Effects of Time Dilation on the Measurements of the Hubble Constant

Naser Mostaghel

doi:10.4236/ijaa.2018.84024

Abstract

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.

Highlights

The recently reported measured value for the Hubble constant by the Plank team [1] is H=0 67.66 ± 0.42 km ⋅ s−1 ⋅ Mpc−1
We show that starting the evaluation from the present time proceeding toward the surface of last scattering yiel= ds H0 74.2119 km ⋅ s−1 ⋅ Mpc−1 which is consistent with the value measured by Reiss et al It is concluded that, because of time dilation, the direction of evaluation of the Hubble time is the cause of discrepancy or tension between the two measured values
Because in the above two measurements the reversal of the proper time of a single world-line from a future-pointing to a past-pointing has resulted in different values for the Hubble constant; the time symmetry is broken [6]

Summary

Introduction

The recently reported measured value for the Hubble constant by the Plank team [1] is H=0 67.66 ± 0.42 km ⋅ s−1 ⋅ Mpc−1. We show that including the time dilation and starting the evaluation from the surface of last scattering proceeding toward the present time yiel= ds H0 67.8236 km ⋅ s−1 ⋅ Mpc−1. This value of H0 is remarkably consistent with the Plank measured value. We show that starting the evaluation from the present time proceeding toward the surface of last scattering yiel= ds H0 74.2119 km ⋅ s−1 ⋅ Mpc−1 which is consistent with the value measured by Reiss et al It is concluded that, because of time dilation, the direction of evaluation of the Hubble time is the cause of discrepancy or tension between the two measured values

Evaluation of the Reference Hubble Constant

Evaluation of the Effects of Time Dilation on the Hubble Constant

Time Dilation Based on the Schwarzschild Solution

Conclusion and Remarks