We show that, when measuring the Hubble constant by starting the evaluation from the time of the big bang era, the effect of time dilation results in a decrease in the value of the Hubble constant. But when evaluating the Hubble constant by starting the evaluation from the present time, the effect of time dilation results in an increase in the value of the Hubble constant. To elucidate the process, the time dilation is calculated both directly and through Schwarzschild solution of the Einstein equation for the gravitational time dilation. It is concluded that both measured values are valid but because of time dilation, different starting times for the evaluation of the Hubble constant have resulted in different measured values for the Hubble constant.
References
[1]
Aghanim, N., Akrami, Y., Ashdown, M., et al. (2018) Plank 2018 Results. VI. Cosmological Parameters. https://arxiv.org/abs/1807.06209
[2]
Riess, A.G., Casertano, S., Yuan, W., et al. (2018) Milky Way Cepheid Standards for Measuring Cosmic Distances and Application to Gaia DR1: Implications for the Hubble Constant. https://arxiv.org/abs/1804.10655
[3]
Freedman, W.L. (2017) Cosmology at Crossroads: Tension with the Hubble Constant. https://arxiv.org/abs/1706.02739
[4]
Donna Weaver, D. and Villard, R. (2018) Improved Hubble Yardstick Gives Fresh Evidence for New Physics in the Universe. NASA. https://www.nasa.gov/feature/goddard/2018/improved-hubble- yardstick-gives-fresh-evidence-for-new-physics-in-the-universe/
[5]
Devlin, H. (2018) The Answer to Life, the Universe and Everything Might Be 73. Or 67. The Guardian. https://www.theguardian.com/science/2018/may/10/the-ans wer-to-life-the-universe-and-everything-might-be-73-or-67
[6]
Ripalda, J.M. (2010) Time Reversal and Negative Energies in General Relativity. arXiv:gr-qc/9906012, v14.
[7]
Peacock, J. (1999) Cosmological Physics. Cambridge University Press, Cambridge.
[8]
Mostaghel, N. (2018) The Role of Time in Cosmic Expansion. American Journal of Astronomy and Astrophysics, 6, 9-21.
[9]
NIST, CODATA VALUE: Wien Wavelength Displacement Law Constant. http://physics.nist.gov/cgi-bin/cuu/Value?bwien
Fixsen, D.J. (2009) The Temperature of the Cosmic Microwave Background. The Astrophysical Journal, 707, 916-920. https://doi.org/10.1088/0004-637X/707/2/916
[12]
Wikipedia, Gravitational Time Dilation. https://en.wikipedia.org/wiki/Gravitational_time_dilation
