## Resolving the Tension Between Planck H0=66.931 and Riess et al H0=73.242

**Authors:** Bruce Wallman

There is an open question in cosmology about the significance of the difference between the 2016 Planck collaboration value H0=66.93±0.62 km/s/Mpc and the 2016 Riess et al value H0=73.24±1.74 km/s/Mpc. This paper shows that both the Planck collaboration and Riess et al values are valid. Tracing the cosmological redshift z from SN1a several thousand megaparsecs in the past to those that exploded closer to today describes an increase in our perception of Hv as distance to us lessens. A best fit power function of vr=73.227*Dp0.9907 for recessional velocity versus proper distance (where vr is recessional velocity and Dp is proper distance) is derived connecting these two values of H0 using 1836 SN1a in the NED database3. Taking the derivative of this formula to get Hubble slope gives the power function Hv=dvr/dDp= 72.546*Dp -0.0093. When this formula is used to describe an extrapolation of the universe from near the Milky Way galaxy to the Cosmic Microwave Background (CMB), it describes a change of about 7 km/s/Mpc in the Hubble value for the observable universe increasing smoothly from 66.4 for our measures at the CMB to 73.4 km/s/Mpc locally as the universe expands. Most of the increase occurs in the last 1000 Mpc as was stated in Riess, Perlmutter, and subsequent SN1a studies. This is consistent with ΛCDM cosmology4. After converting distance in megaparsecs to light-seconds, it is possible to show Hv is an acceleration that varies from 6.45 angstrom/s/lt-s when measuring the CMB to 7.13 angstrom/s/lt-s in the local universe.

**Comments:** 7 Pages.

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### Submission history

[v1] 2019-06-08 07:29:57

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