 1956, pp. 951-953. doi:10.1107/S0365110X56002655