## Derivation of Three Fundamental Masses and Large Numbers Hypothesis by Dimensional Analysis

**Authors:** Dimitar Valev

Three mass dimension quantities have been derived by dimensional analysis by means of fundamental constants – the speed of light in vacuum (c), the gravitational constant (G), the Planck constant (h_bar) and the Hubble constant (H). The extremely small mass m1 ~ (h_bar*H)/c^2 ~ 10^(-33) eV has been identified with the Hubble mass mH, which seems close to the graviton mass mG. The enormous mass m2 ~ c^3/(G*H) ~ 10^53 kg is close to the mass of the Hubble sphere and practically coincides with the Hoyle-Carvalho formula for the mass of the observable universe. The third mass m3 ~ [(H*h_bar^3)/G^2]^(1/5) ~ 10^7 GeV could not be unambiguously identified at present time. Besides, it has been found remarkable fact that the Planck mass mPl ~ Sqrt [(h_bar*c)/G] appears geometric mean of the extreme masses m1 and m2. Finally, the substantial large number N = Sqrt [c^5/(2*G*h_bar*H^2) ≈ 5.73×10^60 has been derived relating cosmological parameters (mass, density, age and size of the observable universe) and fundamental microscopic properties of the matter (Planck units and Hubble mass). Thus, a precise formulation and proof of Large Numbers Hypothesis (LNH) has been found.

**Comments:** 12 pages

**Download:** **PDF**

### Submission history

[v1] 2012-08-13 12:47:23

**Unique-IP document downloads:** 227 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*