Confidence Level Estimator of Cosmological Parameters
Author(s)
G. Sironi*
ABSTRACT
Cosmological Models frequently suggest the existence of physical, quantities, e.g. dark energy, we cannot yet observe and measure directly. Their values are obtained indirectly setting them equal to values and accuracy of the associated model parameters which best fit model and observation. Apparently results are so accurate that some researchers speak of precision cosmology. The accuracy attributed to these indirect values of the physical quantities however does not include the uncertainty of the model used to get them. We suggest a Confidence Level Estimator to be attached to these indirect measurements and apply it to current cosmological models.
Cosmological Models frequently suggest the existence of physical, quantities, e.g. dark energy, we cannot yet observe and measure directly. Their values are obtained indirectly setting them equal to values and accuracy of the associated model parameters which best fit model and observation. Apparently results are so accurate that some researchers speak of precision cosmology. The accuracy attributed to these indirect values of the physical quantities however does not include the uncertainty of the model used to get them. We suggest a Confidence Level Estimator to be attached to these indirect measurements and apply it to current cosmological models.
Cite this paper
Sironi, G. (2012) Confidence Level Estimator of Cosmological Parameters. Journal of Modern Physics, 3, 1216-1222. doi: 10.4236/jmp.2012.329157.
Sironi, G. (2012) Confidence Level Estimator of Cosmological Parameters. Journal of Modern Physics, 3, 1216-1222. doi: 10.4236/jmp.2012.329157.
References
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[39] J. O. Berger, et al., “Bayesian Robustness,” IMS, Hayward, 1996. [40] A. Cho, “A Recipe for Cosmos,” Science, Vol. 330, No. 12, 2010, pp. 1615-1616. doi:10.1126/science.330.6011.1615 [41] L. Amendola, R. Gannouji, D. Polarski and S. Tsyikawa, “Condition for the Cosmological Viability of f(R) Dark Energy Models,” Physical Review D, Vol. 75, No. 8, 2007, pp. 83504-83560. doi:10.1103/PhysRevD.75.083504 [42] J. Dunkley, et al., “The Atacama Cosmology Telescope Cosmological Parameyters from the 2008 Power Spectrum,” Astrophysical Journal, Vol. 739, No. 9, 2011, pp. 52-72. doi:10.1088/0004-637X/739/1/52 [43] R. G. Vishwakarma and J. V. Narlikar, “A Critique of Supernova Data Analysis in Cosmology,” Research in Astronomy and Astrophysics, Vol. 10, No. 1, 2010, pp. 1195-1198. [44] R. Swinburne, “Introduction to Bayes’s Theorem,” In: R. Swinburne, Ed., Bayes’s Theorem, Oxford University Press, Oxford, 2002, pp. 1-55. [45] S. J. 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[1] K. Popper, “Conjecture and Refutations: The Growth of Scientific Knowledge,” Taylor and Francis, Abingdon, 1989. [2] P. R. Bevington and K. D. Robinson, “Data Reduction and Error Analysis for the Physical Sciences,” McGraw-Hill, London, 1992. [3] A. A. Penzias and R. A. Wilson, “A Measurement of Excess Antenna Temperature at 4080 Mc/s,” Astrophysical Journal, Vol. 142, No. 7, 1965, pp. 419-421. doi:10.1086/148307 [4] H. Bondi and T. Gold, “The Steady State Theory of the Expanding Universe,” Monthly Notices of the Royal Astronomical Society, Vol. 108, No. 2, 1948, pp. 252-270. [5] F. Hoyle, “A New Model of the Expanding Universe,” Monthly Notices of the Royal Astronomical Society, Vol. 108, No. 3, 1948, pp. 372-382. [6] P. J. E. Peebles, “Principles of Physical Cosmology,” Princeton University Press, Princeton, 1993. [7] A. H. Guth, “The Inflationary Universe,” Perseus Book, Reading, 1997. [8] R. B. Partridge, “3K: The Cosmic Microwave Background Radiation,” Cambridge University Press, Cambridge, 1995. doi:10.1017/CBO9780511525070 [9] D. J. Fixsen and J. C. Mather, “The Spectral Results of the Far Infrared Absolute Spectrophotometer on COBE,” Astrophysical Journal, Vol. 581, No. 12, 2002, pp. 817-822. doi:10.1086/344402 [10] G. F. Smoot et al., “Low Frequency Measurements of the Cosmic Bacground Radiation Spectrum,” The Astrophysical Journal Letters, Vol. 291, No. 4, 1985, pp. L23-L27. doi:10.1086/184451 [11] M. Zannoni, et al., “TRIS I: Absolute Measurements of the Sky Brightness Temperature at 0.6, 0.82 and 2.5 GHz,” Astrophysical Journal, Vol. 688, No. 11, 2008, pp. 12-23. doi:10.1086/592133 [12] C. L. Bennett, et al., “Four-year COBE DMR Cosmic Microwave Background Observations: Maps and Basic Results,” Astrophysical Journal, Vol. 464, No. 6, 1996, pp. L1-L4. doi:10.1086/310075 [13] D. Larson, et al., “Seven-Years Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters,” The Astrophysical Journal Supplement, Vol. 192, No. 16, 2011, pp. 1-19. [14] R. B. Friedman, et al., “Small Angular Scale Measurements of the Cosmic Microwave Background Temperature Power Spectrum from QUaD,” Astrophysical Journal, Vol. 700, No. 8, 2009, pp. L187-L191. doi:10.1088/0004-637X/700/2/L187 [15] A. Kogut, et al., “Five-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature-Po-larization Correlatioin,” The Astrophysical Journal Supplement, Vol. 148, No. 9, 2003, pp. 161-173. doi:10.1086/377219 [16] F. Piacentini, et al., “A Measurement of the Polarization-Temperature Angular Cross-Power Spectrum of the Cosmic Microwave Background from the 2003 Flight of BOOMERANG,” Astrophysical Journal, Vol. 647, No. 8, 2006, pp. 833-839. doi:10.1086/505557 [17] G. Polenta, et al., “The BRAIN CMB Polarization Experiment,” New Astronomy Reviews, Vol. 51, No. 3, 2007, pp. 256-259. doi:10.1016/j.newar.2006.11.065 [18] M. L. Brown, et al., “Improved Measurements of the Temperature and Polarization of the Cosmic Microwave Background from QUaD,” Astrophysical Journal, Vol. 705, No. 4, 2009, pp. 978-999. doi:10.1088/0004-637X/705/1/978 [19] S. Perlmutter, et al., “Measurements of Omega and Lambda from 42 High Redshift Supernovae,” Astrophysical Journal, Vol. 517, No. 6, 1999, pp. 565-586. doi:10.1086/307221 [20] G. Bertone, D. Hooper and J. Silk, “Particle Dark Matter: Evidence, Candidates and Constraints,” Physics Reports, Vol. 405, No. 1, 2005, pp. 279-390. doi:10.1016/j.physrep.2004.08.031 [21] W. J. Percival, et al., “Baryon acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample,” Monthly Notices of the Royal Astronomical Society, Vol. 401, No. 2, 2010, pp. 2148-2168. doi:10.1111/j.1365-2966.2009.15812.x [22] N. Panagia, “High Redshift Supernovare: Cosmological Implications,” Nuovo Cimento B, Vol. 120, No. 6, 2005, pp. 667-680. [23] G. Ghirlanda, G. Ghisellini and C. Firmani, “Gamma ray Bursts as Standard Candles to Constrain the Cosmological Parameters,” New Jersey Postal History Society, Vol. 8, No. 7, 2006, pp. 123-124. [24] M. Macció, et al., “Coupled Dark Energy: Constraints from N-Body Simulations,” Physical Review D, Vol. 69, No. 12, 2004, pp. 123516-123540. doi:10.1103/PhysRevD.69.123516 [25] P. de Bernardis, et al., “Multiple Peaks in the Angular Power Spectrum of the Cosmic Microwave Background Significance and Consequences for Cosmology,” Astrophysical Journal, Vol. 564, No. 1, 2002, pp. 559-666. doi:10.1086/324298 [26] P. Valageas and J. Silk, “The Reheating an Reionization History of the Universe,” Astronomy & Astrophysics, Vol. 347, No. 7, 1999, p. 20 [27] A. G. Riess, et al., “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant,” The Astronomical Journal, Vol. 116, No. 9, 1998, pp. 1009-1038 [28] J. P. Ostriker and P. J. Steihardt, “Cosmic Concordance,” arXiv:astro-ph/9505066v1, 1995. [29] M. Kowalski, et al., “Improved Cosmological Constraints from New, Old and Combined Supernova Data Sets,” Astrophysical Journal, Vol. 686, No. 10, 2008, pp. 749-778. doi:10.1086/589937 [30] D. P. Landau and K. Binder, “A Guide to Monte-Carlo Simulations in Statistical Physics,” Cambridge University Press, Cambridge, 2009. doi:10.1017/CBO9780511994944 [31] Planck Science Team, “Planck Science Team Home,” 2012. http://www.rssd.esa.int/index?project=Planck [32] E. Komatsu, et al., “Five-Year Wilkinson Microwave Anisotropy Probe Observations: Cosmological Interpretation,” The Astrophysical Journal Supplement, Vol. 180, No. 2, 2009, pp. 330-376. doi:10.1017/CBO9780511994944 [33] A.G. Riess et al., “A Redetermination of the Hubble Constant with the Hubble Space Telescope from a Differential Distance Ladder,” Astrophysical Journal, Vol. 699, No. 7, 2009, pp. 539-563. doi:10.1088/0004-637X/699/1/539 [34] E. Komatsu, et al., “Seven-Year Wilkinson Microwave Anisotropt Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters,” The Astrophysical Journal Supplement, Vol. 192, No. 18, 2011, pp. 1-47. [35] J. R. Primack, “Precision Cosmology,” New Astronomy Re- views, Vol. 49, No. 5, 2005, pp. 25-34 [36] S. L. Bridle, O. Lahav and J. P. Ostriker, “Precision Cosmology? Not Just Yet ...,” Science, Vol. 299, No. 3, 2003, pp. 1532-1533. doi:10.1126/science.1082158 [37] J. Joyce, “Bayes Theorem,” In: E. N. Zalta, Ed. The Stanford Encyclopedia of Philosophy, The Metaphysics Research Lab, Stanford, 2008. http://plato.stanford.edu/entries/bayes-theorem/ [38] J. K. Ghosh, M. Delampady and T. Samanta, “An Introduction to Bayesian Analysis,” Springer, New York, 2006. [39] J. O. Berger, et al., “Bayesian Robustness,” IMS, Hayward, 1996. [40] A. Cho, “A Recipe for Cosmos,” Science, Vol. 330, No. 12, 2010, pp. 1615-1616. doi:10.1126/science.330.6011.1615 [41] L. Amendola, R. Gannouji, D. Polarski and S. Tsyikawa, “Condition for the Cosmological Viability of f(R) Dark Energy Models,” Physical Review D, Vol. 75, No. 8, 2007, pp. 83504-83560. doi:10.1103/PhysRevD.75.083504 [42] J. Dunkley, et al., “The Atacama Cosmology Telescope Cosmological Parameyters from the 2008 Power Spectrum,” Astrophysical Journal, Vol. 739, No. 9, 2011, pp. 52-72. doi:10.1088/0004-637X/739/1/52 [43] R. G. Vishwakarma and J. V. Narlikar, “A Critique of Supernova Data Analysis in Cosmology,” Research in Astronomy and Astrophysics, Vol. 10, No. 1, 2010, pp. 1195-1198. [44] R. Swinburne, “Introduction to Bayes’s Theorem,” In: R. Swinburne, Ed., Bayes’s Theorem, Oxford University Press, Oxford, 2002, pp. 1-55. [45] S. J. Press, “Bayesian Statistics,” Wiley, New York 1989 [46] AA.VV., “Bayes Theorem,” In: R. K. Bock, K. Bos, S. Brandt, J. Myrheim and M. Regler, Eds., Formulae and Methods in Experimental Data Evaluation, EPS-CERN, Geneva, 1984, p. 7.