The Vacuum Universe: the Vacuum Deposit and the Dimensional Hierarchy

Ding-Yu Chung

In this paper, it is proposed that the universe not only gains its existence from the
vacuum but also fattens itself with the vacuum. It is the vacuum universe. The vacuum
is deposited in the inflationary universe before the inflation. During the inflation, the
deposited vacuum is spent to acquire space. In terms of elementary particles, the
deposited vacuum is spent to dilute (fractionalize) the primordial high mass particles
(the mixed 9-branes) to form the low mass hierarchical mixed branes from 9 to 3 whose
masses decrease with the space-time dimension numbers. This formation of the
hierarchical mixed branes is followed by the internal empty space formation. The
internal empty space is generate internally by the annihilation of some of the mixed
branes through charge symmetry. The energy released is cosmic radiation. The
inflationary emergence of the hierarchical mixed branes and the non-inflationary
emergence of cosmic radiation after the inflation constitute the hybrid inflation. The
mixed 3-brane is the mixture of leptons and quarks. During the internal empty space
formation, the four-dimensional "dimensional orbitals" form in the space surrounding the
mixed 3-brane. From these dimensional orbitals, the periodic table of elementary
particles is constructed to account for all leptons, quarks, gauge bosons, and hadrons.
Their masses can be calculated with only four known constants: the number of spatial
dimensions, the mass of electron, the mass of Z, and e, and the calculated masses are
in good agreement with the observed values. The universe is the cyclic universe that
goes through the six transitions: the pre-inflation, the inflation, the big bang-band, the
quintessence, the big crush, and the deflation transitions. The universe is an endless
fattening free lunch.



1. Introduction

In this paper, it is proposed that the universe not only gains its existence from the
vacuum but also fattens itself with the vacuum. It is the vacuum universe. The pre-
inflationary universe gains its existence from a vacuum fluctuation with positive energy
matter and corresponding negative energy gravity. The inflationary universe fattens
itself with a deposited vacuum. As shown later, the vacuum is deposited in the
inflationary universe before the inflation. During the inflation, the deposited vacuum is
spent to acquire space. In terms of elementary particles, the deposited vacuum is spent
to dilute (fractionalize) the primordial high mass particles (the mixed 9-branes) to form
the low mass hierarchical mixed branes from 9 to 3 whose masses decrease with the
space-time dimension numbers as in the dimensional hierarchy [1].
In the dimensional hierarchy, the masses of space dimensions follow the
hierarchical dimensional mass formula based on the Planck mass and the space-time
dimension numbers as follows.

1


MD = MP 2 (11 - D) (1)

where MD is mass of a dimension, D is space-time dimension number, MP is the Planck
mass, and is fine structure constant, the probability of a fermion emitting or absorbing
a boson. The mass of the eleventh dimension is the Planck mass.
The hierarchical dimensional mass formula is derived from the assumption that
each space dimension is occupied by a fermion and a boson as FD BD. The probability to
transforming a fermion into its boson in the adjacent dimension is same as the fine
structure constant, , the probability of a fermion emitting or absorbing a boson. The
probability to transforming a boson into its fermion partner in the same dimension is also
the fine structure constant, . This hierarchy can be expressed in term of the dimension
space-time number, D,

M D-1, B = M D, F D, F, (2)

M D, F = M D, B D, B, (3)

where MD, B and MD,F are the masses for a dimensional boson and a dimensional
fermion, respectively, and D, B or D,F is the fine structure constant, which is the ratio
between the energies of a dimensional boson and its dimensional fermionic partner.
Assuming is the same for all dimensional fermions and dimensional bosons, Eq. (1) is
derived. (As shown later, with one exception, = e, the fine structure constant for the
electromagnetic field, so Eq.(1) is only approximately correct.)
The process of depositing vacuum is described in Section 2 for the pre-
inflationary universe and the inflationary universe. After the inflation, the observable
universe consists of the hierarchical mixed branes from the mixed 3- to 9- branes. The
ordinary universe consists of the mixed 3-brane as the mixture of leptons and quarks.
From the dimensional hierarchy, the periodic table of elementary particles can be
constructed to account of all leptons, quarks, gauge bosons, hadrons, and their masses
as described in Section 3. In Section 4, the cyclic universe is proposed. The conclusion
is that space-time dimension and the vacuum are the ultimate sources of information
and change.


2. The Interbrane-vacuum Mixing: the Pre-inflation and the Inflation

The pre-inflationary universe is derived from a vacuum fluctuation. In this paper,
the pre-inflationary universe consists of a eleven space-time with two identical boundary
9-branes separated by a finite gap spanning a bulk space for gravity. In the bulk space,
there is also the vacuum as the bulk vacuum. It is based on the Horava-Witten model
on eleven dimensional supergravity on a manifold with boundary [2]. Basically, it is a
joining of two eleven dimensional membranes. In the ekpyrotic universe model [3] and
its modification, the pyrotechnic universe model [4] based on Horava-Witten theory, the


2


boundary 3-branes (hidden and visible 3-branes) are different. There are a number of
other models [5] for brane inflation.
The inflationary universe starts with the interbrane-vacuum mixing between the
boundary 9-branes and between the 9-branes and the bulk vacuum. As shown later,
this mixing is the most fundamental mixing, combining the space dimensions from the
two boundary 9-branes and combining the 9-branes and the bulk vacuum. It is
analogous to the combining of two n units DNA to form 2n units of DNA during sexual
reproduction to generate a new life. The product is the mixed 9-brane that has the
combined space dimensions from both boundary 9-branes and the vacuum deposited
within the mixed 9-brane. The inflationary universe has a new set of space-time,
separated from the space-time of the pre-inflationary universe.
Symmetrical to the pre-inflationary universe, the inflationary universe consists of
the two boundary mixed 9-branes with a bulk space for gravity during the interbrane-
vacuum mixing as in Fig. 1. (This inter-universal symmetry becomes the pattern for the
symmetry between the electric and the magnetic fields.)



boundary mixed 9-brane

boundary 9-brane boundary 9-brane
bulk space


boundary mixed 9-brane



Fig. 1: the symmetry between the pre-inflationary universe with the two boundary 9-
branes and the inflationary universe with two boundary mixed 9-branes

This inter-universal symmetry prevents the deposited vacuum in the mixed 9-
branes to convert the boundary mixed 9-branes to the low mass mixed branes by the
vacuum dilution (fractionalization). The symmetry behaves as a high pressure to keep
bubbles (the vacuum) from expanding. Therefore, the deposited vacuum in the
boundary mixed 9-branes is a false vacuum, and the gravity in the bulk space for the
mixed 9-branes is a false gravity.
As soon as all of the boundary 9-branes are depleted, the high mass boundary
mixed 9-branes are diluted (fractionalized) by the deposited vacuum to become the low
mass hierarchical mixed branes with the true vacuum and the true gravity. This vacuum
dilution process has two different modes: the big band mode for the hidden universe
and the big bang mode for the observable universe is from the big bang mode as Fig. 2
and Fig.3.




3


hidden universe (the big band) observable universe (the big bang)

boundary mixed 9-brane boundary mixed 9-brane

boundary 9-brane boundary 9-brane

Fig. 2: the historical diagram for the formation of the observable and hidden universes

interbrane-vacuum mixing big band mode
+
+
vacuum deposit boundary mixed 9-branes hierarchical mixed
boundary 9-branes with deposited vacuum branes
and bulk vacuums big bang mode



internal empty space formation

+ h
+
empty mixed 3-brane hierarchical mixed branes with cosmic radiation
dimensional orbitals

Fig. 3: the interbrane-vacuum mixing (vacuum deposit) and the vacuum dilution
process (the big band mode and the big bang mode)

In the big band mode, the mixed 9-brane is converted into the hierarchical mixed
branes from 3 to 9, whose masses follow the hierarchical dimensional mass formula as
Eq. (1) where p-brane has p + 1 space-time dimension, D. The false gravity for only the
mixed 9-branes is also converted into the true gravity for all mixed branes. Each mixed
brane has an attached massive gravity. There is no empty space internally among the
mixed branes in the big band mode, even though there is an infinite vacuum external to
the big band mode for the mixed branes to expand.
In the big bang mode, the formation of the hierarchical mixed branes is followed
by the internal empty space formation. The mechanism to generate the empty space
internally is to assign symmetrical and opposite charges to the two internal boundary
branes within the mixed brane, the resulting internal annihilation (implosion) dislocate
energy from the mixed brane, and the internal empty space (the empty mixed 3-brane)
is formed. The dislocated energy is cosmic radiation resided in the empty mixed 3-
brane (empty space). The attached gravity to the mixed branes that are annihilated
changes from the massive form to the massless form of negative energy for the
corresponding released positive energy from the mixed branes.

4


The mixed branes that are not annihilated have asymmetrical charges (CP
nonconservation), in such way that the mixed brane has two asymmetrical sets (main
and auxiliary) of space dimensions from the two boundary branes within the mixed
brane. The auxiliary set is dependent on the main set, so the mixed brane appears to
have only one set of space dimensions. The attached gravity to the mixed branes that
are not annihilated is also in the massless form of negative energy for the
corresponding positive brane mass.
The mixed branes in the big band mode have space dimensions from 3 to 9.
The internal empty space in the big bang mode allows all the mixed branes to have the
same number of space dimensions. It is achieved by adding the virtual space
dimensions to the space surrounding the core mixed branes in the manner of the
Kaluza-Klein structure. The virtual space dimensions are the space dimensions in
between the core brane space dimension and the gravity (the eleventh space-time
dimension). The masses of the space dimensions follow the hierarchical dimensional
mass formula as Eq. (1).
The core mixed brane absorbs the hierarchical virtual dimensions as the scalar
fields through Higgs mechanism. The surrounding hierarchical virtual dimensions are
converted into the "dimensional orbitals" with the same space-time dimension as the
core mixed brane. It is analogous to the conversion of the material from a collapsed tall
three-dimensional building into the material to extend the land of a virtually two-
dimensional flat seashore.
When there is not enough mass-energy in the core brane for the masses of the
dimensional orbitals, there are continuous emission and absorption of virtual particles
from and to the core mixed branes. Gravity resided in the empty 3-mixed brane is also
a part of the hierarchical dimensional orbitals for the mixed branes. These dimensional
orbitals are the force fields for the mixed branes in the big bang mode.
Since the core mixed branes have two sets (main and auxiliary) of space
dimensions, there are also two sets of the dimensional orbitals. For the mixed 3-brane
in the big bang mode, there are two sets of the hierarchical seven dimensional orbitals
(including gravity) and the non-hierarchical three core brane space dimensions. The
mixed 3-brane is the mixture of leptons and quarks.
The big band mode is used in the hidden universe. There is no internal empty
space in the big band mode, so the false gravity and the false vacuum are converted
into the true gravity and the true vacuum slowly and sequentially to avoid any rupture
internally to create the internal empty space. It is manifested in the extremely slow
stepwise fractionalization and condensation from the mixed 9-brane to the mixed 3-
brane and back to the mixed 9-brane, resulting in expansion and contraction, like a big
elastic rubber band (big band). The hidden universe is non-inflationary.
The big bang mode is used in the observable universe. The cosmic way to
obtain the internal empty space in the big bang mode is to stretch the universe rapidly
in a superluminal expansion to achieve a "rupture", resulting in the formation of an
"internal gap" as the internal empty space. Therefore, the empty mixed 3-brane and
cosmic radiation emerge only after the superluminal inflationary emergence of all of the
hierarchical mixed branes without the virtual space dimensions. Consequently, the

5


inflationary emergence of the mixed branes and the non-inflationary emergence of
cosmic radiation constitute the hybrid inflation [6].
The two universes have parallel sets of space-time. The gravity of the hidden
universe other than the gravity with mixed 3-brane is hidden from the observable
universe because it is massive, and is not compatible.

3. The Ordinary Universe: the Periodic Table of Elementary Particles

The observable universe consists of the mixed branes from 3 to 9. The ordinary
(baryonic) universe in the observable universe consists of the mixed 3-brane, which is
the mixture of leptons and quarks. Exotic dark matter in the observable universe
consists of the mixed branes from 4 to 9. As shown later, exotic dark matter cannot be
seen, but it can be observed by gravity. The ordinary (baryonic) matter is one of the
seven mixed branes at equal mass proportions, so the baryonic mass fraction is 1/7
(0.14). The universal baryonic mass fraction was found to be 0.13 by the observations
of primordial deuterium abundance [7]. The calculated value agrees well with the
observed value.
For ordinary matter (the mixed 3-brane), there are two sets (main and auxiliary)
of the seven dimensional orbitals. The total number of dimensional orbitals is 14 as
shown in Fig. 4.



D = 5 6 7 8 9 10 11




Fig. 4: 14 dimensional orbitals in the mixed 3-brane: 7 main dimensional orbitals (solid
line), and 7 auxiliary dimensional orbitals (dot line), D = main dimensional orbital
number

As shown in Fig. 4, the fifth main dimensional orbital is the start of the main
dimensional orbitals. To be adjacent to the start of the auxiliary dimensional orbitals, the
seventh main dimensional orbitals mixes with the fifth orbitals. Such mixing is
manifested by the symmetry mixing in the electroweak interaction between U (1) for the
fifth main dimensional orbital and SU (2) for the seventh main dimensional orbitals.
Other than gravity (the eleventh main dimensional orbital), each dimensional
orbital carries certain discrete functions. The main dimensional orbitals are for all major
functions, and the auxiliary dimensional orbitals are for mostly quarks.
Each main dimensional orbital except gravity is assigned to carry gauge
symmetry and space-time symmetry. The charge as represented by the two internal
boundary branes within a mixed brane has U(1) gauge symmetry carried by the fifth
main dimensional orbital. During the annihilation in the vacuum dilution process of the
big bang mode, the two internal boundary branes become massless energy, so the fifth
6


main dimensional orbital is a massless orbital. All other dimensional orbitals except
gravity are short-range massive dimensional orbitals. Only the mixed 3-brane (ordinary
matter) has the fifth main dimensional orbital, so without the fifth main dimensional
orbital, exotic dark matter consists of permanently neutral higher dimensional particles.
It cannot emit light, and cannot form atoms.
The dependence of the auxiliary dimensional orbitals (quarks) on the main
dimensional orbitals (leptons) is represented by the colors as in color SU(3) to become
colorless as in U(1), so a quark composite must have integer charge and hypercharge,
like leptons, in order to be an independent existence. It is carried by the sixth main
dimensional orbital.
The gauge symmetry within each family for leptons and quarks is represented by
SU(2) carried by the seventh main dimensional orbital. It is the symmetry between two
leptons (e and ) or between two quarks (u and d). The same set of gauge symmetry
groups is assigned to the eighth, the ninth, and the tenth main dimensional orbitals as
U(1), U(1), and SU(2), respectively.
Various space-time symmetries reflect the existences of fermions. P
nonconservation is required to achieve chiral symmetry for massless leptons
(neutrinos), so masses of higher neutrinos in the lepton family are not too large to fit in
the lepton family. In order to have a long-term existence of fermions, CP
nonconservation is required to distinguish matter from anti-matter. P and CP
nonconservations are in pairs of the right and the left. The seventh, the eighth, the
ninth, and the tenth main dimensional orbitals are assigned to have P (left), CP (right),
CP (left), and P (right) nonconservation, respectively. There is no nonconservation for
the fifth and the sixth main dimensional orbitals.
The combination of the gauge symmetry and the space-time symmetry for the
main dimensional orbitals from 5 to 10 results in U(1), SU(3) to become U(1), SU(2)L,
U(1)R, U(1)L, and SU(2)R, respectively. The eleventh main dimensional orbital is for
gravity in the massless form as the negative energy for the corresponding positive
energy and mass.
The lack of perfect symmetry between electric and magnetic fields is a reflection
of the lack of perfect symmetry between the boundary 9-branes and the boundary
mixed 9-branes as in Fig. 1. The two boundary 9-branes represent two electric
charges. The mixing (moving) of the boundary 9-branes generates the two boundary
mixed 9-branes, representing two magnetic charges. The observable universe inherits
only one boundary mixed 9-brane, which has to assume the role of two magnetic
charges at the same time and same place. Therefore, there are separable electric
charges, but no separable magnetic charges.
The structure of the mixed 3-brane with dimensional orbitals resembles to the
structure of atomic orbital. Consequently, the periodic table of elementary particles is
constructed to account of all leptons, quarks, gauge bosons, and hadrons as described
in details in Reference 1. It is briefly reviewed here.
For the gauge bosons, the seven main dimensional orbitals are arranged as
F5 B5 F6 B6 F7 B7 F8 B8 F9 B9 F10 B10 F11 B11, where B and F are boson and fermion in
each orbital. The masses of the main dimensional orbital bosons can be derived from
Eqs. (2) and (3). Assuming D,B = D,F , the relation between the bosons in the
7


adjacent main dimensional orbitals, then, can be expressed in terms of the main
dimensional orbital number, D,
M D-1, B = M D, B 2 D , (4)

where D= 6 to 11, and E5,B and E11,B are the energies for the main dimensional orbital five
and the main dimensional orbital eleven, respectively. The lowest energy is the
Coulombic field, E5,B= M6,F = Me,
The bosons generated are the main dimensional orbital bosons or BD. Using only
0
e, the mass of electron, the mass of Z , and the number (seven) of dimensional orbitals,
the masses of BD as the gauge boson can be calculated as shown in Table 1.

Table 1. The Masses of the main dimensional orbital bosons:
= e, D = main dimensional orbital number
BD MD GeV (calculated) gauge Interaction, symmetry
boson
B5 Me 3.7x10-6 (given) A electromagnetic, U(1)
B6 Me/ 7x10-2 1/2 strong, SU(3) U(1)
B 2 0
7 M6/w cos w 91.177 (given) ZL weak (left), SU(2)L
B8 M7/2 1.7x106 XR CP (right) nonconservation, U(1)R
B9 M8/2 3.2x1010 XL CP (left) nonconservation, U(1)L
B 0
10 M9/2 6.0x1014 ZR weak (right), SU(2)R
B11 M10/2 1.1x1019 G gravity

In Table 1, = e (the fine structure constant for electromagnetic field), and w is
not same as of the rest, because there is a mixing between B5 and B7 as the symmetry
mixing between U(1) and SU(2) in the standard theory of the electroweak interaction, and
sinw is not equal to 1. As shown in Reference 1, B5, B6, B7, B8, B9, and B10 are A
(massless photon), 0 0
1/2, ZL , XR, XL, and ZR , respectively, responsible for the
electromagnetic field, the strong interaction, the weak (left handed) interaction, the CP
(right handed) nonconservation, the CP (left handed) nonconservation, and the P (right
handed) nonconservation, respectively. The calculated value for w is 29.690 in good
agreement with 28.70 for the observed value of w [8]. The calculated energy for B11 is
1.1x1019 GeV in good agreement with the Planck mass, 1.2x1019 GeV.
The two sets of seven dimensional orbitals result in 14 dimensional orbitals (Fig. 5)
for gauge bosons, leptons, and quarks. The periodic table for elementary particles is
shown in Table 2.





8


Lepton mixed 3-brane
e e  l9 l10
7 7 8

D = 5 6 7 8 9 10 11
a = 0 1 2 3 4 5 0 1 2

d7 s7 c7 b7 t7 b8 t8
u7
u5 d6 3  q9 q10
Quark mixed 3-brane

Fig. 5. leptons and quarks in the dimensional orbits
D = main dimensional number, a = auxiliary dimensional number

Table 2. The Periodic Table of elementary particles
D = main dimensional orbital number, a = auxiliary dimensional orbital number
D a = 0 1 2 a = 0 1 2 3 4 5

Lepton Quark Boson
5 l5 = e q5 = u5 = 3e B5 = A
6 l6 = e q6 = d6 = 3e B6 = 1/2
7 l 0
7 =  7 7 q7 = 3 u7/d7 s7 c7 b7 t7 B7 = ZL
8 l8 = 8 q8 = ' b8 t8 B8 = XR
9 l9 q9 B9 = XL
10 F 0
10 B10 = ZR
11 F11 B11 = G

D is the dimensional orbital number for the seven main dimensional orbitals. The
auxiliary dimensional orbital number, a, is for the seven auxiliary dimensional orbitals,
mostly for subquarks. All gauge bosons, leptons, and subquarks are located on the
seven dimensional orbitals and seven auxiliary dimensional orbitals. Quarks and heavy
leptons ( and ) are in seven auxiliary spatial dimensions. Most leptons are dimensional
orbital fermions, while all quarks are the sums of subquarks.
The fermion mass formula for massive leptons and quarks is derived from
Reference 1 as follows.
M M M
F =
D , a F + AF
D ,0 D , a

a
3
= M M a 4
F + B
D ,0 D - ,
1 0
2 (5)
a = 0
a
3
= M M a 4
F + F D
D ,0 D ,0
2 a = 0



9


Each fermion can be defined by dimensional orbital numbers (D's) and auxiliary
dimensional orbital numbers (a's). The compositions and calculated masses of leptons
and quarks are listed in Table 3.

Table 3. The Compositions and the Constituent Masses of Leptons and Quarks
D = main dimensional orbital number and a = auxiliary dimensional orbital number
Da Composition Calc. Mass
Leptons Da for leptons
e 50 e 0
e 60 e 0.51 MeV (given)
 70  0
80 0
 60 + 70 + 71 e +  + 7 105.6 MeV
60 + 70 + 72 e +  + 7 1786 MeV
Quarks Da for quarks
u 50 + 70 + 71 u5 + q7 + u7 330.8 MeV
d 60 + 70 + 71 d6 + q7 + d7 332.3 MeV
s 60 + 70 + 72 d6 + q7 + s7 558 MeV
c 50 + 70 + 73 u5 + q7 + c7 1701 MeV
b 60 + 70 + 74 d6 + q7 + b7 5318 MeV
t 50 + 70 + 75 + 80 + 82 u5 + q7 + t7 + q8 + t8 176.5 GeV

There are only three generations of leptons and quarks, because according to
calculation, only three generations of quarks can fit in exactly seven auxiliary
dimensional orbitals. The calculated masses are in good agreement with the observed
constituent masses of leptons and quarks [9,10]. The mass of the top quark found by
Collider Detector Facility is 176  13 GeV [9] in a good agreement with the calculated
value, 176.5 GeV.
As shown in Reference 1, the masses of hadrons can also be calculated based on
binding energy derived from the auxiliary dimensional orbitals. The calculated values for
the masses of hadrons are in good agreement with the observed values.
The masses of leptons, quarks, gauge bosons, and hadrons can be calculated
with only four known constants: the number of spatial dimensions, the mass of electron,
the mass of Z, and e. Most importantly, the calculation shows that exactly seven main
and seven auxiliary dimensional orbitals are needed for all fundamental interactions,
leptons and quarks.


4. The Cyclic Universe

The hidden universe and the observable universe have parallel sets of space-
time. The hidden universe is hidden from the observable universe until the
quintessence transition [11], when the hidden universe fractionalizes into mixed 3-

10


brane, compatible with the empty mixed 3-brane in the observable universe. The empty
mixed 3-brane provides the place for the gravity in the hidden universe to be a
massless force field as the gravity in the observable universe. It is manifested as the
fifth dimension bulk space for massless anti-gravity as in the Randall - Sundrum
mechanism [12] as Fig.6.

Fig. 6: Quintessence

5 th dimension
observable hidden universe
bulk for anti-
empty mixed mixed 3-brane
gravity or gravity
3-brane (quintessence)


It is anti-gravity because the franctionalization of the hidden universe is expansion.
This anti-gravity is massless quintessence, causing the late cosmic accelerating
expansion in the observable universe.
After a certain period, the hidden universe starts the condensation (contraction)
phase. The hidden universe mixed 3-brane starts to condense into mixed 4-brane,
inducing gravity in the fifth dimension bulk space. Consequently, quintessence in the
observable universe causes the cosmic accelerating contraction. The quintessence
transition involves both the accelerating expansion and the accelerating contraction for
the observable universe. Quintessence controls the rate of expansion and contraction
for the observable universe during the quintessence period to make them contracting at
the same rate, so eventually both the observable universe and the hidden universe end
at the same time.
When all hidden universe mixed 3-branes are converted into mixed 4-branes, the
bulk space ceases to exist, and the observable universe starts to contract in a normal
rate. At the end of the contraction, the observable universe becomes essentially a
cosmic black hole, and the hidden universe becomes mixed 9-brane. This is the big
crush transition, the reverse of the big bang.
After the big crush, the observable universe and the hidden universe form two
boundary hierarchical mixed branes separated by a finite gap (bulk space) for gravity.
As gravity transfers from the boundary mixed branes to the bulk space, the mixed
branes start to migrate to the bulk space for the interbrane mixing. During this
interbrane mixing, mixed branes are reversed back to unmixed branes, forming the
deflationary universe with a new set of space-time, separated from the space-time of
the observable-hidden universe, as Fig. 7.





11


boundary unmixed brane
boundary observable
bulk space boundary hidden
mixed brane mixed brane

boundary unmixed brane



Fig. 7: symmetry between the two boundary mixed branes and the two boundary
unmixed branes with a new set of space-time

In the deflationary universe, the unmixed branes form two boundary unmixed
branes. After all the boundary mixed branes are depleted, the boundary unmixed
branes undergo deflation to return all of the deposited vacuum to the original form, the
bulk vacuum. The universe again becomes the pre-inflationary universe consisting of
two boundary 9-branes, separated by a finite gap spanning an intervening bulk volume
for gravity and bulk vacuum as in Fig. 8. Another cycle of the universe starts.

boundary 9-brane (pre-inflationary universe) boundary 9-brane (pre-inflationary universe)

boundary unmixed 9-brane
boundary hierarchical unmixed brane

hidden boundary mixed 9-brane observable boundary hierarchical brane

Fig. 8: the historical diagram for the formation of the pre-inflationary universe

The cyclic universe is goes through the six transitions: the pre-inflation, the
inflation, the big bang-band, the quintessence, the big crush, and the deflation as Fig. 9.
The universe is an endless fattening free lunch.

the pre-inflation

the inflation the deflation


the big bang-band the big crush
the quintessence

Fig. 9: cyclic universe: the six cosmic transitions


5. Conclusion

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The mechanism in cosmology involves a vacuum fluctuation and a vacuum
deposit. Vacuum fluctuation is manifested by the two positive energy boundary 9-branes
separated by the bulk space for the corresponding negative energy gravity. The
deposited vacuum is spent by the inflation to acquire space, and by the boundary mixed
9-branes to form hierarchical mixed branes and empty space. Derive from the
dimensional hierarchy, the periodic table of elementary particles can be constructed to
account for all elementary particles and hadrons and their masses in a good agreement
with the observed values.
Normally, space-time dimension and the vacuum are considered as an immutable
background for physical entities. In this paper, physical entities are the manifestation of
space-time dimension and the vacuum, as proteins are the manifestation of DNA.
Space-time dimension and the vacuum are the ultimate sources of information, and
during the critical periods in the universe, they are also the ultimate sources of change.


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