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Statistical Challenges in Modern Astronomy II pp 67–81Cite as

Modern Statistical Methods for Cosmological Testing

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Abstract

Statistically efficient and equitable methods for cosmological analysis and testing on the basis of objective samples of extragalactic sources are presented. Nontrivial such methods inevitably assume that the population of sources has well-defined uniformity features, or that departures from uniformity follow a designated pattern (parametric or otherwise). The most basic assumption, almost universally made in analysis at lower redshifts, is that of ‘luminosity uniformity’ (LU); i.e., that the intrinsic brightnesses of the sources form a well defined statistical population that is independent of the positions of the sources, in a designated redshift range. A secondary assumption, which can be utilized only in conjunction with LU, is that of ‘spatial uniformity’ (SU).

Assuming only LU, the problem of the maximum likelihood estimation of the luminosity function (L; i.e., the distribution of the intrinsic brightnesses) on the basis of a sample that is selected without discrimination on the basis of flux, down to a given limit, is soluble in closed form when the L is a step function, in which form LFs are commonly reported in observational studies. The solution, known as ROBUST, is applied to a number of well-known flux limited samples of galaxies and quasars. At low redshifts, the corresponding directly observable predictions of Friedman-Lemaître cosmology (FLC) are extremely deviant, in fact more so than those of any redshift-distance power law up to the cubic. The second power law appears optimal, and this is predicted by the chronometric cosmology (CC) proposed by Segal. At high redshifts, CC remains consistent with observation, without the hypothetical ‘evolution’ required by FLC for consistency. At all redshifts, the deviations of the FLC predictions for cosmology independent directly observable quantities are as predicted by CC for the results of analysis predicated on FLC.

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Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, Room 2-244, Cambridge, MA, 02139, UK

    I. E. Segal

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  1. I. E. Segal
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Editors and Affiliations

  1. Department of Statistics, Pennsylvania State University, University Park, PA, 16802, USA

    G. Jogesh Babu

  2. Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA, 16802, USA

    Eric D. Feigelson

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© 1997 Springer Science+Business Media New York

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Segal, I.E. (1997). Modern Statistical Methods for Cosmological Testing. In: Babu, G.J., Feigelson, E.D. (eds) Statistical Challenges in Modern Astronomy II. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1968-2_4

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  • DOI: https://doi.org/10.1007/978-1-4612-1968-2_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7360-8

  • Online ISBN: 978-1-4612-1968-2

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