




































    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

1 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

DARK MATTER AND DARK ENERGY CAN BE HELD IN THE 3-COSMIC 

FRAMEWORK THROUGH ORIGINAL STRING THEORY 

 

Hsien-Jung Ho 

New idea Research Center 

Email: newidea.ho@gmail.com 

DOI: https://doi.org/10.5281/zenodo.13982179 

 

 
Abstract: Scientific development has reached a very high level today, but in the natural sciences, research still 

encounter bottlenecks. The problems posing the greatest headache for scientists lay with dark matter and dark 

energy. Dark matter of the Universe is a hypothetical form of matter, which puzzles scientists more than 80 years 

and no solution yet. Most experts think dark matter is abundant in the Universe and has had a strong influence on 

its structure and evolution. In the observable Universe, there is no indication that the Universe is expanding at an 

accelerating rate, and cosmologists have hypothesized the existence of some unknown "dark energy" to explain 

this phenomenon. 

In 2018, Plank Satellite detects tiny temperature fluctuations in the radiation of the Universe. These distributions 

of fluctuation reflect the baryon density of the Universe before galaxies have yet to form. Normal matter from 

galaxies and stars accounts for only 4.94 % of the Universe's composition, with the rest missing substance, 

including dark matter, which accounts for 26.64 %, and mysterious dark energy, which accounts for 68.42%, so, 

the invisible composition of Universe is 95.06 %. Scientists believe that dark energy is the force that tears the 

Universe apart, but dark matter condenses all things, and that the interaction of these two forces forms the structure 

of the Universe, as we know it today. 

As long as we can understand the assembling speed of the galaxy, we can understand dark matter, also understand 

the power of dark energy tearing the Universe at the same time. Therefore, dark matter may be the best tool to 

study dark energy in the end. To understand dark matter now, we will probably get an answer from the most 

famous “String Theory”. 

Keywords: Dark matter, Dark Energy, Density, Universe  

 

Introduction: The original String Theory is based on nine-dimensional space and one-dimensional time, i.e., a 

ten-dimensional space-time, which is considered to universally exist. According to “Causality”, an effect cannot 

occur before its cause, which means time has one direction and cannot be divided into some different parts. So 

one-dimensional time is taken as a common standard in order of events in the Universe. Following the “Anthropic 

mailto:topacademicjournals@gmail.com


    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

2 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

Principle”, which is the simple fact that we live in a Universe set up to allow our existence, three-dimensional 

space and one-dimensional time are taken as one cosmos as our living world. Therefore, the nine-dimensional 

space can be divided into three portions, and each portion has a common time standard, which means that there 

is a 3-cosmic framework in the Universe, called the triple cosmoses, i.e., multiverse. 

In the triple cosmoses, according to String Theory among any cosmoses, there are no basic interactive forces of 

nature except gravity, i.e., the graviton in the field of gravity can penetrate all the cosmoses; however, the 

electromagnetic wave (light) cannot. So dark matter may be situated in the cosmoses other than ours; in other 

words, the triple cosmoses can contain dark matter. The best method of exploring dark matter is to start from the 

Earth where we live. 

In the current Earth model utilized in seismological investigations, such as body-wave travel times, surface-wave 

dispersion, and free oscillation periods for researching the chemical composition and the density distribution of 

the Earth, one can analyze some data of the Earth. We use the Preliminary Reference Earth Model (PREM) as the 

standard Earth model. According to the characteristics of Earth's interior, equitably examining its constitution, 

composition, density, and pressure from a different view of the core, the special arguments are put forward. 

There are some arguments in the topic of the CMB as in the following: 1. In 1948, Ramsey and in 1973, Lyttleton 

have challenged the concept of an iron core that the CMB is the boundary of Ramsey's phase-change not silicates 

and iron core interface. 2. In 1965, Knopoff showed that bulk modulus keeps constant that density distribution 

should be continuous at the CMB. 3. In 1968, Buchbinder studied the variation in reflection amplitudes of seismic 

wave and found that show a phase-change at the CMB. 4. In 1987, Morelli and Dziewonski found the topography 

of CMB more than 10 km that shows the relief is dynamically supported and provides coupling between the solid 

mantle and the fluid core. 

It is inferred that solid rock and molten rock, or the magma change states interactively and the density distribution 

is continuous at the CMB, therefore, we figure out a new Earth model as figure 1. 

mailto:topacademicjournals@gmail.com


    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

3 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

 
Figure 1. Seismic velocity and density in the Earth’s interior of PREM and the new earth model. 

 

1. In 1995, Hecht discovered under the frozen wastes of Siberia that platinum has come all the way from the core 

to ground shows a single convection cell. 2. In 2018, Perrin discovered the intact remains of a natural nuclear 

fission reactor in a uranium mine at Oklo of Gabon and demonstrated from the radioactive elements can generate 

nuclear energy in the core. 3. In 2023, Horton et al. argue that the extremely high-3He/4He helium measured in 

terrestrial igneous rocks, in olivine’s from Baffin Island lavas, whose primordial helium may be leaking from 

Earth's core. 4. In August 2002, Oak Ridge Lab of United States report a new achievement in scientific research 

that 6371 km below the surface of the Earth's center has a diameter of 8 km, consisting of uranium and plutonium 

fast breed natural fission reactors, which can generate the fission heat. 

From above statements we can figure out in the interior of Earth a great convection cell that the flow of the magma 

and the solid or molten rock migrating up to the crust and down across the CMB to the lowermost F-layer of the 

outer core as figure 2. In the low viscosity F-layer of the outer core, the high temperature causes some elements 

and oxides of magma to undergo oxidation-reduction reactions and separate due to its gravity. The great amount 

of heat is produced from chemical reactions in the F-layer and radioactive element generated nuclear energy in 

the Earth’s interior which serves as the main power source for the geo-dynamo of the great convection cell [1]. 

mailto:topacademicjournals@gmail.com


    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

4 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

 

Figure 2. A schematic diagram of a great convection cell and heat flow, and the composition of Earth’s interior. 

Based on the new conception and applying a simplified method calculates the data of the Earth that the density 

distribution follows the divisions of PREM divided into 94 levels, including 82 thin shells. The thickness of each 

shell is not greater than 100 km and so small compared with the Earth's radius of 6371 km that the density is 

regarded as linear variation within it. Then, a simplified method is applied to calculate the information of the 

Earth in order to simplify the calculating work. The formula for the mass M of a uniform sphere can be derived 

through M = (4/3) πρR3. The mass ∆M of each shell in the Earth's interior can be calculated through 

∆M＝ (4/3)πρtRt
3－(4/3)πρbRb

3 (1) 

Where: ρt, ρb are the densities at the top and the bottom, respectively, of one shell, and Rt, Rb are the radii of the 

top and the bottom in a shell. Because the difference between Rt and Rb is so small and the density is regarded as 

linear variation in the shell, the mean value  of both ρt and ρb is substituted for ρt and ρb in order to simplify 

the calculation. Then equation (1) becomes 

∆M＝ (4/3)π (R t
3－R b

3) (2) 

The moment of inertia ∆Ｉ of each shell in the Earth's interior can be calculated through 

mailto:topacademicjournals@gmail.com


    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

5 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

∆Ｉ＝ (8/15)π (Rt
５－Rb

5) (3) 

From fluid mechanics, in a region of uniform composition, which is in a state of hydrostatic stress, the gradient 

of hydrostatic pressure is expressed by 

dP/dR＝－ ɡρ (4) 

Where: P, R are the pressure and the radius, respectively, at the region; ρ is the density at that depth; ɡ is the 

acceleration due to gravity at the same depth. If the effect of the Earth's rotation is negligible, the potential 

theory shows that ɡ is resulted only from the attraction of the mass M within the sphere of radius R through 

ɡ＝GM／R2 (5) 

Where: G is the gravitational constant (6.6726×10-11m3/kg.s2). Equation (5) substitutes into equation (4) and 

integrate it. In order to simplify the calculation, ρ and M are substituted by  and , which are considered the 

constants in the thin shell and irrelative to the P and R. The result becomes 

∆P＝(1/Rb－1/Rt)G  (6) 

Where: ∆P is the difference in pressure between the top and the bottom in a layer of the Earth, and  is the 

mass of a sphere as the mean value of the masses of the sphere within the top radius Rt and the bottom radius Rb, 

respectively, of a shell. Equation (6) cannot be applied to the center of the Earth where is a discontinuous point. 

To integrate the portion of the center, the other form is applied as  

∆Pc＝(2/3)πG 2Rc2                                                            (7)  

Where: ∆ Pc is the difference in pressure between the radius Rc and the center of the Earth at the center portion. 

The acceleration due to gravity ɡ of each layer can be derived from equation (5). According to the observation 

data, the moment of inertia about the polar axis of the earth is 0.3309MeRe2 and about an equatorial axis is 

0.3298MeRe2. The earth is regarded as a sphere, of which the moment of inertia is determined to be 80286.4×1040 

g.cm2 by taking the mean value of both figures, where Me is the earth's mass of 5974.2×1024 g and Re is the 

equatorial radius of 6378.14 km. 

To examine the accuracy of applied equations, we apply the density distribution of the PREM to calculate the 

Earth's mass, moment of inertia, pressure and acceleration due to gravity. The calculated values of the earth's data 

using simplified method from the density distribution of the PREM as compared with the values of the current 

data in Table 1 (http://newidea.org.tw/pdf/S60.pdf). The calculated data of the PREM are listed in compared with 

that of the current data and the PREM are listed and Table 2. 

Table 2. The calculated values of simple method from the density distribution of the Earth as compared with the 

data and the PREM and the current Earth. 

mailto:topacademicjournals@gmail.com
http://newidea.org.tw/pdf/S60.pdf


    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

6 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

Data of the Earth Mass Moment of 

inertia 

Pressure at 

CMB 

Pressure 

at Earth 

center 

Gravity at 

CMB 

Gravity 

at Earth 

surface 

Unit 1024 g 1040g.cm2 K bar K bar cm/sec2 cm/sec2 

PREM & Current 5974.200 80286.400 1357.509 3638.524 1068.230 981.560 

Calculated values 5973.289 80205.664 1358.335 3655.973 1068.680 981.959 

Difference  % -0.0152 -0.1006 +0.0608 +0.4796 +0.0421 +0.0406 

 

From Table 2 the deviations of the calculated Earth's values from the data of the PREM and the current Earth are 

nearly within 0.1％, except the pressure at the Earth center. It indicates that the calculated values are very close 

to the current data and the simplified method is acceptable and useful; however, the calculated pressure of 

3655.973 kbar at the Earth's center is higher than the data of the PREM of 3638.524 kbar by 0.4796 %, about 8 

times of deviation at the CMB. We compare all the calculated pressures of the simplified method with that of the 

PREM by the curve of deviation E in the pressure P of the PREM in Figure 3. 

 

Figure 3: The pressure P of the PREM and the deviation E of the calculated pressure of simplified method from 

the value of P. 

The deviations E of Pressure curve from the crust to the CMB is showed nearly as a straight line, indicating that 

the calculated pressures have the systematic errors in view of the error theory. But from the CMB to the Earth's 

center, the slope of curve E sharply increases above the dashed line, which is the straight line extended from the 

mailto:topacademicjournals@gmail.com


    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

7 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

CMB. It indicates that there is a considerable discrepancy within the core. We may suppose that the structure of 

the core in the PREM, which greatly affects its core pressure, is something wrong. 

The insufficiencies of the Earth's mass and moment of inertia, called the missing mass and moment of inertia, 

both are relative to the gravity that belong to the dark matter in astrophysics. It can only be obtained by comparing 

the observed data of the Earth but cannot be detected directly and answered clearly through the ordinary Earth 

sciences. In order to solve the problems of the insufficiencies, a new study of the Earth is attempted by 

utilizing the contemporary physics. If we can successfully explain that the insufficiencies exist in a suitable 

condition, a new Earth model will be established. 

Proceeding with the assumption, the missing mass and moment of inertia of the Earth are taken as the cold dark 

matter, which may constitute a normal planet. In order to find some solution in this article, the dark matter is 

compared to Mars. The average radius of Mars is 3397 km, and the mass 642.40×1024 g. In 1989, Kaula et al 

studied the moment of inertia of Mars and got the maximum allowable mean value is 0.3650 MR², i.e., 

2689.8×1040 g.cm2. The insufficient data of new Earth models roughly approach to the Mars’, so the dark matter 

is considered as a planet, called a dark planet, of which the form is similar to Mars and its characteristics are based 

on the inner planets of the solar system. In order to cut a figure of the dark planet, it is considered as a sphere, 

whose radius and density can be calculated from the insufficiencies of the Earth’s mass and moment of inertia 

through the simplified method. The data of the dark planet can be calculated as following. 

Considering the density of rock on the surface of the Earth and the Moon, the surface density 2.70 g/cm3of the 

dark planet is proposed. Under the condition that the density of a layer is proportional to its depth, a trial value 

of density at the center of the dark planet is selected and applying the equations (2) and (3) to calculate the mass 

and the moment of inertia of each shell, the total mass and moment of inertia of it should be gotten. Because the 

radius and the center density of the dark planet are the hypothetical values, but the total mass and moment of 

inertia are necessary to correspond to the insufficiencies of the Earth's; therefore, it is necessary to use a trial- 

and-error approach to determine the proper radius and the center density. Since the Earth's orbit around the Sun 

may be affected by the gravity of the dark planet, but no abnormal effect on the Earth has been observed. An 

assumption is suggested that the gravity centers of the Earth and the dark planet coincide with each other at the 

same point. It is inferred from the phenomenon in which the same side of the Moon always faces the Earth that 

means the Earth and the dark planet may rotate synchronously. 

Assuming that the gravity centers of the Earth and the dark planet coincide at a single point, and both rotate 

synchronously, the total values of mass and moment of inertia may be obtained from the sum of them. Based on 

mechanics, the gravity at each shell inside the Earth is affected by the mass of the Earth and the dark planet within 

its radius. The pressure difference ∆  between the top and the bottom of a shell within the Earth is calculated 

through: 

∆ ＝ ( 1/Rb－ 1/Rt )G  (8) 

mailto:topacademicjournals@gmail.com


    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

8 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

Where:  is the mean value of the total mass of the Earth and the dark planet within the radius Rt and Rb. 

Equation (8) cannot be applied to the Earth's center. The average density  of the central portion combined 

with the Earth and the dark planet within the radius Rc can be calculated through 

＝ ( Mc＋Md )／[(4/3)πRc3] (9) 

Where: Mc and Md are the masses of central portion in the Earth and in the dark planet, respectively. The 

difference of pressure ∆  between the top and the center of the central portion in the Earth can be obtained 

through 

∆ ＝(2/3)πG Rc2                                                                                               (10) 

Based on the characteristics of the inner planets of the solar system except Mercury, the bigger the radius of a 

planet, the higher the average density is, so the radius and the average density of a suitable dark planet must be 

compatible with the characteristics of inner planet in solar system. The data of the new Earth models and dark 

planet are compared with the data of the current Earth and the PREM in the Table 3. 

 

 

 

Table 3. The calculated data of the new earth models compared with the data of the current earth and the PREM K
in

d
 

o
f 

E
arth

's m
o
d
el 

The Earth planet The dark planet 

S
u
itab

ility
 

R
ad

iu
s 

A
v
er

ag
e 

d
en

si
ty

 

M
as

s 

M
o
m

en
t 

o
f 

in
er

ti
a 

C
en

te
r 

d
en

si
ty

 

C
en

te
r 

p
re

ss
u
re

 

M
o
m

en
t 

o
f 

in
er

ti
a 

R
ad

iu
s 

A
v
er

ag
e 

d
en

si
ty

 

M
as

s 

M
o
m

en
t 

o
f 

in
er

ti
a 

M
o
m

en
t 

o
f 

in
er

ti
a 

Unit km g/cm3 1024g 1040 

g.cm2 

g/cm3 kbar C km g/cm3 1024g 1040 

g.cm2 

C  

PREM 637

1 

5.5150 5974.2

00 

80286.40

0 

13.088

48 

3638.524 0.330

9 

      

New 

Model 

637

1 

4.7284 5121.8

20 

76126.84

1 

9.4982

1 

2805.297 0.366

2 

3700.3

75 

4.0161 852.38

0 

4159.559 0.3564 goo

d 

 

The precise data of the Earth and the dark planet are calculated from the density distribution of the new Earth 

model, the data of the Earth planet is listed in Tables 4 (http://newidea.org.tw/pdf/S91.pdf), the dark planet is 

listed in Table 5 (http://newidea.org.tw/pdf/S92.pdf) and the global data of the new Earth model in Table 6 

(http://newidea.org.tw/pdf/S93.pdf). The pressure P and the acceleration due to gravity ɡ of the new Earth model 

compared with the PREM are shown in Figure 4. In this suitable model the slope of density curve from a depth 

of about 400 km of the upper mantle through zones C, D and E to the upper boundary of F-layer is nearly a straight 

line, which means the density increase in proportion to its depth in accord with general physical phenomenon, so 

mailto:topacademicjournals@gmail.com
http://newidea.org.tw/PDF/S64.pdf
http://newidea.org.tw/pdf/S91.pdf
http://newidea.org.tw/pdf/S92.pdf
http://newidea.org.tw/pdf/S93.pdf


    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

9 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

the new Earth model is acceptable as the proper new one. 

 

Figure 4. The Diagram of the gravity ɡ and the pressure P compares between the new Earth model and the PREM. 

The average radius of Mars is 3397 km, the mass 642.40×1024 g, and the average density 3.912 g/cm3. Both values 

of the radius and the average density of the dark planet in the new Earth model are bigger than those of Mars, 

therefore, this model is found to be the more suitable one. 

We can find the pressure curve of the new Earth model is smoother than that of the PREM below the CMB. In 

the gravity curve of the new Earth model, there are two deflection points in the curve that the one is at 

2670.625 km in depth at the radius of the dark planet, and the other is at the inner Core Boundary (ICB). The 

Earth has a mass of 5121.820×1024g, a moment of inertia of 76126.841×1040 g.cm2, an average density of 

4.7284 g/cm3. The Earth's center has a density of 9.49821 g/cm3and the pressure of 2805.297 kbar. The 

reduced values of the Earth's data from those of the current Earth are due to the existence of the dark planet. 

The dark planet has a radius of 3700.375 km, a moment of inertia of 4159.559×1040g.cm2, an average density of 

4.0161 g/cm3and a mass of 852.380×1024g about 1.33 times of Mars. The data of the new Earth model compared 

with those of the current Earth and the PREM are listed in Table 7. 

Table 7. The data of the new earth model compared with the data of the current Earth and the PREM. 

Data of planet Radius Mass Inertia of 

moment 

Average 

density 

Center 

density 

Center 

pressure 

Coef- 

ficient 

Unit km 1024g 1040 

g.cm2 

g/cm3 g/cm3 kbar C 

PREM & 

Current Earth 

6371.000 5974.200 80286.400 5.515 13.08848 3638.524 0.3309 

Earth planet 6371.000 5121.820 76126.841 4.7284 9.49821 2805.297 0.3662 

Dark planet 3700.375 852.380 4159.559 4.0161 7.96097 1115.272 0.3564 

mailto:topacademicjournals@gmail.com


    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

10 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

 

We apply the different density distribution curves of the model in the core to calculate the data of Earth and then 

compare it with the existing current data of Earth. The insufficient mass and moment of inertia are the missing 

matter which are taken as the parts of dark matter, and then a suitable new Earth model is developed. Apply the 

simplified method to evaluate the Earth's mass and moment of inertia, which are found to be only 85.73％ and 

94.82％ respectively of the current data. By the two insufficiencies of Earth's mass and moment of inertia, 

formulating the reasonable assumptions, a dark planet inside the earth has been figured out, then calculate gravity 

and pressure in every depth within the Earth to check suitability or not. Finally, a planet of dark matter, called 

dark planet, with a radius of 3700.375 km, about 1.33 times of Mars, is reasonably inside the Earth in the extra 

dimensions of space other than ours. 

It is hard to examine the existence of the dark matter directly; however, that can be recognized from Chandler 

wobble. Referring to the orientation of the rotation axis of the Earth in space in addition to both precession and 

nutation, there is a wobble on the instantaneous axis of rotation of the Earth itself. The wobble alters the position 

of a point on the Earth relative to the pole of rotation. In 1891, Chandler pointed out that there are two distinct 

kinds of the wobble periods. One is a period of 12 months, and the other is a period of 433 days, about 14 months. 

The former, called annual wobble, is obviously affected by the seasonal climate. The latter, called Chandler 

wobble, has not been solved the problem for more than one hundred years. The Chandler wobble is a small 

deviation that amounts to change of about nine meters at the point in the surface of the rotation axis of the Earth. 

It is inferred from the phenomenon in which the same side of the Moon always faces the Earth that means the 

Moon and the Earth rotate synchronously. The same phenomenon will happen to the Earth and the dark planet 

that both rotate synchronously, but the rotation axes of both are impossible coinciding with each other; i.e., an 

angle between the two rotation axes produces the Chandler wobble as the precession and nutation because of the 

Sun and the Moon on non-parallel rotation axes with the Earth’s. Therefore, the effect of Chandler wobble may 

confirm the existence of a dark planet inside the Earth but in the other cosmos than ours[2]. 

To research dark energy, we apply the eight data of cosmological parameters of Wilkinson Microwave Anisotropy 

mailto:topacademicjournals@gmail.com


    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

11 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

Probe (WMAP) results and Planck Satellite results from 2003 to 2018 for 15 years, to form the Table 8 of 

cosmological parameters from them. 

Table 8. The cosmological parameters from WMAP and Planck Satellite 

Source 

 

Symbol 

WMAP 

 1st year. 

WMAP  

3rd year 

WMAP  

5th year 

WMAP  

7th year 

WMAP  

9th year 

Planck 

Satellite 

2013 

Planck 

Satellite 

2015 

Planck 

Satellite 

2018 

Ho 71.0 70.4 70.5 70.2 70.0 68.14 67.31 67.32 

ΩɅ 73.0% 73.2% 72.6% 72.5% 72.1% 69.64% 68.5% 68.42% 

Ωm 27.0% 26.8% 27.3% 27.44% 27.9% 30.36% 31.5% 31.58 

Ωb 4.4 % 4.41% 4.56% 4.58% 4.63% 4.79% 4.9% 4.94% 

Ωc 22.34% 22.39% 22.8% 22.9% 23.3% 25.43% 26.42% 26.64% 

t0 13.7Gyr 13.73 Gyr 13.72 Gyr 13.76 Gyr 13.74 Gyr 13.784 Gyr 13.80 Gyr 13.80 Gyr 

 

From the table, the dark energy density ΩɅ from 1-year WMAP results to Planck 2018 results VI for 15 years, the 

value from 73.22% decreases gradually down to 68.42%, decreasing 4.8%, but the total matter density Ωm from 

1-year WMAP results to Planck 2018 results VI, the value from 26.78% increases gradually up to 31.58%, 

increasing 4.8%. The dark energy loss is equal to the increase of total matter that is consistent with “The Big Bang 

Theory”. 

The cosmological parameters of Planck 2018 results VI are taken as the current situation of the Universe, we may 

imagine that at the firstly time of the Big Bang, the full energy (100% energy density) of the Universe gradually 

loses, after 13.8 billion years later, remains 68.42% energy density, which is called dark energy density ΩɅ, and 

creates 31.58% total matter density Ωm, so, we should take the current dark energy as the residual energy of the 

Universe after the Big Bang. Due to the current composition of the Universe, dark energy accounts for 68.42%, 

which is much larger than the 31.58% of matter. It can be seen that the Universe is still expanding rapidly.  

After the Big Bang, 68.42% dark energy density ΩɅ is remainder today, but the lost 31.58% dark energy density 

transforms into total matter density Ωm, which contains 4.94 % baryon density Ωb  (normal matter) in our cosmos 

and 26.64 % cold dark matter density Ωc in other cosmoses than ours. According to the table 8, Ωc from the value 

mailto:topacademicjournals@gmail.com


    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

12 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

22.34% increases gradually up to 26.64%, increasing 4.3%, and Ωb in our cosmos from the value 4.44% increases 

gradually up to 4.94%, only increasing 0.54%, and the ratio of both is 8:1. Because matter transforms from energy 

after Big Bang, the baryon densityΩb increasing value is very small, which indicates energy in our cosmos is so 

poor that we can label our cosmos as the low-energy-density. On the contrary, the matter in other cosmoses, i.e., 

the dark matter for our world, has an increase value of 8 times, indicating that dark matter density Ωc in the other 

cosmoses has increased greatly, so we can label the other cosmoses as the high-energy-density cosmoses. After 

WMAP and Planck Satellite detected, the current actual temperature of cosmic microwave background radiation 

(CMBR) is only 2.725 °K, which is awfully close to the absolute zero (0°K = −273.15℃), therefore, our cosmos 

of low-energy-density cannot contribute to expand at an accelerating expansion. 

Under the 3-cosmic framework of the Universe, the rate of expansion in the high-energy-density cosmoses will 

be much higher than that of a low-energy-density cosmos as ours. The cosmoses of high- energy-density cannot 

directly contribute to the expansion of our low-energy-density cosmos, but when the high-energy-density 

cosmoses rapidly expand, their matter (i.e., dark matter) will expand at high pace that will use gravitational force 

to drag on the stars of our cosmos away at the same pace. Due to gravity, the dragging effect causes the effect of 

pulling the stars of our cosmos accelerating expansion [3].  

Based on the applications of ten-dimensional space-time of String theory, a 3-cosmic framework of the Universe 

is developed that the problems of dark matter and dark energy in astrophysics may be solved as above [4], but 

still needs to be proved by the fine outcomes of physicists' new research. 

REFERENCES 

Ho, Hsien-Jung, 1993. Reconstruction of the Earth Model and Discovery of the Interior Dark Matter, First 

Symposium on UFO Cross Strait. China Ufology Institute, DOI: 

https://doi.org/10.29924/REMDM.DB/Collection0001. 

Ho, Hsien-Jung, 2019. Based on the Space-Time of String Theory Exploring Dark Matter Inside the Earth, 

Journal of Scientific and Engineering Research, 2019, 6(8):166-191. http://newidea.org.tw/pdf/S71.pdf. 

Ho, Hsien-Jung, 2022. The 3-Cosmic Framework of the Universe Can Hold Dark Matter and Dark Energy, 

Journal of Scientific and Engineering Research, 2022, 9(4): 67-77. DOI: 

mailto:topacademicjournals@gmail.com
https://doi.org/10.29924/REMDM.DB/Collection0001
http://newidea.org.tw/pdf/S71.pdf


    

 Academic Journal of Science, Engineering and Technology 

Vol. 9, Issue 5; September-October 2024; 

ISSN: 2837-2964 

Impact Factor: 6.67 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

 
 

 

 

13 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

https://doi.org/10.5281/zenodo.10518988. 

Ho, Hsien-Jung, 2023. There is 3-Cosmic Framework in the Universe ─ Including Dark Matter and Dark Energy, 

Newidea Research Center, ISBN 978-986-86319-3-9. http://newidea.org.tw/pdf/S90.pdf. 

mailto:topacademicjournals@gmail.com
https://doi.org/10.5281/zenodo.10518988
http://newidea.org.tw/pdf/S90.pdf

