In the observable universe, number of particles are estimated to be 10^80 and if there were some discrepancy in Physics with the explanations of the observable universe or with its each particle then it should confine to factor 10^80. I submit that 10^80 is a huge figure that forms if one puts eighty zeros after 1. But if the discrepancy is of the factor 10^120 then either it is beyond the total number of particles constituting the universe or the physicists might have gravely erred in their calculations. It might be a freak happening that resulted in such a huge quantity. After all, freaks are also the creations of nature or probably the nature itself has erred here.This discrepancy of 10^120 is the largest and worst cosmological confusion which can be abbreviated CC and rightly so for cosmological constant as it is the cosmological constant based on Quantum mechanical model. Quantum mechanical model says, energy density of the vacuum is in the the range of 10^113 Joules per metre cube whereas General Relativity calculates it in the range of 10^-9 Joule per metre cube. An attempt is made to resolve this discrepancy using Spacetime transformation and gravitational gamma Г. Gravitational gamma Г is a term that appears in Schwarzschild solution of general relativity equations.
I submit that vacuum is not nothing but is everything and quantum mechanical model of the vacuum has very large energy density. In the words of John Archibald Wheeler, “Empty space is not empty… The density of field fluctuation energy in the vacuum argues that elementary particles represent percentage‐ wise almost completely negligible change in the locally violent conditions that characterise the vacuum.” That means there are violent conditions or fluctuations although vacuum on large scale appears smooth. Spacetime model has the capability of creating matter, forces, fields and particles. In fact, matter even the entire universe is assumed as spacetime as has been explained in my earlier article, “Matter Is No More Than Fluctuations In Vacuum*.”
I submit that the energy density of the vacuum, due to uncertainty principle, varies from point to point causing fluctuations. In other words, energy density at different points goes on varying even though there is no mass causing gravity. But even then at two points, due to fluctuations of energy density, rate of time may vary, causing difference in time by Planck time. These fluctuations can only be felt at a distance limited to Planck length or at microscopic scale but on macroscopic scale the space time, according to Quantum Mechanical model, appears smooth with no disturbances. 
( Above figure shows simplified representation of chaotic dipole waves in Spacetime that form vacuum energy at age of the universe corresponding to Гu1.) These fluctuations at Planck length are assigned the term Quantum Foam and are also explained as creations of virtual particles or photons and their antiparticles which annihilate. Force of attraction between two conducting plates kept at a geometrically small distance, corroborates the factum of quantum fluctuations. 
(Above figure shows simplified representation of chaotic dipole waves in Spacetime that form vacuum energy at age of the universe corresponding to Гu2 where Гu2 = 3.Гu1). This is force of attraction commonly called Casimir Effect has also been practically observed when such conditions get simulated between two sailing ships. Variation in energy level of hydrogen atom called Lamb shift also evidences presence of vacuum fluctuations. These fluctuations also cause variation in coulomb laws between two charged particles. All these phenomena conclusively prove existence of vacuum fluctuations and their effects.
These fluctuations can be visualised as being generated by harmonic oscillator of angular frequency w. Since minimum cavity length for this oscillator is half wavelength for reflection of the wave, energy associated with such oscillator is calculated by equation E = ½. h bar. w , commonly known as zero point energy where h bar is Planck constant divided by 2. pi or h/2π. This equation can also be written as E = ½. h bar.c/λ bar where λ bar is wavelength divided by 2π as c velocity of light is equal to product of λ bar and angular frequency. For this harmonic oscillator, volume where in, this energy is associated is a cube of length λ bar or its volume is λ bar^3 where sign ^ denotes raised to the power. Energy density or energy per unit volume is given by equation
E = (½. h bar.c/λ bar)/ λ bar^3 = ½. h bar.c/ λ bar^4 = ½.h bar.w^4/c^3 ———–(1)
The above equation is obtained on substituting λ bar by c/w.
This angular frequency w may vary have all frequencies from 0 to infinity and in such case energy density would be infinite but w at the most can have maximum achievable angular frequency that corresponds to Planck time tp. Maximum achievable angular velocity is, therefore, Planck angular frequency wp corresponding to time period of Planck time tp. According to Milonni, in such a case of harmonic oscillator, energy density would correspond to Planck angular velocity divided by Planck volume. Planck angular frequency, wp = 1/tp = [c^5/(h bar.G)]^1/2 = 1.85 x 10^43 rev per second. Substituting this value in equation (1), we get Planck energy density of vacuum Up = 4 x 10^113 Joules/metre cube. This is shockingly highest energy density.
Here why Planck frequency and Planck length have been chosen for the purpose of calculation of energy density, is explained here under. It is noteworthy that minimum length and maximum angular velocity have been considered equal to Planck length and Planck angular frequency as it is the Planck distance which is minimum measurable and achievable. A length can not be measured if it is smaller than Planck length. A fraction of Planck length is not achievable, Planck distance can not be subdivided. It is the limiting minimum distance. If instead of Planck distance, zero distance is taken then energy density would scale to infinity, a quantity that can neither be achieved nor defined. In the same way, minimum time that can be measured or achieved is Planck time and this time can not be further subdivided. Angular frequency which is inverse of Planck time, is therefore, highest achievable. We can not take angular frequency as infinity as that will lead to indeterminate infinite energy of harmonic oscillator. Constant like Planck time, Planck length, Planck mass or extreme universal quantities which can be achieved.
So far, quantum vacuum at micro scale in relation to Spacetime was discussed. However, General Relativity lays down that energy warps the spacetime curvature which gives rise to gravity. Spacetime is smooth on macroscopic scale and there are no fluctuations as are observed in quantum mechanical model at Planck length with Planck frequency. The distance between the particles is limited to the extent of formation of blackhole meaning thereby that such distance is the limiting minimum distance so as to avoid formation of blackhole.This limiting distance is also in conformity with Quantum mechanical model. According to General Relativity, the universe would collapse to a blackhole if its energy density exceeds the critical value of energy density. The observed energy density of the universe 10^-9 Joules/metre cube is with in margin of error of 1% of equalling critical density.
If on comparing the energy density of 4 x 10^113 Joules/metre cube as derived from Quantum Mechanical model with that 10^-9 Joules/metre cube calculated on the basis of General Relativity, the energy density given by Quantum mechanical model is observed ridiculously large. It is larger by the factor as large as 10^122, in physics it is generally termed discrepancy factor of 10^120.
Assuming energy density on the basis of Quantum mechanical model as correct, then in this expanding universe, we need 4x 10^113 Joules of energy for one cubic metre expansion. Requirement of 4x 10^113 J of energy even for single cubic metre expansion is a huge quantity beyond imagination. To keep this energy density 4x 10^113 Joules/metre cube constant, we need a regular source to generate this much huge energy. If the existing mass were to be converted in to energy to make up the requirement caused by expanding universe, entire observable mass in the universe may fall short of as such huge energy would be required. It needs some other explanation to justify the constancy of this energy density.
To reconcile mammoth energy 4x 10^113 J/metre cube with minuscule figure of 10^-9 J/metre cube, support of Spacetime Transformation Model is needed. Einstein Field equations in General Relativity were solved by Schwarzschild wherein the term gravitational gamma Г appears. Gravitational gamma Г is defined as the rate of time in coordinate clock to the local rate of time in gravity and is given by equation
Г ≡ dt/dτ = 1/[1-2Gm/(c^2.R)]^1/2—————(2)
where G is universal gravitational constant, m mass of particle, R circumferential radius. Stationary clock infinitely far away from the mass in Schwarzschild’s universe is designated the “coordinate clock” with a rate of time designated dt or one can say that it is rate of time in hypothetical universe where there is zero gravity. In the same stationary frame of reference, the local rate of time in gravity near the mass is designated dτ.
In equation (2), the term 2Gm/(c^2.R) is always between 0 and 1 otherwise denominator of this equation will become imaginary quantity and that is not a possibility. If 2Gm/(c^2.R) is small then gravitational field is weak and we can expand it by Binomial Theorem as
Г ≡ dt/dτ = [1-2Gm/(c^2.R)^-1/2]= 1 + ½.2Gm/(c^2.R)+ —-
= 1+Gm/(c^2.R) + neglecting other terms being small
= 1 + β
A particle if thrown with a velocity equal to (2Gm/R)^1/2 from a gravitating mass m, it leaves the mass for ever with this escape denoted as Ve. Substituting this value in equation (2), we get Г equal to 1/[1 – (Ve/c)^2]^1/2————————(3).
In special relativity also, the term γ equals 1/[1 – (V/c)^2]^1/2. Only difference is that velocity in SR is replaced by escape velocity in General Relativity GR in equation of gravitational gamma.
It is submitted that at the time of Big Bang, there was no gravity and the term 2Gm/(c^2.R) was 0. Therefore at that time, gravitational gamma Г was 1. The maximum value Г at other extreme would be at the event horizon of blackhole as ∞ and the particle would be pulled in the blackhole with escape velocity when 2Gm/(c^2.R) equals 1. Value of Г at earth surface is 1 + 7x 10^-10 . Г, therefore, always has a value more than 1 where ever there is gravity.
Our location in the universe is similar to cavity surrounded by mass. In fact, the situation of the universe is like that which is surrounded by shell that is increasing its mass every second. If we consider a cavity at the centre of the universe, escape velocity from the cavity would be 22 pc more than that from surface of the earth. This increase in escape velocity in turn will increase the value of gravitational gamma as is evident from equation (3). That means at a point, there will be increased gravitational gamma if it is surrounded by mass. Our universe as submitted above is considered surrounding by shell with increasing mass which results in increasing gravitational gamma as the universe ages. It is submitted that this background gravitational gamma Гu is attributed to the matter outside and causes the rate of time, the gravitational potential, the escape velocity etc. However the internal matter affects acceleration due to gravity. Increase in value of gravitational gamma is causing the cosmological expansion. Present value of gravitational gamma can be calculated from various method but its value here is calculated from cosmic microwave background temperature. Assuming the model where the universe started from Planck sphere at Planck temperature ( ½ Ep/k ) 7.08 x 10^31 degree K and its present temperature 2.725 degree K, Г can be calculated as Tps/Tcmb = 7.08 x 10^31/2.725 = 2.6 x 10^31.
Reconciliation
We have already defined gravitational gamma as rate of time in in clock at hypothetical universe with zero gravity to rate of time in the universe with gravity or Г = dt/dτ or dt = Г.dτ. Now, a case is considered where an impulse of one second is emitted in hypothetical universe with zero gravity and simultaneously in the universe with gravity. Here dt is 1. Since the universe has gravity, Г will have some value more than 1. Therefore 1 = Г dτ and that indicates dτ should be less than 1 as Г is more than one. That means, rate of time is short or less in gravity or time is being dilated in gravity. From this, T0= Tg/Г where To is time in zero gravity and Tg is time in gravity. From conservation of momentum, we can calculate Mo = Mg/Г. The suffix 0 denotes parameters in hypothetical universe with zero gravity and suffix g denotes parameter in the universe with gravity.
Applying these transformation to the present universe which has gravitational gamma Гu (as 2.6×10^31 as calculated above), following equations hold good. T1 = Tu/ Гu, M1 = Mu/Гu, where suffix 1 denotes parameters in Planck Spacetime and u to parameters in the present universe. Similarly unit of length are also transformed by equation, L1 = Гu.Lu. From these transformations of time, mass, length, transformations of energy, energy density can be calculated as given below.
Energy transformation Energy at Planck Spacetime E1 in mass, length and time dimensions is M1.L1^2/T1^2. On substituting the value of M1, L1, T1 and simplifying, energy at Planck Spacetime E1 = Гu^3. Mu.Lu^2/Tu^2 = Гu^3.Eu. That is E1 = Гu^3.Eu.—————————–(4)
Volume transformation Volume V1 at Planck space time = L1xL1xL1. On substituting value of L1 as Гu.Lu, V1 = L1^3 = Гu^3.Lu^3.————————–(5)
Energy density transformation Energy density at Planck Spacetime Up = E1/V1 = (Гu^3.Eu)/ Гu^3.Lu^3 = Eu/Vu = Uu or Up = Uu.———————————————-(6). That is energy density at Planck Spacetime is same as energy density in the present universe and since there is no gravitational gamma in the equation, there is no effect of cosmological expansion on energy density of the universe and it remains constant. Invariance of energy density is explained as that with cosmological expansion, gravitational gamma increases and one joule of energy at Planck Spacetime gets transformed to Гu^3 times one joule in present universe. In the present universe Гu^3 is equal to 1.8 x 10^94. Гu and resultant Гu^3 are always more than 1 when there is cosmological expansion and that reduces the value of one joule in the present universe by 1/ Гu^3 although it is still called joule as it was called at Planck Spacetime. In fact, with cosmological expansion, unit of energy joule is shrunk but its numerical multiplier increases accordingly. In this way, one joule at Planck Spacetime is equal to Гu^3 or 1.8 x 10^94 joules in the present universe.
To illustrate it further, I give an example of a tourist who starts his journey from India with 10000 rupees in his pocket and goes to Pakistan where travel agents exchanges his money with Pakistani rupees and gives him equivalent 15000 Pakistani rupees. Now the tourist has 15000 rupees in stead of 10000 rupees. Here the unit of currency rupee has shrunk but numerical figure of rupees has increased. He then proceeds to Kathmandu, Nepal and the agent again exchanges the currency with Nepalese rupees and gives him equivalent 16000 rupees. Here again the unit of currency rupee has shrunk further but numerical figure of rupees has increased. In all these three countries, currency is rupee and tourist in a way can be said to have gained numerical figure of rupees from 10000 to 15000 to 16000 but rupee unit of currency has shrunk. In the same way as wheel of time rotates, cosmological expansion shows its effect by increasing numerical figure of unit of energy joule. Unit of rupees shrinks and numerical figure of rupees increases. Similarly with cosmological expansion, unit of length shrinks, numerical figure increases, unit of time expands, its numerical figure decreases, unit of mass expands, its figure decreases. Then how can we make distinction between units at different cosmological age of universe? Only distinction which we can make is by relating joule to that time or Гu when it is being measured. When we calculate energy density, enlarged multiplier of energy in numerator cancels the equally enlarged multiplier of length cube in denominator resulting in same energy density irrespective of time or Гu at which it is being measured.
Energy density calculated on the basis of Quantum mechanical model as 4x 10^113 Joules/metre cube remains same as the universe expands by Hubble’s law. Extra energy required for expanding space is countered by extra volume generated as elaborated in the preceding paragraph and as such creation of mammoth energy is not required for maintaining the energy density.
Next moot question is reconciliation of energy density of 4x 10^113 Joules/metre cube calculated on Quantum mechanical model with 10^-9 Joules/metre cube calculated on the basis of General Relativity or discrepancy of factor 10^120. It is submitted that at Planck time, when universe was a sphere of Planck length, its entire energy had the quantised angular momentum ie consisting of fermions of angular momentum of odd number divided by two. and Boson of angular momentum of whole number. But now almost all the vacuum energy does not have quantised angular momentum. The spacetime transformation model of the universe proposes that over the age of the universe there has been no change in the total energy density of the universe. Energy density at Planck Spacetime is equal to energy density of observable universe plus energy density of vacuum or Up = Uobs + Uvac**. Over time the transformation of spacetime has resulted in a dramatic decrease in the observable energy density of the universe and an equal increase in vacuum energy density of the universe. Now Uvac is approximately equal to 10^122.Uobs***. This vacuum energy, in fact, acts as a homogeneous superfluid which does not interact but prevents the universe from gravitational collapse. This vacuum energy can be envisaged as background shade and being devoid of angular momentum does not interact to form observable universe. Before paring with article, I sum up by submitting that although there is discrepancy factor of 10^122, this does not require generation of additional energy as according to Spacetime transformation model, the numerical value of energy increases by cube of gravitational gamma and that is offset by increase in numerical value of volume by same factor of cube of gravitational gamma and that keeps energy density constant. In Quantum mechanical model, the universe is considered created from Planck time and Planck sphere, entire energy at Planck time possessed quantised angular momentum but with passage of time, vacuum energy with no angular momentum formed. Energy with quantised angular momentum evolved observable universe, gravitational gamma increased with time and cosmological expansion occurred and that caused contraction of unit of length, expansion in unit of time and mass. At present energy density of vacuum is approximately equal to 10^122 times energy density of observable universe. Energy density on the basis of GR is energy density of observable universe with quantised momentum whereas energy density of vacuum on the basis of Quantum mechanical is vacuum energy density which has the properties of superfluid that is non quantised and does not interact but contributes to background gravitational gamma. Thus comparing energy density on the basis of Quantum mechanical model with energy density on the basis of GR is analogous to comparing apple with orange. Reference: The Universe Is Only Spacetime ©2012 john@onlyspacetime.com Image Credit: The Universe Is Only Spacetime ©2012 john@onlyspacetime.com. End. Notes: 1. *Kindly read “Matter Is No More Than Fluctuations In Vacuum,” at https://niume.com/post/147680. 2. Sign ^ means raised to the power. For example λ bar^3 is equal to λ bar x λ bar x λ bar or λ bar cube. 3. ** Uvac means vacuum energy density. 4. *** Uobs means energy density of observable universe.
Writer: He is an Electronics and Electrical Communication Engineering graduate and was earlier Scientist, then Instrument Maintenance Engineer, then Civil Servant in Indian Administrative Service (IAS). After retirement, he writes on subjects, Astronomy, Mathematics, Yoga, Humanity etc.
Narinder 