An Analytical Estimate of the Hubble Constant

Naser Mostaghel

doi:doi:10.11648/j.ajaa.20150303.13

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An Analytical Estimate of the Hubble Constant

Naser Mostaghel

Published in American Journal of Astronomy and Astrophysics (Volume 3, Issue 3)

Received: 19 March 2015 Accepted: 31 March 2015 Published: 27 April 2015

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Abstract

Currently the present-time value of the Hubble constant is estimated through finding the optimum fit to the observationally measured data. Here, assuming a flat universe with zero cosmological constant, based on the conservation of total mass-energy and a correction for the effect of time dilation, the total present-time value of the energy density parameter is found to be equal to 0.703091. Based on the Friedmann-Robertson-Walker (FRW) equation, the first law of thermodynamics, and Einstein’s Equivalence Principle, we present an analytical approach which yields a value for the Hubble constant equal to H_0=69.05398 km s^(-1) 〖Mpc〗^(-1). Using this value, Hubble diagrams are constructed. These diagrams are remarkably consistent with the available observational data.

Published in	American Journal of Astronomy and Astrophysics (Volume 3, Issue 3)
DOI	10.11648/j.ajaa.20150303.13
Page(s)	44-49
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Hubble Constant, Density Parameter, Distances and Redshift, Expanding Universe

References

[1]	E. Hubble, “A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae,” Proceedings of the National Academy of Sciences of the United States of America, 15:3, 168-173 (1929). http://www.pnas.org/content/15/3/168
[2]	L. Wendy, W. L. Freedman, F. B. Madore, “ The Hubble Constant,” Annual Review of Astronomy and Astrophysics, 48:673-710, (2010).
[3]	Tammann, G. A. (2005) “The Ups and Downs of the Hubble Constant,” arXiv:astro-ph/0512584v1, Reviews in Modern Astronomy, Volume 19, pp. 1-29, (2008).
[4]	N. Falcon, A. Aguirre, “Theoretical Deduction of the Hubble Law Beginning with a MoND Theory in Context of the ΛFRW-Cosmology,” International Journal of Astronomy and Astrophysics, 4, pp. 551-559, (2014). http://dx.doi.org/10.4236/ijaa.2014.44051
[5]	D. Larson, J. Dunkley, G. Hinshaw, E. Komatsu, M. R. Nolta, C. L. Bennett, et al., “Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results,” Astrophysical Journal Supplement Series, 192:16, pp. 1-19 (2011).
[6]	P. A. R. Ade, N. Aghanim, M. I. R. Alves, C. , Armitage-Caplan, M. Amaud, M. Ashdown, et al., “Planck 2013 Results, I. Overview of Products and Scientific Results,” http://arxiv.org/abs/1303.5062 v2, pp. 1-49 (2013).
[7]	C. L. Bennett, D. Larson, J. L. Weiland, N. Jarosik, G. Hinshaw, N. Odegard, et al., “Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Maps and Results,” Astrophysical Journal Supplement Series, 208:20, pp. 1-54 (2013).
[8]	M. J. Reid, J. A. Braatz, J. J. Condon, K. Y. Lo, C. Y. Kuo, C. M. V. Impellizzeri, et al. “The Megamaser Cosmology Project IV. A Direct Measurement of the Hubble Constant From UGC 3789,” Astrophysical Journal, 767:154, pp. 1-11, (2013).
[9]	J. A. Peacock, Cosmological Physics, Cambridge University Press, 1999, pp. 75-77.
[10]	C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation, W. H. Freeman and Company, San Francisco, 1973, pp. 726-728.
[11]	A. G. Riess, “Nobel Lecture: My Path to the Accelerating Universe,” Reviews of Modern Physics, Vol. 84, pp. 1165-1175, (2012).
[12]	B. P. Schmidt, “Nobel Lecture: Accelerating Expansion of the Universe through Observation of Distant Supernovae,” Reviews of Modern Physics, Vol. 84, pp. 1151-1163, (2012).
[13]	S. Perlmutter, “Nobel Lecture: Measuring the Acceleration of the Cosmic Expansion Using Supernovae,” Reviews of Modern Physics, Vol. 84, pp. 1127-1149, (2012).
[14]	S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, P. G. Castro, et al. “Measurements of Ω and Λ From 42 High-Redshift Supernovae,” The Astrophysical Journal, 517:565-586, (1999).
[15]	P. J. E. Peebles, Principles of Physical Cosmology, Princeton University Press1993, pp. 321.
[16]	R. Amanullah, C. Lidman, D. Rubin, G. Aldering, P. Astier, K. Barbary, et al., “ Spectra and Hubble Space Telescope Light Curves of Six Types Ia Supernovae at 0.511< z <1.12 and the Union2 Compilation,” The Astrophysical Journal, 716:712-738, (2010), data available at http://supernova.lbl.gov/Union/figur...n2_mu_vs_z.txt
[17]	B. F. Mador, I. P. Steer, “NASA/IPAC Extragalactic Database Master List of Galaxy Distances,” NED-4D, (2008). http://ned.ipac.caltech.edu/level5/NED4D/

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APA Style

Naser Mostaghel. (2015). An Analytical Estimate of the Hubble Constant. American Journal of Astronomy and Astrophysics, 3(3), 44-49. https://doi.org/10.11648/j.ajaa.20150303.13

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ACS Style

Naser Mostaghel. An Analytical Estimate of the Hubble Constant. Am. J. Astron. Astrophys. 2015, 3(3), 44-49. doi: 10.11648/j.ajaa.20150303.13

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AMA Style

Naser Mostaghel. An Analytical Estimate of the Hubble Constant. Am J Astron Astrophys. 2015;3(3):44-49. doi: 10.11648/j.ajaa.20150303.13

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@article{10.11648/j.ajaa.20150303.13,
  author = {Naser Mostaghel},
  title = {An Analytical Estimate of the Hubble Constant},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {3},
  number = {3},
  pages = {44-49},
  doi = {10.11648/j.ajaa.20150303.13},
  url = {https://doi.org/10.11648/j.ajaa.20150303.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20150303.13},
  abstract = {Currently the present-time value of the Hubble constant is estimated through finding the optimum fit to the observationally measured data. Here, assuming a flat universe with zero cosmological constant, based on the conservation of total mass-energy and a correction for the effect of time dilation, the total present-time value of the energy density parameter is found to be equal to 0.703091. Based on the Friedmann-Robertson-Walker (FRW) equation, the first law of thermodynamics, and Einstein’s Equivalence Principle, we present an analytical approach which yields a value for the Hubble constant equal to H_0=69.05398 km s^(-1)  〖Mpc〗^(-1). Using this value, Hubble diagrams are constructed. These diagrams are remarkably consistent with the available observational data.},
 year = {2015}
}

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TY  - JOUR
T1  - An Analytical Estimate of the Hubble Constant
AU  - Naser Mostaghel
Y1  - 2015/04/27
PY  - 2015
N1  - https://doi.org/10.11648/j.ajaa.20150303.13
DO  - 10.11648/j.ajaa.20150303.13
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 44
EP  - 49
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20150303.13
AB  - Currently the present-time value of the Hubble constant is estimated through finding the optimum fit to the observationally measured data. Here, assuming a flat universe with zero cosmological constant, based on the conservation of total mass-energy and a correction for the effect of time dilation, the total present-time value of the energy density parameter is found to be equal to 0.703091. Based on the Friedmann-Robertson-Walker (FRW) equation, the first law of thermodynamics, and Einstein’s Equivalence Principle, we present an analytical approach which yields a value for the Hubble constant equal to H_0=69.05398 km s^(-1)  〖Mpc〗^(-1). Using this value, Hubble diagrams are constructed. These diagrams are remarkably consistent with the available observational data.
VL  - 3
IS  - 3
ER  -

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Author Information

Naser Mostaghel

Dept. of Civil Engineering, University of Toledo, Ohio, USA

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APA Style

Naser Mostaghel. (2015). An Analytical Estimate of the Hubble Constant. American Journal of Astronomy and Astrophysics, 3(3), 44-49. https://doi.org/10.11648/j.ajaa.20150303.13

Copy | Download

ACS Style

Naser Mostaghel. An Analytical Estimate of the Hubble Constant. Am. J. Astron. Astrophys. 2015, 3(3), 44-49. doi: 10.11648/j.ajaa.20150303.13

Copy | Download

AMA Style

Naser Mostaghel. An Analytical Estimate of the Hubble Constant. Am J Astron Astrophys. 2015;3(3):44-49. doi: 10.11648/j.ajaa.20150303.13

Copy | Download

@article{10.11648/j.ajaa.20150303.13,
  author = {Naser Mostaghel},
  title = {An Analytical Estimate of the Hubble Constant},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {3},
  number = {3},
  pages = {44-49},
  doi = {10.11648/j.ajaa.20150303.13},
  url = {https://doi.org/10.11648/j.ajaa.20150303.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20150303.13},
  abstract = {Currently the present-time value of the Hubble constant is estimated through finding the optimum fit to the observationally measured data. Here, assuming a flat universe with zero cosmological constant, based on the conservation of total mass-energy and a correction for the effect of time dilation, the total present-time value of the energy density parameter is found to be equal to 0.703091. Based on the Friedmann-Robertson-Walker (FRW) equation, the first law of thermodynamics, and Einstein’s Equivalence Principle, we present an analytical approach which yields a value for the Hubble constant equal to H_0=69.05398 km s^(-1)  〖Mpc〗^(-1). Using this value, Hubble diagrams are constructed. These diagrams are remarkably consistent with the available observational data.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - An Analytical Estimate of the Hubble Constant
AU  - Naser Mostaghel
Y1  - 2015/04/27
PY  - 2015
N1  - https://doi.org/10.11648/j.ajaa.20150303.13
DO  - 10.11648/j.ajaa.20150303.13
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 44
EP  - 49
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20150303.13
AB  - Currently the present-time value of the Hubble constant is estimated through finding the optimum fit to the observationally measured data. Here, assuming a flat universe with zero cosmological constant, based on the conservation of total mass-energy and a correction for the effect of time dilation, the total present-time value of the energy density parameter is found to be equal to 0.703091. Based on the Friedmann-Robertson-Walker (FRW) equation, the first law of thermodynamics, and Einstein’s Equivalence Principle, we present an analytical approach which yields a value for the Hubble constant equal to H_0=69.05398 km s^(-1)  〖Mpc〗^(-1). Using this value, Hubble diagrams are constructed. These diagrams are remarkably consistent with the available observational data.
VL  - 3
IS  - 3
ER  -

Copy | Download