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The Cosmological Constant Constrained with Union2.1 Supernovae Type Ia Data

Derivation and Evaluation of Several FRW and Carmeli Models Presenting Underwhelming Support for the Standard Model

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Abstract

We derive several, detailed relationships in terms of the Friedmann-Robertson-Walker (FRW) generalization which describe the Universe during both the radiation and matter dominated epochs. We explicitly provide for the influence of radiation, rather than burying this term within the matter term. Several models allow the cosmological constant (CC) to vary with universe expansion in differing manners. We evaluate these and other popular models including the ΛCDM(standard model), quintessence as presented by Vishwakarma, Equation of State (EoS) and the Carmeli model with data from the 580 Union2.1 supernovae type Ia collection, using several minimization routines and find models built about the CC, the ΛCDM models, fare no better than those without.

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Author information

Authors and Affiliations

  1. Engineering Physics, Hacettepe University, 06800, Ankara, Turkey

    Ahmet M. Öztas

  2. 4S Fuel Research, Inc., Mesa, AZ, 85206, USA

    Michael L. Smith

Authors
  1. Ahmet M. Öztas
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  2. Michael L. Smith
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Correspondence to Michael L. Smith.

Appendix: Tabulated Results

Appendix: Tabulated Results

Table 2 Results from least squares fits of eight models a using a robust minimization routine of luminosity distances (Mpc) vs. redshifts with χ 2/N-FP as the reduced χ 2 and ΔB I C as relative values
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Table 3 Results from least squares fits of 8 common models a using a Gauss-Newton minimization routine of luminosity distances (Mpc) vs. the expansion factor, ν/ν 0 with χ 2/N-FP as the reduced χ 2 and ΔB I C as relative values
Full size table
Table 4 Results from least squares fits of 9 models a using a Gauss-Newton minimization routine of luminosity distances (Mpc) vs. redshifts with χ 2/N-FP as the reduced χ 2 and ΔB I C as relative values
Full size table
Table 5 Results from least squares fits of 7 models a using a robust minimization routine of luminosity distances (Mpc) vs. the expansion factor, ν/ν 0 and floating parameter, with χ 2/N-FP as the reduced χ 2 and ΔB I C as relative values
Full size table
Table 6 Results from least squares fits of 7 common models a using a robust minimization routine of luminosity distances (Mpc) vs. redshifts with floating parameter; ordered as the reduced χ 2 and ΔB I C as relative values
Full size table
Table 7 Results from least squares fits of 9 models a using a Gauss-Newton minimization routine of luminosity distances (Mpc) vs. redshifts with χ 2/N-FP and floating parameter, as the reduced χ 2 and ΔB I C as relative values
Full size table
Table 8 Results from least squares fits of 8 models a using the Gauss-Newton minimization routine of luminosity distances (Mpc) vs. the expansion factor, ν/ν 0 and floating parameter; organized with χ 2/N-FP as the reduced χ 2 and ΔB I C as relative values
Full size table

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Öztas, A.M., Smith, M.L. The Cosmological Constant Constrained with Union2.1 Supernovae Type Ia Data. Int J Theor Phys 53, 2636–2661 (2014). https://doi.org/10.1007/s10773-014-2061-5

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