Measuring the Expansion Velocity of the Universe

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The intent of this paper is to derive as much as possible a value for the expansion velocity of the universe. This is not the Hubble parameter, although it will be derived as an addition. The expansion velocity is taken as the value of the recession velocity in co-moving space. The co-moving space is modeled as a simple arc of a circle. The expansion velocity is the value at one radian of arc. It is not assumed to be the speed of light, but expected to be some value less. Under assumptions discussed in the paper a lower limit is derived as approximately 0.868480c.

Also derived is a distance reference. The distance is in co-moving space from the surface of last scattering to ‘now’ and at ‘now’ found to be 17.03331 billion light-years.

Theory predicts a maximum time horizon of 13.8683 billion years and a related minimum H0 of 70.5069 km/sec/Mpc.

The values and relations obtained are compared with existing measurements -- both supernovae data and gamma ray burst are used. The data is found to be very linear when using the Doppler redshift relation to determine a recession velocity in our flat observational universe and compared to the transformed recession velocity in co-moving space. Hubble’s Law is precisely honored in co-moving space.

Initial datafits while linear gave values of 14.170 billion years and 69.01 km/sec/Mpc (with an expansion velocity of 0.849999c). Since this is outside the limits predicted, honoring the theory would suggest that the data ‘calibration’ is in question. Note that a distance modulus magnitude shift of -0.065 (nearer) would shift the results to 13.85 billion years and 70.6 km/sec/Mpc. (And resulting in a measured expansion velocity of 0.869609c).

This same correction would move a (model dependent) Hubble constant of 72 value to about 74.2 km/sec/Mpc - the recent change reported by Reiss, et. al. (May 2009) [1].

The results of this model imply that gravity is not needed on the cosmological scale to explain the measurements seen to date. It further supports the concept that the gravitational field may be due to a loss of photon exchange such as used to explain Quantum Electrodynamics (QED). This loss resulting in a net attraction. This extension of QED is not presented in this paper but is intended as later work. This is a basis paper only.

Conclusions reached

Starting with what has not been precisely proved.

While the data does tend to correlate to the theoretical value of Dref at 17.0333 billion light-years, the data is of too poor a quality to say that this precise value is confirmed.

Further, the value of Dref is used as a basis to calculate the expansion velocity. This means the datafit results for the expansion velocity (ve) are no more precisely determined than Dref.
Like all other models this one is waiting for more precise data in order to confirm its parameter values. However, unlike most others it does have theoretically derived values as ‘targets’ for further investigation.

What has been shown, however, is very important:

The role of using Doppler for explaining cosmological redshift cannot be ignored. With proper geometric transformation there is a linear relation between Doppler calculated recession velocity and the co-moving space measured distance.

Since this approach yields a linear (and constant) expansion velocity over the entire range of data currently available, the only reasonable conclusion is that the universe is expanding at a constant velocity. NO ACCELERATION OR DECELERATION.

This means that the cosmological redshift is not an effect of gravitation -- however its scaling value (Dref) may be determined by the ‘birth of gravity’ at the time of last scattering.

What is supported but not proven:

The datafit results for the derived value of Dref is taken as support for the idea that gravitation is due to pair production. The reports of large ‘clouds’ of pair production surrounding known highly compacted galactic core objects is also supportive.

This is also a support for the idea that it is only baryonic matter that can PRODUCE a gravitational field. The effects of a gravitational field, however, can still show up with photons, etc. This obviously has a direct impact on much of the assumed dark matter.
With the apparent data support for a constant expansion of the universe, the need for such concepts as dark energy to supply acceleration seems to be gone.

References cited:
[1] Reiss, et. al. (May 2009) A Redetermination of the Hubble Constant with the Hubble Space Telescope from a Differential Distance Ladder (arXiv:0905.0695)

[2] Kowalski, et. al. (2008) Improved Cosmological Constraints from New, Old and Combined Supernova Datasets (arXiv:0804.4142)

[3] Schaefer (Dec 2006) The Hubble Diagram to Redshift >6 from 69 Gamma-Ray Bursts (arXiv:astro-ph/0612285)


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