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# On the Eternal Role of Planck Scale in Machian Cosmology

Version 1
: Received: 17 October 2018 / Approved: 18 October 2018 / Online: 18 October 2018 (08:42:57 CEST)

Version 2 : Received: 25 October 2018 / Approved: 25 October 2018 / Online: 25 October 2018 (09:51:27 CEST)

Version 3 : Received: 30 October 2018 / Approved: 2 November 2018 / Online: 2 November 2018 (02:30:57 CET)

Version 2 : Received: 25 October 2018 / Approved: 25 October 2018 / Online: 25 October 2018 (09:51:27 CEST)

Version 3 : Received: 30 October 2018 / Approved: 2 November 2018 / Online: 2 November 2018 (02:30:57 CET)

How to cite:
U.V, S.S.; Lakshminarayana, S. On the Eternal Role of Planck Scale in Machian Cosmology. *Preprints* **2018**, 2018100407 (doi: 10.20944/preprints201810.0407.v3).
U.V, S.S.; Lakshminarayana, S. On the Eternal Role of Planck Scale in Machian Cosmology. Preprints 2018, 2018100407 (doi: 10.20944/preprints201810.0407.v3).

## Abstract

With reference to Planck scale, Mach's relation 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). In analogy with currently believed cosmic acceleration, with a decreasing trend of total matter density ratio, cosmic expansion velocity can be shown to be increasing. By considering ${H}_{0}\cong 70$ km/sec/Mpc, estimated current cosmic mass, radius, total matter density, expansion velocity, temperature and age are: $4.3352\times {10}^{53}\text{}\mathrm{kg},$ $3.207\times {10}^{26}\text{}\mathrm{m},$ $3.138\times {10}^{-27}\text{}\mathrm{kg}{.\mathrm{m}}^{-3},$ $2.43c,$ $2.721\text{}\mathrm{K}$ and $19.78\text{}\mathrm{Billion}\text{}\mathrm{years}$ respectively. Point to be noted is that, with reference to Planck scale, cosmic temperature seems to be redshifted by a factor ${\left({Z}_{T}\right)}_{t}\cong \sqrt{1+\mathrm{ln}\left({H}_{pl}/{H}_{t}\right)}-1$ where $\left({H}_{pl},{H}_{t}\right)$ represent Planck scale and time dependent Hubble parameters respectively. As a peculiar case, considering the equality of current Hubble parameter and current angular velocity, current cosmic rotational kinetic energy can be estimated to be 0.667 times the current critical energy. It needs further study.

## Keywords

Planck scale; Mach’s relation; quantum cosmology; critical density; ordinary matter; dark matter; thermal redshift; expansion velocity; rotational kinetic energy; dark energy; Hubble’s law

## Subject

PHYSICAL SCIENCES, Astronomy & Astrophysics

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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