Diameter and mass of the whole Universe

Diameter and mass of the whole Universe

Venkatram Nalla

Independent researcher, India and Singapore

http://doi.org/10.6084/m9.figshare.21508392.v5

Finding size of the whole Universe is fascinating as it is larger than observable Universe and expanding rapidly. From the dimension analogy, here I would like to estimate diameter of the whole Universe.

Recently there was a discussion on Young’s modulus Y of space-time [1, 2]. The question raised was, what is the Young’s modulus Y of space-time as experienced by a gravitational wave (GW), originally discussed at 2018 Hamilton Lecture at Princeton “Exploring the Universe with Gravitational Waves”. One response was that Y_space−timeis frequency dependent and given by

where f is the frequency of the gravitational wave, and G the Newtonian Gravitational constant. Above equation reveals interesting relation between Gravitational constant and speed of light. Using similar analogy Newton’s gravitational constant G was previously derived [3]. Analogy of matching dimensions, Newton’s gravitational constant can be written in terms of speed of light, mass and diameter of the Universe. From dimensional analysis equation can be written as,

But we are not fully aware of diameter and mass of the whole Universe; only parameters known to us are for observable Universe. If we consider M_u= N_m X M_ou and D_u = N_d X D_ou, whereas M_ou and D_ou are mass and diameter of observable Universe, N_m and N_d are mass and diameter ratio factors for whole Universe and observable Universe. Equation 2 can be written as:

By substituting known parameters, Newton’s gravitational constant G = 6.67 × 10^-11 Kg^-1m³s^-2, speed of light in vacuum c = 3× 10⁸ m/s, diameter of observable Universe D_ou= 8.8× 10²⁶ m. It is estimated that, observable Universe has 95% of dark matter and dark energy [4-7]. Mass of the ordinary/ baryonic mater of the observable Universe is 1.5 × 10⁵³ Kg, from this, estimated total mass of the observable Universe is M_ou = 3 × 10⁵⁴ Kg. From dimensional analysis equation 3 can be written as,

Ratio of diameter and mass factors for whole Universe and observable Universe is 2.5265, this constant is dimensionless universal constant. From the recent publication estimated N_d ≥ 251 [8] and mass factor can be estimated as.

Conclusions:

Estimated mass factor of the whole Universe is 99.347 times larger than the observable Universe, which is lower dense than the observable Universe.

Interestingly, (2 X 1/fine-structure constant)/108 = (2 X 137)/108 = 2.54 is nearly same as above universal constant in equation 4.

108: https://en.wikipedia.org/wiki/108_(number)

137: https://en.wikipedia.org/wiki/Fine-structure_constant

References:

[1]. Kirk T. McDonald, “What is the Stiffness of Spacetime?”, (2018).

http://physics.princeton.edu/∼mcdonald/examples/stiffness.pdf

[2]. A. C. Melissinos, "Upper limit on the Stiffness of space-time", arXiv:1806.01133, (2018).

[3]. Nalla, Venkatram (2020): Origin of Universal Gravitational constant, vacuum permittivity and permeability. figshare. Preprint. https://doi.org/10.6084/m9.figshare.13135163.v3

[4]. Paul Davies (2006). The Goldilocks Enigma, “Cosmic jackpot : why our universe is just right for life”, First Mariner Books. p. 43. ISBN 978-0-618-59226-5.

[5]. Dark Energy, Dark Matter, https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy

[6]. J. S. Farnes, “A unifying theory of dark energy and dark matter: Negative masses and matter creation within a modified ΛCDM framework”, A&A, 620, A92 (2018).

DOI: https://doi.org/10.1051/0004-6361/201832898

[7]. The LIGO Scientific Collaboration and The Virgo Collaboration, The 1M2H Collaboration, The Dark Energy Camera GW-EM Collaboration and the DES Collaboration, The DLT40 Collaboration, The Las Cumbres Observatory Collaboration, The VINROUGE Collaboration & The MASTER Collaboration, “A gravitational-wave standard siren measurement of the Hubble constant”, Nature 551, 85–88 (2017).

[8]. Vardanyan, M., Trotta, R. and Silk, J. , Applications of Bayesian model averaging to the curvature and size of the Universe. Monthly Notices of the Royal Astronomical Society: Letters, 413: L91-L95, (2011). https://doi.org/10.1111/j.1745-3933.2011.01040.x

https://www.forbes.com/sites/startswithabang/2019/03/05/how-much-of-the-unobservable-universe-will-we-someday-be-able-to-see/?sh=71649dbcf827

https://www.space.com/24073-how-big-is-the-universe.html

https://www.forbes.com/sites/startswithabang/2021/08/25/how-small-was-the-universe-at-the-start-of-the-big-bang/?sh=24000fef5f79

https://en.wikipedia.org/wiki/List_of_mathematical_constants

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