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Sparse Formulae for the Distance Modulus in Cosmology

DOI: 10.4236/jhepgc.2021.73057, PP. 965-992

Keywords: Cosmology, Observational Cosmology, Distances, Redshifts, Radial Velocities, Spatial Distribution of Galaxies, Magnitudes and Colours, Luminosities

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Abstract:

We review the distance modulus in twelve different cosmologies: the ΛCDM model, the wCDM model, the Cardassian model, the flat case, the ?CDM cosmology, the Einstein—De Sitter model, the modified Einstein—De Sitter model, the simple GR model, the flat expanding model, the Milne model, the plasma model and the modified tired light model. The above distance moduli are processed for three different compilations of supernovae and a supernovae + GRBs compilation: Union 2.1, JLA, the Pantheon and Union 2.1 + 59 GRBs. For each of the 48 analysed cases we report the relative cosmological parameters, the chi-square, the reduced chi-square, the AIC and the Q parameter. The angular distance as function of the redshift for five cosmologies is reported in the framework of the minimax approximation.

References

[1]  Planck Collaboration (2018) Planck 2018 Results. VI. Cosmological Parameters. arXiv:1807.06209. (Preprint)
[2]  Riess, A.G., Casertano S, Yuan W, Macri, L.M. and Scolnic, D. (2019) Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛCDM. The Astrophysical Journal, 876, Article No. 85. (Preprint)
https://doi.org/10.3847/1538-4357/ab1422
[3]  Di Valentino, E., Anchordoqui, L.A., Akarsu, O., Ali-Haimoud, Y., Amendola, L., Arendse, N., et al. (2020) Cosmology Intertwined II: The Hubble Constant Tension. arXiv:2008.11284. (Preprint)
[4]  Riess, A.G., Filippenko, A.V., Challis, P. and Clocchiatti, A. (1998) Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. The Astronomical Journal, 116, Article No. 1009. (Preprint)
https://doi.org/10.1086/300499
[5]  Suzuki, N., Rubin, D., Lidman, C., Aldering, G., Amanullah, R., Barbary, K. and Barrientos, L.F. (2012) The Hubble Space Telescope Cluster Supernova Survey. V. Improving the Dark-Energy Constraints above Z Greater than 1 and Building an Early-Type-Hosted Supernova Sample. The Astrophysical Journal, 746, Article No. 85.
https://doi.org/10.1088/0004-637X/746/1/85
[6]  Betoule, M., Kessler, R., Guy, J., Mosher, J., Hardin, D., Biswas, R., et al. (2014) Improved Cosmological Constraints from a Joint Analysis of the SDSS-II and SNLS Supernova Samples. Astronomy and Astrophysics, 568, Article No. A22.
https://doi.org/10.1051/0004-6361/201423413
[7]  Jones, D.O., Scolnic, D.M., Riess, A.G., Rest, A., Kirshner, R.P., Berger, E., et al. (2018) Measuring Dark Energy Properties with Photometrically Classified Pan-STARRS Supernovae. II. Cosmological Parameters. The Astrophysical Journal, 857, Article No. 51. (Preprint)
https://doi.org/10.3847/1538-4357/aab6b1
[8]  Scolnic, D.M., Jones, D.O., Rest, A., Pan, Y.C., Chornock, R., Foley, R.J., et al. (2018) The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample. The Astrophysical Journal, 859, Article No. 101. (Preprint)
https://doi.org/10.3847/1538-4357/aab9bb
[9]  Oliveira, F.J. (2016) Cosmic Time Transformations in Cosmological Relativity Journal of High Energy Physics, Gravitation and Cosmology, 2, 253-279.
https://doi.org/10.4236/jhepgc.2016.22022
[10]  Gupta, R. (2018) SNe Ia Redshift in a Nonadiabatic Universe. Universe, 4, Article No. 104. (Preprint)
https://doi.org/10.3390/universe4100104
[11]  Amarzguioui, M., Elgarøy, Ø., Mota, D.F. and Multamäki, T. (2006) Cosmological Constraints on f(R) Gravity Theories within the Palatini Approach. A&A, 454, 707-714. (Preprint)
https://doi.org/10.1051/0004-6361:20064994
[12]  Odintsov, S.D., Gómez, D.S.C. and Sharov, G.S. (2019) Testing Logarithmic Corrections to R2-Exponential Gravity by Observational Data. Physical Review D, 99, Article ID: 024003.
https://doi.org/10.1103/PhysRevD.99.024003
[13]  Corda, C. (2009) Interferometric Detection of Gravitational Waves: The Definitive Test for General Relativity International Journal of Modern Physics D, 18, 2275-2282. (Preprint)
https://doi.org/10.1142/S0218271809015904
[14]  Lin, H.N., Li, X. and Tang, L. (2019) Non-Parametric Reconstruction of Dark Energy and Cosmic Expansion from the Pantheon Compilation of Type Ia Supernovae Chinese Physics C, 43, Article ID: 075101. (Preprint)
https://doi.org/10.1088/1674-1137/43/7/075101
[15]  Kazım Camlbel, A., Semiz, I. and Akif Feyizoğlu, M. (2020) Pantheon Update on a Model-Independent Analysis of Cosmological Supernova Data. Classical and Quantum Gravity, 37, Article ID: 235001.
https://doi.org/10.1088/1361-6382/abba48
[16]  Hogg, D.W. (1999) Distance Measures in Cosmology. arXiv:astro-ph/9905116. (Preprint)
[17]  Peebles, P.J.E. (1993) Principles of Physical Cosmology. Princeton University Press, Princeton.
[18]  Zaninetti, L. (2016) Pade Approximant and Minimax Rational Approximation in Standard Cosmology Galaxies, 4, Article No. 4.
https://doi.org/10.3390/galaxies4010004
[19]  Turner, M.S. and White, M. (1997) CDM Models with a Smooth Component. Physical Review D, 56, Article No. R4439. (Preprint)
https://doi.org/10.1103/PhysRevD.56.R4439
[20]  Tripathi, A., Sangwan, A. and Jassal, H.K. (2017) Dark Energy Equation of State Parameter and Its Evolution at Low Redshift. Journal of Cosmology and Astroparticle Physics, 6, Article No. 012. (Preprint)
https://doi.org/10.1088/1475-7516/2017/06/012
[21]  Wei, J.J., Ma, Q.B. and Wu, X.F. (2015) Utilizing the Updated Gamma-Ray Bursts and Type Ia Supernovae to Constrain the Cardassian Expansion Model and Dark Energy. Advances in Astronomy, 2015, Article ID: 576093. (Preprint)
https://doi.org/10.1155/2015/576093
[22]  Abramowitz, M. and Stegun, I.A. (1965) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York.
[23]  von Seggern, D. (1992) CRC Standard Curves and Surfaces. CRC Press, New York.
[24]  Thompson, W.J. (1997) Atlas for Computing Mathematical Functions. Wiley-Interscience, New York.
[25]  Gradshteyn, I.S., Ryzhik, I.M., Jeffrey, A. and Zwillinger, D. (2007) Table of Integrals, Series, and Products. Academic Press, New York.
[26]  Olver, F.W.J., Lozier, D.W., Boisvert, R.F. and Clark, C.W. (2010) NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge.
[27]  Zaninetti, L. (2019) The Distance Modulus in Dark Energy and Cardassian Cosmologies via the Hypergeometric Function International Journal of Astronomy and Astrophysics, 9, 231-246. (Preprint)
https://doi.org/10.4236/ijaa.2019.93017
[28]  Freese, K. and Lewis, M. (2002) Cardassian Expansion: A Model in Which the Universe Is Flat, Matter Dominated, and Accelerating. Physics Letters B, 540, 1-8. (Preprint)
https://doi.org/10.1016/S0370-2693(02)02122-6
[29]  Freese, K. (2003) Generalized Cardassian Expansion: A Model in Which the Universe Is Flat, Matter Dominated, and Accelerating. Nuclear Physics B: Proceedings Supplements, 124, 50-54. (Preprint)
https://doi.org/10.1016/S0920-5632(03)02076-0
[30]  Baes, M., Camps, P. and Van De Putte, D. (2017) Analytical Expressions and Numerical Evaluation of the Luminosity Distance in a Flat Cosmology. Monthly Notices of the Royal Astronomical Society, 468, 927-930. (Preprint)
https://doi.org/10.1093/mnras/stx537
[31]  Zaninetti, L. (2019) A New Analytical Solution for the Distance Modulus in Flat Cosmology. International Journal of Astronomy and Astrophysics, 9, 51-62. (Preprint)
[32]  Starobinsky, A.A. (1980) A New Type of Isotropic Cosmological Models without Singularity. Physics Letters B, 91, 99-102.
https://doi.org/10.1016/0370-2693(80)90670-X
[33]  Guth, A.H. and Weinberg, E.J. (1981) Cosmological Consequences of a First-Order Phase Transition in the SU5 Grand Unified Model. Physical Review D, 23, 876-885.
https://doi.org/10.1103/PhysRevD.23.876
[34]  Ratra, B. and Peebles, P.J.E. (1988) Cosmological Consequences of a Rolling Homogeneous Scalar Field. Physical Review D, 37, 3406-3427.
https://doi.org/10.1103/PhysRevD.37.3406
[35]  Steinhardt, P.J. and Caldwell, R.R. (1998) Introduction to Quintessence. In: Byun, Y.I. and Ng, K.W., Eds, Cosmic Microwave Background and Large Scale Structure of the Universe, Vol. 151, Astronomical Society of the Pacific, San Francisco, 13.
[36]  Avsajanishvili, O., Huang, Y., Samushia, L. and Kahniashvili, T. (2018) The Observational Constraints on the Flat φCDM Models. European Physical Journal C, 78, Article No. 773. (Preprint)
https://doi.org/10.1140/epjc/s10052-018-6233-y
[37]  Mamon, A.A., Bamba, K. and Das, S. (2017) Constraints on Reconstructed Dark Energy Model from SN Ia and BAO/CMB Observations. European Physical Journal C, 77, Article No. 29. (Preprint)
https://doi.org/10.1140/epjc/s10052-016-4590-y
[38]  Einstein, A. and de Sitter, W. (1932) On the Relation between the Expansion and the Mean Density of the Universe. Proceedings of the National Academy of Sciences of the United States of America, 18, 213-214.
https://doi.org/10.1073/pnas.18.3.213
[39]  Krisciunas, K. (1993) Look-Back Time the Age of the Universe and the Case for a Positive Cosmological Constant. Journal of the Royal Astronomical Society of Canada, 87, Article No. 223. (Preprint)
[40]  Ryden, B. (2003) Introduction to Cosmology. Addison Wesley, San Francisco, CA.
[41]  Lang, K. (2013) Astrophysical Formulae: Space, Time, Matter and Cosmology Astronomy and Astrophysics Library. Springer, Berlin.
[42]  Heymann, Y. (2013) On the Luminosity Distance and the Hubble Constant. Progress in Physics, 3, 5-6.
[43]  Milne, E.A. (1933) World-Structure and the Expansion of the Universe. Zeitschrift fur Astrophysik, 6, 1.
[44]  Chodorowski, M.J. (2005) Cosmology under Milne’s Shadow. Publications of the Astronomical Society of Australia, 22, 287-291. (Preprint)
https://doi.org/10.1071/AS05016
[45]  Adamek, J., Di Dio, E., Durrer, R. and Kunz, M. (2014) Distance-Redshift Relation in Plane Symmetric Universes. Physical Review D, 89, Article ID: 063543. (Preprint)
https://doi.org/10.1103/PhysRevD.89.063543
[46]  Brynjolfsson, A. (2004) Redshift of Photons Penetrating a Hot Plasma. arXiv:astro-ph/0401420
[47]  Brynjolfsson, A. (2006) Magnitude-Redshift Relation for SNe Ia, Time Dilation, and Plasma Redshift. ArXiv:astro-ph/0602500
[48]  Marmet, L. (2018) On the Interpretation of Spectral Red-Shift in Astrophysics: A Survey of Red-Shift Mechanisms—II. arXiv e-prints arXiv:1801.07582. (Preprint)
[49]  Zaninetti, L. (2015) On the Number of Galaxies at High Redshift. Galaxies, 3, 129-155.
https://doi.org/10.3390/galaxies3030129
[50]  Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1992) Numerical Recipes in FORTRAN. The Art of Scientific Computing. Cambridge University Press, Cambridge.
[51]  Akaike, H. (1974) A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control, 19, 716-123.
https://doi.org/10.1109/TAC.1974.1100705
[52]  Liddle, A.R. (2004) How Many Cosmological Parameters? Monthly Notices of the Royal Astronomical Society, 351, L49-L53.
https://doi.org/10.1111/j.1365-2966.2004.08033.x
[53]  Godlowski, W. and Szydowski, M. (2005) Constraints on Dark Energy Models from Supernovae. In: Turatto, M., Benetti, S., Zampieri, L. and Shea, W., Eds, 1604-2004: Supernovae as Cosmological Lighthouses, Vol. 342, Astronomical Society of the Pacific, San Francisco, 508-516
[54]  Bevington, P.R. and Robinson, D.K. (2003) Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill, New York.
[55]  Wei, H. (2010) Observational Constraints on Cosmological Models with the Updated Long Gamma-Ray Bursts Journal of Cosmology and Astroparticle Physic, 8, Article No. 020. (Preprint)
https://doi.org/10.1088/1475-7516/2010/08/020
[56]  Etherington, I.M.H. (1933) On the Definition of Distance in General Relativity. Philosophical Magazine, 15, 761-773.
https://doi.org/10.1080/14786443309462220
[57]  Remez, E. (1934) Sur la détermination des polynômes d’ approximation de degré donnée. Communications of Kharkov Mathematical Society, 10, Article No. 41
[58]  Remez, E. (1957) General Computation Methods of Chebyshev Approximation. The Problems with Linear Real Parameters. Publishing House of the Academy of Science of the Ukrainian SSR, Kiev.
[59]  Braatz, J.A., Reid, M.J., Humphreys, E.M.L., Henkel, C., Condon, J.J. and Lo, K.Y. (2010) The Megamaser Cosmology Project. II. The Angular-Diameter Distance to UGC 3789. The Astrophysical Journal, 718, 657-665. (Preprint)
https://doi.org/10.1088/0004-637X/718/2/657
[60]  Kuo, C.Y., Braatz, J.A., Reid, M.J., Lo, K.Y., Condon, J.J., Impellizzeri, C.M.V. and Henkel, C. (2013) The Megamaser Cosmology Project. V. An Angular-diameter Distance to NGC 6264 at 140 Mpc. The Astrophysical Journal, 767, Article No. 155. (Preprint)
https://doi.org/10.1088/0004-637X/767/2/155
[61]  Melia, F. and Yennapureddy, M.K. (2018) The Maximum Angular-Diameter Distance in Cosmology. Monthly Notices of the Royal Astronomical Society, 480, 2144-2152. (Preprint)
https://doi.org/10.1093/mnras/sty1962
[62]  Eales, S., Dunne, L., Clements, D., Cooray, A., De Zotti, G., Dye, S., et al. (2010) The Herschel ATLAS. Publications of the Astronomical Society of Pacific, 122, 499-515. (Preprint)
[63]  Tamura, Y., Oguri, M., Iono, D., Hatsukade, B., Matsuda, Y. and Hayashi, M. (2015) High-Resolution ALMA Observations of SDP.81. I. The Innermost Mass Profile of the Lensing Elliptical Galaxy Probed by 30 Milli-Arcsecond Images. Publications of the Astronomical Society of Japan, 67, 72. (Preprint)
https://doi.org/10.1093/pasj/psv040
[64]  ALMA Partnership (2015) The 2014 ALMA Long Baseline Campaign: Observations of the Strongly Lensed Submillimeter Galaxy HATLAS J090311.6+003906 at z=3.042. The Astrophysical Journal Letters, 808, Article No, L4. (Preprint)
https://doi.org/10.1088/2041-8205/808/1/L4
[65]  Rybak, M., Vegetti, S., McKean, J.P., Andreani, P. and White, S.D.M. (2015) ALMA Imaging of SDP.81—II. A Pixelated Reconstruction of the CO Emission Lines. Monthly Notices of the Royal Astronomical Society: Letters, 453, L26-L30. (Preprint)
https://doi.org/10.1093/mnrasl/slv092
[66]  Hatsukade, B., Tamura, Y., Iono, D., Matsuda, Y., Hayashi, M. and Oguri, M. (2015) High-Resolution ALMA Observations of SDP.81. II. Molecular Clump Properties of a Lensed Submillimeter Galaxy at z=3.042. Publications of the Astronomical Society of Japan, 67, Article No. 93. (Preprint)
[67]  Wong, K.C., Suyu, S.H. and Matsushita, S. (2015) The Innermost Mass Distribution of the Gravitational Lens SDP.81 from ALMA Observations. The Astrophysical Journal, 811, Article No. 115. (Preprint)
https://doi.org/10.1088/0004-637X/811/2/115
[68]  Hezaveh, Y.D., Dalal, N. and Marrone, D.P. (2016) Detection of Lensing Substructure Using ALMA Observations of the Dusty Galaxy SDP.81. The Astrophysical Journal, 823, Article No. 37 (Preprint)
https://doi.org/10.3847/0004-637X/823/1/37
[69]  Zaninetti, L. (2017) The Ring Produced by an Extra-Galactic Superbubble in Flat Cosmology. Journal of High Energy Physics, Gravitation and Cosmology, 3, 339-359.
https://doi.org/10.4236/jhepgc.2017.32029
[70]  Mohr, P.J., Taylor, B.N. and Newell, D.B. (2012) CODATA Recommended Values of the Fundamental Physical Constants: 2010. Reviews of Modern Physics, 84, 1527-1605.
https://doi.org/10.1103/RevModPhys.84.1527
[71]  Padé, H. (1892) Sur la représentation approchée d’une fonction par des fractions rationnelles. Annales scientifiques de l'école Normale Supérieure, 9, 3-93.
https://doi.org/10.24033/asens.378
[72]  Baker, G. (1975) Essentials of Padé approximants. Academic Press, New York.
[73]  Baker, G.A. and Graves-Morris, P.R. (1996) Padé approximants. Vol. 59, Cambridge University Press, Cambridge.

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