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# Gamma and Beta Model of Growing and Rotating Planck Ball

Version 1
: Received: 15 February 2019 / Approved: 20 February 2019 / Online: 20 February 2019 (11:37:37 CET)

Version 2 : Received: 4 March 2019 / Approved: 5 March 2019 / Online: 5 March 2019 (06:43:15 CET)

Version 2 : Received: 4 March 2019 / Approved: 5 March 2019 / Online: 5 March 2019 (06:43:15 CET)

How to cite:
U.V., S.S.; Lakshminarayana, S. Gamma and Beta Model of Growing and Rotating Planck Ball. *Preprints* **2019**, 2019020189 (doi: 10.20944/preprints201902.0189.v1).
U.V., S.S.; Lakshminarayana, S. Gamma and Beta Model of Growing and Rotating Planck Ball. Preprints 2019, 2019020189 (doi: 10.20944/preprints201902.0189.v1).

## Abstract

With reference to Planck scale, Mach’s relation, increasing support for large scale cosmic anisotropy & preferred directions and by introducing two new parameters Gamma and Beta, right from the beginning of Planck scale, we make an attempt to estimate ordinary matter density ratio, dark matter density ratio, mass, radius, temperature, age and expansion velocity (from and about the Planck mass in all directions). By considering ${H}_{0}\cong 70$ km/sec/Mpc, estimated current cosmic mass, radius, total matter density, expansion velocity, temperature and age are: 4.3352 × 10

^{53 }kg, 3.207 × 10^{26}m, 3.138 × 10^{−27}kg·m^{−3}, 2.43*c*, 2.721 K and 19.78 Billion years respectively. Point to be noted is that, with reference to Planck scale, ratio of Hubble parameter*H*to angular velocity_{t}*ω*can be expressed with $\left({H}_{t}/{\omega}_{t}\right)\cong {\gamma}_{t}\cong \left[1+\mathrm{ln}\left({H}_{pl}/{H}_{t}\right)\right]\cong \sqrt{3{H}_{t}^{2}{c}^{2}/8\pi G\left(a{T}_{t}^{4}\right)}$ where_{t}*H*represents Planck scale angular velocity and $\left(a{T}_{t}^{4}\right)$ is the thermal energy density. $\left({H}_{0}/{\omega}_{0}\right)\cong {\gamma}_{0}\cong 141.26$ and ${\omega}_{0}\cong 1.606\times {10}^{-20}\text{rad/sec}\cong \text{5}\text{.068}\times {10}^{-13}\text{rad/year}\text{.}$It needs further study. Proceeding further, from the beginning of Planck scale, a) With a ‘decreasing’ trend of total matter density ratio, cosmic expansion velocity can be shown to be increasing. b) With an ‘increasing’ trend of total matter density ratio, cosmic expansion velocity can be shown to be decreasing. c) With a constant trend of total matter density ratio, cosmic expansion velocity can be shown to be constant. In this model, in understanding the currently believed cosmic acceleration, there is no need to consider dark energy._{pl}## Subject Areas

Planck scale; Mach’s relation; quantum cosmology; critical density; ordinary matter; dark matter; expansion velocity; angular velocity; Hubble’s law

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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