Einstein’s field equation is

G μ ν + Λ g μ ν = κ T μ ν (1)

where G μ ν is Einstein Tensor

G μ ν = R μ ν − 1 2 R g μ ν (2)

R μ ν is Ricci curvature Tensor.

R is scalar curvature.

G μ ν is metric tensor.

T μ ν is stress-energy tensor.

Λ is cosmological constant.

G is gravitational constant and,

c is velocity of light.

κ is Einstein’s gravitational constant.

κ = 8 π G c 4 = 2.077 × 10 − 43   N

Physically it elaborates curvature of space time in the presence of matter.

And the right-hand side indicates stress energy momentum of that curvature of space time.

The following are the classical Equations for space time [10] after considering final revision

m = 7.9905778 × 10 − 17 × d 1 / 3 (3)

γ d 8 / 3 = 1.526087946 × 10 − 16 (4)

As per classical concept of space time, every mass will be associated with its own space time for its existence, space (more precisely space time). The distance between any two points depends on the space time associated to that mass. If that space time is less than the required, that space time cannot be flat and will have a curvature. Here space time density plays an important role. If mass density and space time density are same, the space time is flat.

Figure 1 [11] shows that if these masses are super positioned, the points 1 to 9 look like a curve.

For each flat space, the point is different depending upon distance “d” in Figure 1 it is a1 or 1j.

At this point, two forces will be acted in opposite direction and it gives velocity to any mass placed at this point. The difference between these two velocities is zero for a flat space. If it is not flat, the difference creates a curvature for distance “d” in order to keep the density with the mass which is associated to it. The curvature is proportional to stress energy tensor or momentum to move any matter on that curvature. The velocity created by the net force on that matter represents curvature. The curvature is proportional to stress energy tensor and the proportionality constant is Einstein’s gravitational constant κ.

Mathematically,

V E − V C = κ (5)

H d − K d = κ (6)

H d 2 − κ d − K = 0 (7)

d = κ ± κ 2 + 4 H K 2 H (8)

We have

Einstein’s gravity constant κ = 8 π G c 4 = 2.077 × 10 − 43   N .

[10] Hubble’s constant H = 4.1394908592 × 10 − 19 sec − 1 .

[10] constant K = 4.84533 × 10 − 27   m 2 ⋅ s − 2 .

Substitute these values in (8)

d = κ ± κ 2 + 4 H K 2 H

Since κ value is negligible comparing with the term 4HK

d = ± 4 H K 4 H 2

d = ± K H (9)

c d 2 = G t p m (10)

d = plancklength = l p

m = planckmass = m p

c 2 l p = G m p ( ∵ l p t p = c )

c 2 l p = G m p

∴ l p = G m p c 2

c 2 t p = K ( ∵ K = G t p ( m l p ) ) (11)

We know l p = K c .

And t p = K c 2 .

m p = K c G [ ∵ K = G t p ( m l p ) ]

As per Planck scale,

m p = ℏ c G

∴ ℏ c G = K c G

∴ K = ℏ G c (12)

The constant “K” derived in (12) must be associated to Planck hole in quantum mechanics.

So, if we consider the synchronization of general relativity and quantum mechanics, K value which is in terms of Planck parameters in (12) can be substituted in (9). Constants “K” and “H” in (9) are associated to outer space time only.

As shown in Figure 2, this diameter of outer space time contracted to another space time. The outer space time diameter “d” is different and inner space time diameter “d” is different. But from the basic principle, quantum mechanics and general relativity must be same. Outer space time represents general relativity and inner represents quantum mechanics. Both must be same. So, parameters will be changed to synchronize both the space times.

Say outer space time is attributed to general relativity for which parameter denoted by suffix “g” and for space time of quantum mechanics denoted by suffix “q”.

The parameters are:

K_g, H_g, d_g, G_g, ħ_g and c_g, inside space time are K_q, H_q, d_o, G_q, ħ_q and c_q.

(9) can be written as

∴ d g = K g H g (13)

And (12) can be written as

K q = ℏ q G q c q (14)

Now substitute K_g of (13) in (14) to make d g = d q ,

∴ d g = ℏ q G q c q H g 2 (15)

If we apply it to hydrogen atom, the lowest state electron, is related to fine structure constant which is

d_g = diameter of Hydrogen atom [12] = 1.0583544213 × 10⁻¹⁰ mt.

H_g is theoretical value of Hubble’s constant [10] 4.1394908592 × 10⁻¹⁹ sec⁻¹.

Its K_q is the space time constant for graviton and follows Equation (9)

∴ d g = K q H g (16)

Here, both diameter of hydrogen atom d_g and the theoretical value of Hubble’s constant H_g are with respect to our four-dimensional space time in which curvature is gravity and space time forms a quantum particle with space time diameter of graviton.

Instead of graviton, if we take any other fundamental force particle which is interpreted in terms of space time diameter, the gravitational constant “G” will be changed and other parameters like velocity of light “c” and reduced Planck constant ħ will be unchanged. It implies that the space time curvature will be changed. Graviton interprets the force of gravity as space time curvature.

In [10] diameter of hydrogen atom considered because, it is related to fine structure constant and is used in calculating space time diameters of fundamental forces as shown in Table 1. It is a modified Table from [13] .

Space time diameter for photon [13] is 6.783124 × 10⁻²⁰ mt.

Space time diameter for graviton [13] is 1.5466374059 × 10⁻⁴⁷ mt.

Planck diameter [12] is in between these two. 1.616229 × 10⁻³⁵ mt.

Planck diameter is also a space time diameter as per definition. So, there must exist a fundamental force. Its force carrying particle is interpreted by space time diameter equal to Planck length i.e., 1.616229 × 10⁻³⁵ mt.

We have an equation relating coupling constant and space time diameter [13]

d x 4 = 2.116991 × 10 − 77 × α x 3 (17)

where d_x is space time diameter of any fundamental force and α x is coupling constant of that force.

For d = plancklength   l p = 1.616229 × 10 − 35   mt the coupling constant is

α = 1.4771712831 × 10 − 21 (18)

We can rewrite it as

α p = 1.4771712831 × 10 − 21 (19)

Since the calculation in the equation is with respect to photon.

With respect to standard model (Ref: Table 1)

α s = 1.0782272139 × 10 − 23 (20)

Since it is a fundamental force particle, it must be a flat space time with space time diameter equal to Planck length i.e. d = l p = 1.616229 × 10 − 35   mt .

We have Equation (3)

m = 7.9905778 × 10 − 17 × d 1 / 3

∴ m = 2.0202842713 × 10 − 28   kg

∴ m = 1.1332939758 × 10 2   MeV / c 2

∴ m = 113   MeV / c 2

( ∵ 1   eV = 1.6021766208 × 10 − 19 and c = 2.99792458 × 10 8 ) [12]

Thus, there may exist a new fundamental force and its force carrying particle. Since it is a fundamental force particle, it must be a Planck hole in that space time. Therefore, it is a black hole in that space time with zero rest mass with respect to our space time. It is a primordial black hole with space time diameter. Since its space time diameter is less than photon’s space time diameter, it cannot interact with photon. But, if we review the process of expansion [10] , the density of matter in the universe is continuous and the expansion will be compensated by creation of matter and the density of matter is constant and the universe in steady state. Since space time diameter of photon is more than dark matter, prior to interaction with photon, dark matter particles will interact as the time flows. Finally, it comes out as a photon and the continuous creation of these photons and dark matter create matter and energy continuously and compensate the expansion. Thus, dark energy is a phenomenal effect of expansion [10] and matter creation is quantum effect of space time to form dark matter. Finally, we can say the continuous creation of matter is an effect of synchronization of general relativity with quantum mechanics.

Dark matter concept is still a matter of discussion for lot of theoretical and observational astrophysicists and general relativists. MOND theories [14] and concerned experiments [15] suggested to modify Newtonian mechanics and equations for calculation of abnormal gravity regions. But my paper straight away denies that direction of thought since the paper proposed that the dark matter is a fundamental force carrying particle. Every such fundamental force is associated to a separate space time than our four-dimensional space time. Thus, every space time contains a separate signal with maximum velocity. In that space time, it contains a space time diameter and will be considered as zero space for transformations similar to photon in our space time. Thus, for fundamental force of dark matter, the space time diameter is Planck diameter. With respect to our space time, it is a black hole. It can be said as primordial black hole [16] but confined to Planck size only since they are part of continuous creation of matter and exist at any stage of universe [10] . My theory directly considers it as a quantum particle. I have explained that how fundamental force particles linked with space time diameter in previous papers [13] . If it is a black hole, even general relativity or modified Newtonian mechanics are also not enough to explain the singularity point. Thus, my approach is completely different and emphasizes that dark matter is a fundamental force carrying particle.

Few physicists considered the dark matter as a fundamental particle like a gauge boson [17] . Their results show that the mass of dark matter as a gauge boson is ≅17 MeV/c². In this paper, the mass is calculated as 113 MeV/c². Some more research in this direction may advance the science of dark matter for a fruitful experimental verification. The paper [18] also explained various attempts for detection of dark matter particle.