Preprint Article Version 2 This version is not peer-reviewed

# 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)

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.v2). U.V, S.S.; Lakshminarayana, S. On the Eternal Role of Planck Scale in Machian Cosmology. Preprints 2018, 2018100407 (doi: 10.20944/preprints201810.0407.v2).

## Abstract

Considering Planck mass as a representation of baby universe and evolving universe as a growing Planck ball, a heuristic model of quantum cosmology can be developed. By considering the famous relation GM = c2R, a Machian model of evolving quantum cosmology can also be developed with increasing matter content and decreasing matter density. In all directions, ‘from and about’ the baby universe, cosmic expansion velocity can be shown to be increasing with decreasing matter density. Estimated current cosmic mass, radius, matter density, expansion velocity and age are: 4.3352×1053 kg, 3.207×1026 m, 3.318×10-27 kg.m-3, 2.43c and 19.78 Billion respectively. As a peculiar case, considering the equality of current Hubble parameter and current angular velocity, current cosmic rotational kinetic energy can be shown to be 0.667 times the current critical energy! Proceeding further, with reference to Planck scale, cosmic temperature seems to be redshifted by a factor$\left({\left({Z}_{T}\right)}_{t}+1\right)\cong \sqrt{1+\mathrm{ln}\left({H}_{pl}/{H}_{t}\right)}$; where (Hpl, Ht) represent Planck scale and time dependent Hubble parameters respectively.

## Subject Areas

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