1. Introduction

The fundamental question to be answered is: Is the universe a quantum gravitational object or something else? Physicists expressed several opinions with many possible solutions ^{[1, 2]}. By correlating the basics of Quantum mechanics, Special and General theories of relativity and big bang - in this letter the authors outlined a scale independent quantum cosmology.

2. Scale Independent Quantum Cosmology

Some of the other modern cosmologists believe that, during the cosmic evolution, Planck scale quantum gravitational interactions might have an observable effect on the current observable cosmological phenomena. Clearly speaking, with respect to the current concepts of ‘Quantum gravity’ and Planck scale early universal laboratory, current universe can be considered as a low energy scale laboratory. If one is willing to consider the current observable universe as a low energy scale operating laboratory, currently believed cosmic microwave back ground temperature can be considered as the low energy quantum gravitational effect. At any time in the past, i.e as the operating energy scale was assumed to be increasing; past high cosmic back ground temperature can be considered as the high energy quantum gravitational effect. Thinking in this way, starting from the Planck scale and with reference to the decreasing magnitude of cosmic back ground temperature ^[3], quantum gravity can be considered as a scale independent model and the universe can be considered as the best quantum gravitational object.

3. The Unified Planck Scale Mass Unit Connected with Big Bang

With reference to the famous Planck’s constant, the unified quantum mass unit connected with big bang can be expressed as follows. It can be obtained from equations (5,6,7,8 and 9).

(1)

Here, from quantum theory of light ^{[4, 5]},

With 98% accuracy, its classical unified expression can be expressed as follows. In this context interested readers may go through the references ^{[5, 6]}.

(2)

4. The Unified Quantum Scale Hubble Constant Connected with Big Bang

With reference to the General theory of light and Friedmann cosmology, current and past critical mass densities can be expressed as follows.

(3)

With reference to the observable volume of the current and past universe, current and past critical volumes can be can be expressed as follows.

(4)

Characteristic critical masses of the current and past universe can be expressed as follows.

(5)

Scientists proposed several characteristic constants connected with unification and cosmology. Now with reference to the above proposed unified Planck scale quantum mass , unified Hubble’s constant (assumed to be connected with big bang) can be defined as follows.

(6)

Using this characteristic big bang Hubble constant, in a cosmological approach, a suitable proportionality coefficient of the following form can be considered for further study as proposed in the following sections.

5. Different Relations Connected with Quantum Cosmology and Big Bang

Based on the quantum cosmological concepts, the following semi empirical heuristic equations can be given a fundamental significance ^[5] in cosmology. Using these relations current cosmological parameters can be fitted accurately.

Relation between thermal energy density and critical energy density

Basic concept: During cosmic evolution, at any time, thermal energy density is proportional to the critical mass energy density.

(7)

where is a model dependent proportionality coefficient. With reference to the Planck scale and current key cosmological physical parameters, the proportionality coefficient can possibly be fitted in the following way ^[5].

(8)

It is for further study and critical mathematical analysis.

(9)

Note that, at the Planck scale,

For the current universe,

(10)

Relation between cosmic thermal wave lengths and Hubble lengths

Let represent the thermal wavelengths ^[4] related with frequency and wavelength domains respectively. From relations and with reference to the two forms of Wien’s law, at any time in the past,

(11)

For the current universe ^[7],

(12)

Relation between cosmic thermal wave lengths and the Cosmic repulsive force

With usual notation, from General theory of relativity ^{[8, 9, 10]},

(13)

In this historical relation, the most important point to be noted is that, the expression seems to be a proportionality constant. If one is willing to consider its ‘inverse form’, it becomes and seems to play a very crucial role in the evolving cosmology. It can be called as the ‘repulsive force’ of the evolving universe. From above relations it can be expressed as follows. At any time in the past,

(14)

For the current universe,

(15)

Relation between matter energy density, thermal energy density and critical energy density

Basic concept: During cosmic evolution, at any time, matter energy density is the geometric mean of critical mass energy density and thermal energy density.

(16)

For the current universe and with reference to elliptical and spiral galaxies ^[8] whose mass-light ratio is close to 8 to 10,

(17)

Relation between cosmic temperature and temperature fluctuations

Basic concept: During cosmic evolution, at any time, temperature anisotropy is directly proportional to cosmic back ground temperature.

(18)

(19)

For the current universe,

(20)

6. To Fit the Magic Numbers 5%, 27% and 67% of the Modern (accelerating) Cosmology

Current critical mass density can be expressed as:

(21)

For a while guess that, mass density of the current universe suddenly drops to the magnitude of the current ‘matter density’. Then current Hubble length hypothetically increases by a factor

(22)

This can be compared with the currently believed ‘matter density percentage’ of the accelerating universe ^{[7, 8, 9, 10]}. Current critical mass-energy density can be expressed as:

(23)

For a while guess that, mass-energy density of the current universe suddenly drops to the magnitude of the current thermal energy density. Then current Hubble length hypothetically increases by a factor

(24)

This can be compared with the currently believed ‘dark matter density percentage’ of the accelerating universe ^{[7, 8, 9, 10]}. These two accurate coincidences cast doubt on the validity of the third well believed algebraic ‘dark energy density percentage form’ of [100-(5.23+27.35)]% = 67.42%.

7. Reinterpreting Cosmic Red Shift

During cosmic evolution, right from the beginning of formation of hydrogen atoms, as any baby hydrogen atom starts growing, cosmologically, bonding strength increases in between proton and electron causing increasing electron excitation energy to emit increased quantum of energy. With reference to the current strengthened or reinforced hydrogen atom, difference in ‘emitted quantum of energy’ may appear to be the observed cosmological redshift associated with galactic hydrogen atom. Observed Super novae dimming can be understood in this way ^[9]. Based on this new proposal, ‘galaxy receding’ concept suggested by Hubble ^{[11, 12]} can be reviewed and possibly can be relinquished. If cosmic time is running fast or if cosmic size/boundary is increasing fast or if cosmic temperature is decreasing fast then redshift seems to increase fast with reference to the current hydrogen atom. For a while guess that cosmological binding strength of proton and electron in the cosmologically evolving hydrogen atom is inversely proportional to the cosmic temperature, then with usual notation, observed cosmic red shift can be expressed as follows.

(25)

where, represents the current CMBR temperature, represents past cosmic temperature and is the wavelength of photon ‘emitted as well as received’ from the galactic hydrogen atom.

At any time in the past, at any galaxy, emitted photon energy can be expressed as follows.

(26)

Here, is the current redshift, is the energy of emitted photon from the galactic hydrogen atom and is the corresponding energy in the laboratory. is the ’s corresponding wave length in the laboratory.

From laboratory point of view, above concept can be understood in the following way. After some time in future,

(27)

Here, is the energy of photon emitted from laboratory hydrogen atom after some time in future. is the energy of current photon emitted from laboratory hydrogen atom. is the redshift of laboratory hydrogen atom after some time in future. From now onwards, as time passes, in future - can be considered as an index of the absolute rate of cosmic expansion. Within the scope of experimental accuracy of laboratory hydrogen atom’s redshift, it can be suggested that,

8. Planck Scale Model Mechanism for Understanding the Cosmic Red Shift in Hydrogen Atom

In a cosmological approach, starting from the Planck scale, in this section the authors proposed a simple and ad-hoc model mechanism for understanding the binding energy of electron and proton in the hydrogen atom. It is for further study and development. In hydrogen atom, in a cosmological approach, potential energy of electron be:

(28)

where is the cosmologically changing distance between proton and electron. From Bohr’s theory of Hydrogen atom, maximum number of electrons that can be accommodated in any principal quantum shell are . This proposal can be reinterpreted as follows: In Hydrogen atom, in principal quantum shell, electron can exist in different states.

With reference to standard notation of gravitational potential energy, in nuclear physics, quantitatively and qualitatively it is possible to guess that ^[17],

(29)

where, is the rest mass of proton, is the ‘rms’ radius of proton ^{[18, 19]} and is the strong interaction dominating range ^[20].

Note that, may be taken as the approximate ending range of strong interaction from the center of proton. Within the nucleus, at distances larger than 0.7 fm the force becomes attractive between spin-aligned nucleons, becoming maximal at a center-center distance of about 0.9 fm. Beyond this distance nuclear force drops essentially exponentially, until beyond about 2.0 fm separation, the force drops to negligibly small values. At short distances (less than 1.7 fm or so), the nuclear force is stronger than the  between protons; it thus overcomes the repulsion of protons inside the nucleus.

In hydrogen atom, potential energy of possible quantum states be:

(30)

where, and represents the past cosmic temperature. This expression is very simple and tightly connected with quantum nature, gravity and evolving cosmic back ground and needs further study.

Based on the Virial theorem ^[17], in a central force field, quantitatively potential energy is twice of kinetic energy or kinetic energy is half the potential energy. Following this idea,

(31)

Total energy of one electron in possible quantum states be:

(32)

Total energy of one electron out of possible quantum states can be:

(33)

Potential energy of one electron out of possible quantum states can be:

(34)

Orbiting radius of one electron out of possible quantum states can be :

(35)

Kinetic energy of one electron out of possible quantum states can be:

(36)

Orbiting velocity of one electron out of possible quantum states can be:

(37)

Angular momentum of one electron out of possible quantum states can be:

(38)

Here the key point to be noted is that,

(39)

With reference to current cosmic back ground temperature,

(40)

Here it should be noted that, throughout the cosmic evolution, Planck’s constant is a constant whereas the currently believed ‘reduced Planck’s constant’ is a cosmological decreasing variable.

Considering the jumping nature of electrons, now emitted quantum of energy for one electron can be expressed as follows.

(41)

In the current laboratory hydrogen atom,

(42)

Clearly speaking, total energy of one electron can be:

(43)

This idea is connected with quantum nature.

(44)

This idea is connected with final unification of gravity and atomic interactions.

(45)

This idea is connected with cosmic evolution.

9. Discussion

The authors request the science community to kindly look into the following points in true scientific spirit.

1. As suggested by S.W. Hawking ^[13], there is no scientific evidence to Friedmann’s second assumption 14].

2. If it is true that galaxy constitutes so many stars, each star constitutes so many hydrogen atoms and light is coming from any excited electron of any galactic star’s any hydrogen atom, then considering redshift as an index of ‘whole galaxy’ receding may not be reasonable.

3. Merely by estimating ‘galaxy distance’ and without measuring any ‘galaxy’s actual receding speed’, one cannot verify the cosmic acceleration. Note that, in 1947 Hubble himself thought for a new mechanism for understanding the observed red shift ^[12]. In his words: “We may predict with confidence that the 200 inch will tell us whether the red shifts must be accepted as evidence of a rapidly expanding universe, or attributed to some new principle in nature. Whatever may be the answer, the result may be welcomed as another major contribution to the exploration of the universe”.

4. Even though it is very attractive, Einstein could not implement the Mach’s principle ^{[15, 16]} in Hubble-Friedmann-cosmology ^{[7, 8, 9, 10]}.

5. Until 1964, cosmologists could not believe in ‘cosmic back ground temperature’ ^[3].

6. In the past, ‘quantum gravity’ was in its beginning stage and now it is in an advanced theoretical phase.

7. Based on the Hubble’s law and Super novae dimming, currently it is believed that, universe is accelerating ^{[9, 10]}. In the authors’ opinion, if magnitude of past Hubble’s constant was higher than the current magnitude then magnitude of past will be smaller than the current Hubble length . So  the rate of decrease of Hubble constant can be considered as a true index of rate of increase in Hubble length and thus with reference to Hubble length, the rate of decrease of Hubble constant can be considered as a true index of cosmic rate of expansion.

8. In future, certainly with reference to current Hubble's constant, gives the true cosmic rate of expansion. Same logic can be applied to cosmic back ground temperature also. Clearly speaking gives the true cosmic rate of expansion. To understand the ground reality, accuracy of current methods of estimating the magnitudes of must be improved.

10. Conclusion

In this brief report, the authors introduced the words, ‘cosmic critical volume’ and ‘cosmic critical mass’. Sincerely speaking, these two words seem to be connected with “Mach’s principle”. With reference to Mach’s principle, cosmic ‘critical density’, ‘critical volume’ and ‘critical mass’ can be considered as the quantified back ground dynamic properties of the evolving universe. Accommodating Mach’s principle in modern cosmology is a very challenging but ‘inevitable’ task. With reference to the proposed concepts, semi empirical relations and accurate data fitting, now it is imperative to revise the basics of modern cosmology with respect to Quantum gravity ^[21], Mach’s principle and the proposed new redshift interpretation.

Acknowledgements

The first author is indebted to professor K. V. Krishna Murthy, Chairman, Institute of Scientific Research on Vedas (I-SERVE), Hyderabad, India and Shri K. V. R. S. Murthy, former scientist IICT (CSIR) Govt. of India, Director, Research and Development, I-SERVE, for their valuable guidance and great support in developing this subject.

References

[1]	Lukasz Andrzej Glinka. Global One-Dimensionality Conjecture within Quantum General Relativity. Gravitation and Cosmology 16(1), pp. 7-15 (2010).
	In article		CrossRef
[2]	Lukasz Andrzej Glinka, Thermodynamical Quantum Gravity. Applied Mathematics and Physics, vol. 2, no. 3 (2014): 66-72.
	In article		CrossRef
[3]	R.A. Alpher, H.A. Bethe, and G. Gamow. The origin of chemical elements. Phys. rev.73,80,1948.
	In article		CrossRef
[4]	Lianxi Ma et al. Two forms of Wien’s displacement law. Lat. Am. J. Phys. Educ. Vol. 3, No. 3, Sept. 2009.
	In article
[5]	U. V. S. Seshavatharam, and S. Lakshminarayana, On the Evolving Black Holes and Black Hole Cosmology- Scale Independent Quantum Gravity Approach. Frontiers of Astronomy, Astrophysics and Cosmology, vol. 1, no. 1 (2014): 1-15.
	In article
[6]	G.J. Stoney, On the Physical Units of Nature. Phil. Mag. 11 (1881) 381-91.
	In article		CrossRef
[7]	David N. Spergel et al. Planck Data Reconsidered. https://arxiv.org/pdf/1312.3313.pdf.
	In article
[8]	J. V. Narlikar. Introduction to cosmology. Cambridge Univ Press, 2002.
	In article		PubMed
[9]	Perlmutter, S. et al. Measurements of the Cosmological Parameters Ω and Λ from the First Seven Supernovae at z ≥ 0.35. Astrophysical Journal 483 (2): 565, (1997).
	In article		CrossRef
[10]	J. A. Frieman et al. Dark energy and the accelerating universe. Ann.Rev.Astron.Astrophys.46, p385. (2008).
	In article		CrossRef
[11]	Hubble E. P, A relation between distance and radial velocity among extra-galactic nebulae, PNAS, 1929, vol. 15, 1929, pp. 168-173.
	In article
[12]	Hubble, E.P, The 200-inch telescope and some problems it may solve. PASP, 59, pp 153-167, (1947).
	In article		CrossRef
[13]	Hawking S.W. A Brief History of Time. Bantam Dell Publishing Group. 1988
	In article		PubMed
[14]	Friedman, A. Über die Möglichkeiteiner Welt mitconstanter negative Krümmung des Raumes. Zeit. Physik. 21: 326-332. (1924).
	In article		CrossRef
[15]	Sciama, D. W. The Physical Foundations of General Relativity. New York: Doubleday & Co. 1969.
	In article
[16]	Raine, D. J. Mach's Principle in general relativity. Royal Astronomical Society. Vol171, pages 507, 1975.
	In article		CrossRef
[17]	Celso L. Ladera et al. The Virial Theorem and its applications in the teaching of Modern Physics. Lat. Am. J. Phys. Educ. Vol. 4, No. 2, May 2010.
	In article
[18]	P.J. Mohr, B.N. Taylor, and D.B. Newell https://pdg.lbl.gov/2013/reviews/rpp2012-rev-phys-constants.pdf.
	In article
[19]	Michael O. Distler et al. Phys. Lett.B. 696: 343-347, (2011).
	In article		CrossRef
[20]	E.A. Nersesov, Fundamentals of atomic and nuclear physics, (1990), Mir Publishers, Moscow.
	In article		PubMed
[21]	U. V. S. Seshavatharam, and S. Lakshminarayana, Primordial Hot Evolving Black Holes and the Evolved Primordial Cold Black Hole Universe. Frontiers of Astronomy, Astrophysics and Cosmology, vol. 1, no. 1 (2015): 16-23.
	In article