To Understand the Four Cosmological Interactions

Within the expanding cosmic Hubble volume, Hubble length can be considered as the gravitational or electromagnetic interaction range. Product of ‘Hubble volume’ and ‘cosmic crit ical density’ can be called as the “Hubble mass”. The three key assumptions are: 1) within the Hubble volume, each and every point in free space is influenced by the Hubble mass, 2) ‘molar electron mass’ can be considered as the rest mass of a new heavy charged elementary particle and 3) atomic grav itational constant seems to be Avogadro number times the classical gravitational constant. This is a new approach and may be given a chance in understanding the four fundamental cosmological interactions.


Introduction
"Hubble volume" can be considered as a key tool in cosmology and unificat ion. In this paper an attempt is made to understand the basic unified concepts of the four fundamental cos mological interactions. This is a new approach and particle physics and cosmology can be studied in a cohesive mode.

Basic Assumptions in Particle Cosmology
With reference to the Mach's principle [1][2][3][4][5][6] and the Hubble volu me, if "Hubble mass" is the product of cosmic critical density and the Hubble volume [7][8][9], then it can be assumed that, 1) With in the Hubble volume, each and every point in free space is influenced by the Hubble mass.
2) With in the Hubble volume, the Hubble mass plays a vital role in understanding the properties of electro magnetic and nuclear interactions.
3) Within the Hubble volu me, Hubble mass plays a key role in understanding the geometry of the universe.
With reference to the Avogadro number [10] and fro m unification point of view, the utmost fundamental question is: How to understand the origin of "mass" of elementary particles? In this connection it can be assumed that, 1) "Molar electron mass" can be considered as the rest mass of a new heavy charged elementary particle.
2) Ato mic gravitational constant is Avogadro number times the classical gravitational constant. (1) This idea may co me under the subject classification of "strong gravity" and is not in the main stream physics. K.P. Sinha, C. Sivaram, Abdus Salam, E. Recami and colleagues developed the subject in a unified gravitational approach [11][12][13][14][15]. It is reasonable to say that -since the atomic gravitational constant is N times the classical gravitational constant, atoms are themselves arranged in a systematic manner and generate the "gram mole".

Key Concepts in Particle Cosmology
Conce pt -2: The key conceptual lin k that connects the gravitational and non-gravitational forces is -the classical force limit 4 44 1.21026 10 newton Conce pt -7: For any observable charged particle, there e xist two kinds of masses and their mass ratio is 295.0606339. Let this nu mber be .
γ First kind of mass seems to be the 'gravitational or observed' mass and the second kind of mass seems to be the 'electromagnetic' mass. This idea can be applied to proton and electron. This number is obtained in the fo llo wing way. In the Planck scale, similar to the Planck mass, with reference to the elementary charge, a new mass unit can be constructed in the following way.
Here e is the elementary charge. How to interpret this mass unit? Is it a primo rdial massive charged particle? If t wo such oppositely charged particles annihilate, a large amount of energy can be released. This may be the root cause of cosmic energy reservoir. Such pairs may be the chief constituents of black holes. In certain t ime interval with a well defined quantum rules they annihilate and release a large amount of energy in the form of γ photons. In the Hubble volu me, with its pair annih ilat ion, "orig in of the CM BR" can be understood.
where sin W θ is very close to the weak mixing angle Conce pt-9: In modified quark SUSY [17,18], if f Q is the mass of quark fermion and b Q is the mass of quark boson, then and represents the effective quark fermion mass.
The number Ψ can be fitted with the following emp irical relation ( ) In support of these relations an attempt is made to implement the number k in fitt ing the nuclear binding energy constants and other areas of physics like strong interaction range, potential energy of electron in hydrogen atom, electroweak physics etc.

To Fit the Nuclear Binding Energy Constants
The semi-empirical mass formula (SEM F) is used to approximate the mass and various other properties of an atomic nucleus [27,28,29]. As the name suggests, it is based partly on theory and partly on empirical measurements. Based on the 'least squares fit', volu me energy coefficient is 15 asymmetric energy coefficient is a a = 23.21 MeV and pairing energy coefficient is 12 It is noticed that,  [30]. Co lu mn-3 represents the calculated binding energy and column-4 represents the measured binding energy.

Proton-nucleon Stability Relation
It is noticed that where s A is the stable mass number of . Z This is a direct relation. Assuming the proton number , Z in general, for all atoms, lower stability can be fitted directly with the following relat ion [27].

To Fit the Rms Radius of Proton
Let p R be the rms rad ius of proton. Define two radii 1 R and 2 R as follows.
This can be compared with the 2010 CODATA recommended rms radius of proton not clear. Th is is 10 t imes more p recise than all the previous determinations [31,32]. Thus from proton rest mass and rms radius, Here the most interesting thing is that, 2 R is very close to the Bohr rad ius of Hydrogen atom. It is very interesting to note that, with 2 R ionic radii of ato ms can be fitted very easily as ( ) For the above two cases, the characteristic mean distance ( ) λ in between N electrons or in between N protons, can be obtained as It is noticed that, ( ) Here X M is the molar electron mass. Here it is very interesting to consider the role of the Schwarzschild rad ius of the 'electron mass'.

Aplicat ion-3: To Fit the Charged Lepton Rest Masses
Muon and tau rest masses can be fitted in the following way [33]. Let s R be the characteristic nuclear unit size. The key relation seems to be Considering the ratio of the volu mes Now muon and tau masses can be fitted with the following relation [17,18].
Similarly, for proton, its characteristic interaction starting range can be expressed as ( )  Note that elliptical galaxies probably comprise about 60% of the galaxies in the universe and spiral galaxies thought to make up about 20% percent of the galaxies in the universe. Almost 80% of the galaxies are in the form of elliptical and spiral galaxies. For spiral galaxies,