_{1}

^{*}

This paper modifies the Farnes’ unifying theory of dark energy and dark matter which are negative-mass, created continuously from the negative-mass universe in the positive-negative mass universe pair. The first modification explains that observed dark energy is 68.6%, greater than 50% for the symmetrical positive-negative mass universe pair. This paper starts with the proposed positive-negative-mass 11D universe pair (without kinetic energy) which is transformed into the positive-negative mass 10D universe pair and the external dual gravities as in the Randall-Sundrum model, resulting in the four equal and separate universes consisting of the positive-mass 10D universe, the positive-mass massive external gravity, the negative-mass 10D universe and the negative-mass massive external gravity. The positive-mass 10D universe is transformed into 4D universe (home universe) with kinetic energy through the inflation and the Big Bang to create positive-mass dark matter which is five times of positive-mass baryonic matter. The other three universes without kinetic energy oscillate between 10D and 10D through 4D, resulting in the hidden universes when D > 4 and dark energy when D = 4, which is created continuously to our 4D home universe with the maximum dark energy = 3/4 = 75%. In the second modification to explain dark matter in the CMB, dark matter initially is not repulsive. The condensed baryonic gas at the critical surface density induces dark matter repulsive force to transform dark matter in the region into repulsive dark matter repulsing one another. The calculated percentages of dark energy, dark matter, and baryonic matter are 68.6 (as an input from the observation), 26 and 5.2, respectively, in agreement with observed 68.6, 26.5 and 4.9, respectively, and dark energy started in 4.33 billion years ago in agreement with the observed 4.71 ± 0.98 billion years ago. In conclusion, the modified Farnes’ unifying theory reinterprets the Farnes’ equations, and is a unifying theory of dark energy, dark matter, and baryonic matter in the positive-negative mass universe pair. The unifying theory explains protogalaxy and galaxy evolutions in agreement with the observations.

In the Farnes’ unifying theory of dark energy and dark matter [

This paper modifies and reinterprets the Farnes’ unifying theory of dark energy and dark matter in the positive-negative mass universe pair model where positive-mass and negative-mass universes are symmetrical. (The Farnes’ unifying theory does not assume symmetrical positive-negative mass universes.) The first modification is about dark energy. With the symmetry between positive-mass universe and negative-mass universe, the portion of dark energy to be created continuously from the negative-mass universe to our positive-mass universe cannot start from zero to more than 50%. Since the observed portion of dark energy is 68.6% [

To deal with greater than 50% of dark energy and the early existence of dark matter, this paper proposes the positive-negative mass universe pair model where the positive and the negative universes are symmetrical [

To deal with the early existence of positive-mass dark matter in the CMB, the second modification is that the proposed dark matter in the CMB is same as the conventional positive-mass dark matter observed in the CMB. However, after the CMB, the proposed positive-mass dark matter turned into repulsive positive-mass dark matter when the condensed baryonic gas reached the critical surface density (derived from the acceleration constant a_{0} in MOND [

The theoretical calculated percentages of dark energy, dark matter, and baryonic matter are 68.6 (as an input from the observation), 26, and 5.2, respectively, in agreement with observed 68.6, 26.5, and 4.9 [

In Section 2, unifying theory of dark energy and dark matter by Farnes is described. Section 3 explains the positive-negative mass universe pair. Section 4 describes protogalaxy and galaxy evolutions.

In the Farnes’ unifying theory of dark energy and dark matter [

In the Einstein’s field equation,

R μ ν − 1 2 R g μ ν + Λ g μ ν = 8 π G c 4 T μ ν (1)

where R_{μν} is the Ricci curvature tensor, R is the scalar curvature, g_{μν} is the metric tensor, Λ is the cosmological constant, G is Newton’s gravitational constant, c is the speed of light in vacuum, and T_{μν} is the stress-energy tensor.

In a homogeneous and isotopic universe, the Friedmann equation is

H 2 ≡ ( a ˙ a ) 2 = 8 π G 3 ρ + Λ c 2 3 − k c 2 a 2 (2)

and the Friedmann acceleration equation.

( a ¨ a ) = − 4 π G 3 ( ρ + 3 p c 2 ) + Λ c 2 3 (3)

where a is the scale factor, H is the Hubble parameter, ρ is the total mass density of the universe, p is the pressure, k is the curvature parameter or intrinsic curvature of space, and k/a^{2} is the spatial curvature in any time-slice of the universe. k = +1, 0, and −1, indicate a closed, flat, and open universe respectively. In the positive mass universe corresponding to the standard matter-dominated universe solutions with a critical density given by ρ c = 3 H 2 / 8 π G and a total density parameter given by Ω = ρ/ρ_{c}, where Ω = 1, <1, and >1, correspond to critical density, open, and closed universes respectively.

In the Farnes’ unifying theory of dark energy and dark matter [_{μν}

T ′ μ υ = T μ υ + C μ υ (4)

Einstein’s field equations are therefore modified to

R μ ν − 1 2 R g μ ν + Λ g μ ν = 8 π G c 4 ( T μ υ + C μ υ ) (5)

The creation tensor generates negative mass density, ρ_{−}. Farnes proposed that the Friedmann equation can be written in terms of both the cosmological constant and negative mass density, ρ_{−} as follows.

( a ˙ a ) 2 = 8 π G 3 ρ + + Λ c 2 3 − k c 2 a 2 = 8 π G 3 ρ + + 8 π G 3 ρ − − k c 2 a 2 (6)

In this way, the cosmological constant (Λ) is equivalent to the negative-mass density, and Λ = 8 π G ρ − / c 2 . The accelerated cosmic expansion is caused by negative mass which is created continuously through the creation tensor. As these negative masses can take the form of a cosmological constant, the field equations are modified to

R μ ν − 1 2 R g μ ν + Λ g μ ν = 8 π G c 4 ( T μ υ + + T μ υ − + C μ υ ) (7)

In the Farnes’ unifying theory for dark matter, the positive-mass baryonic galaxy is surrounded by a halo of continuously-created negative masses, with constant density ρ_{−} and of total mass M_{−}. The positive mass particle is now immersed in a negative mass fluid that behaves with resemblance to a cosmological constant with Λ = 8 π G ρ − / c 2 .

Negative-mass dark matter repulses each other, while dark matter still attracts to baryonic matter. The solution for the rotation curve with circular velocity, ν, is deduced as follows.

υ = G M * r − Λ c 2 3 r 2 = G M * r − 8 π G ρ − 3 r 2 (8)

where r is the distance from a central point mass M_{⋆} and ρ_{−} is the local negative mass density. For Λ = 0 or ρ_{−} = 0, the standard Keplerian rotation curve is obtained. However, for non-zero values of the cosmological constant or ρ_{−}, the rotation curve is modified. A negative cosmological constant flattens the rotation curve, causing a steady increase at larger galactic radii in agreement with the observed rotation curve.

In a N-body simulations of galaxy formation via negative-mass dark matter and positive-mass baryonic matter, Farnes starts with the galaxy that comprises 5000 particles, with a total positive mass of M_{+} = 1.0. The initial positive mass particle distribution is located at the center of a cube of negative masses with volume 200^{3}. The initial conditions of these negative masses are set to be uniformly distributed in position and with zero initial velocity. The negative mass sea comprises 45,000 particles, with a total mass of M_{−} = −3.0. The negative masses at the outskirts of the cube are mutually-repelled by other surrounding negative masses and the cube begins to expand in volume. Meanwhile, the negative masses within the central portion of the cube are attracted towards the positive mass galaxy. From their initially zero velocities, the negative mass particles are slushed to-and-fro from either side of the positive mass galaxy. Eventually, the negative mass particles reach dynamic equilibrium in a halo that surrounds the positive mass galaxy and which extends out to several galactic radii. The negative mass particles have naturally formed a dark matter halo to have a flat central dark matter distribution with the constant dark matter density core.

With positive mass dark matter, the Navarro-Frenk-White (NFW) profile [

This paper modifies and reinterprets the Farnes’ unifying theory of dark energy and dark matter as negative-mass dark fluid derived from the positive-negative mass universe pair model where positive-mass and negative-mass universes are symmetrical. (The Farnes’ unifying theory does not assume symmetrical positive-negative mass universes.) The first modification is about dark energy. With the symmetry between positive mass and negative mass, the portion of dark energy created through the creation tensor cannot start from zero to more than 50%. Since dark energy is 68.6%, dark energy is more than negative mass, and the creation tensor for dark energy needs modification. The first modification is to modify the origin of dark energy. The second modification is to modify dark matter. Evidence for early existence of dark matter comes from measurements on cosmological scales of anisotropies in the cosmic microwave background [

To deal with more than 50% of dark energy and the early existence of dark matter in the CMB, this paper proposes as described previously [

The oscillating spacetime dimension number oscillates between 11D membrane and 11D membrane through 10D string and between 10D particle and 10D particle through 4D particle as described in the previous papers [

In the membrane-string oscillation, the 11D brane is transformed into the 10D string with an extra dimension. This 11D warped brane world in the 10D string with compact extra dimension is analogous to the 5D warped brane world in our 4D universe with compact extra dimension in the Randall-Sundrum model [

In the same way as the RS1 in the Randall-Sundrum model, two 11D membranes produce the 10D string corresponding to the Tevbrane and the external gravity corresponding to the Planckbrane. The 11D membrane, the 10D string, and the external gravity have about the same energy. The 10D string has the extremely weak internal gravity as in the Tevbrane with an extremely weak gravity in the Randall-Sumdrum model.

The RS1 in the Randall-Sundrum model 5D brane world → compact extra space dimension Tevbrane + Planckbrane two 11D membranes ↔ oscillation between 11D membrane and 10D string 10D string + external gravity (9)

The membrane-string oscillation is reversible, so the 10D string and the external gravity can also reverse back to the 11D membrane.

As described previously [

c ( t ) = c 0 a n , (10)

where c is the speed of light and n are constants. The increase of speed of light is continuous.

In this paper, the speed of light is invariant in a constant space-time dimension number, and the speed of light varies with varying space-time dimension number from 4 to 10 as follows.

c D = c / α D − 4 , (11)

where c is the observed speed of light in the 4D space-time, c_{D} is the quantized varying speed of light in space-time dimension number, D, from 4 to 10, and α is the fine structure constant for electromagnetism. The speed of light increases with the increasing space-time dimension number D. Since the speed of light for >4D particle is greater than the speed of light for 4D particle, the observation of >4D particles by 4D particles violates casualty. Thus, >4D particles are hidden particles with respect to 4D particles. Particles with different space-time dimensions are transparent and oblivious to one another, and separate from one another if possible.

As described previously [_{0}c^{2} modified by Equation (12) is expressed as

E = M 0 c D 2 = M 0 ⋅ ( c 2 / α 2 ( D − 4 ) ) , (12)

M 0 , D , d = M 0 , D − n , d + n α 2 n , (13)

E vacuum , D = E − M 0 , D c 2 , (14)

D , d → VSLDtransformation ( D ∓ n ) , ( d ± n ) (15)

where c_{D} is the quantized varying speed of light in space-time dimension number, D, from 4 to 10, c is the observed speed of light in the 4D space-time, α is the fine structure constant for electromagnetism, E is energy, M_{0} is rest mass, D is the space-time dimension number from 4 to 10, d is the mass dimension number from 4 to 10, n is an integer, and E_{vacuum} = vacuum energy. From Equation (12), 10D has the lowest rest mass, and 4D has the highest rest mass. According to the calculation from Equation (13), the rest mass of 4D is 1/α^{12} ≈ 137^{12} times of the mass of 10D. From Equation (14), 10D has the highest vacuum energy, while 4D particle has zero vacuum energy. A particle with 10D is transformed to a particle with 4D from Equation (15) through the VSLD transformation. Spacetime dimension number decreases with decreasing speed of light, decreasing vacuum energy, and increasing rest mass. The 4D and the 10D have zero and the highest vacuum energies, respectively.

In the normal supersymmetry transformation, the repeated application of the fermion-boson supersymmetry transformation carries over a boson (or fermion) from one point to the same boson (or fermion) at another point at the same mass, resulting in translation without changing mass. Under the varying supersymmetry dimensional (VSD) transformation, the repeated application of the fermion-boson supersymmetry transformation carries over a boson from one point to the boson at another point at different mass dimension number at different mass, resulting in translation and fractionalization or condensation. The repeated VSD transformation carries over a boson B_{d} into a fermion F_{d} and a fermion F_{d} to a boson B_{d−1}, which can be expressed as follows.

M d,F = M d,B α d,B , (16)

M d − 1 , B = M d,F α d,F , (17)

where M_{d,B} and M_{d,F} are the masses for a boson and a fermion, respectively, d is the mass dimension number, and α_{d,B} or α_{d,F} is the fine structure constant that is the ratio between the masses of a boson and its fermionic partner. where M_{d,B} and M_{d,F} are the masses for a boson and a fermion, respectively, d is the mass dimension number, and α_{d,B} or α_{d,F} is the fine structure constant that is the ratio between the masses of a boson and its fermionic partner. Assuming α’s are the same, it can be expressed as

M d,B = M d + 1 , B α d + 1 2 . (18)

The oscillating dimension number transformation between 10D4d and 10D4d through 4D4d involves both the VSLD transformation and the VSD transformation as the stepwise two-step transformation as follows.

stepwise two-step varying transformation ( 1 ) D,d ↔ VSLD ( D ∓ 1 ) , ( d ± 1 ) ( 2 ) D,d ↔ VSD D, ( d ± 1 ) (19)

The repetitive stepwise two-step dimension number oscillation between 10D4d and 10D4d through 4D4d as follows.

10 D 4 d → 9 D 5 d → 9 D 4 d → 8 D 5 d → 8 D 4 d → 7 D 5 d → 7 D 4 d → 6 D 5 d → 6 D 4 d → 5 D 5 d → 5 D 4 d → 4 D 5 d → 4 D 4 d → 5 D 4 d → 5 D 5 d → 6 D 4 d → 6 D 5 d → 7 D 4 d → 7 D 5 d → 8 D 4 d → 8 D 5 d → 9 D 4 d → 9 D 5 d → 10 D 4 d (20)

From Equation (18), the mass of 9D4d is α^{2} ≈ (1/137)^{2} times of the mass of 9D5d through the varying supersymmetry transformation. The transformation from a higher mass dimensional particle to the adjacent lower mass dimensional particle is the fractionalization of the higher dimensional particle to the many lower dimensional particles in such way that the number of lower dimensional particles becomes

N d − 1 = N d / α 2 ≈ N d ( 137 ) 2 (21)

The fractionalization also applies to D for 10D4d to 9D4d, so

N D − 1 = N D / α 2 (22)

Since the supersymmetry transformation involves translation, this stepwise varying supersymmetry transformation leads to a translational fractionalization, resulting in the cosmic expansion. Afterward, the QVSL transformation transforms 9D4d into 8D5d with a higher mass. The two-step transformation repeats until 4D4d, and then reverses stepwise back to 10D4d for the cosmic contraction. The oscillation between 10D and 4D results in the reversible cyclic fractionalization-contraction for the reversible cyclic expansion-contraction of the universe which does not involve irreversible kinetic energy.

In the space structure, attachment space that attaches matter to the space relates to rest mass, and detachment space that detaches matter from the space relates to kinetic energy. Attachment space is the space precursor of the transitional Higgs field, and detachment space is the space precursor of the transitional reverse Higgs field.

In conventional physics, space does not couple with particles, and is the passive zero-energy ground state space. Under spontaneous symmetry breaking in conventional physics, the passive zero-energy ground state is converted into the active, permanent, and ubiquitous nonzero-energy Higgs field, which couples with massless particle to produce the transitional Higgs field-particle composite. Under spontaneous symmetry restoring, the transitional Higgs field-particle composite is converted into the massive particle with the longitudinal component on zero-energy ground state without the Higgs field as follows.

In conventional physics, the nonzero-energy scalar Higgs Field exists permanently in the universe. The problem with such nonzero-energy field is the cosmological constant problem from the huge gravitational effect by the nonzero-energy Higgs field in contrast to the observation [

Unlike passive space in conventional physics, attachment space actively couples to massless particle. Under spontaneous symmetry breaking, attachment space as the active zero-energy ground state space couples with massless particle to form momentarily the transitional non-zero energy Higgs field-particle composite. The Higgs field is momentary and transitional, avoiding the cosmological constant problem. Under spontaneous symmetry restoring, the transitional nonzero-energy Higgs field-particle composite is converted into massive particle with the longitudinal component on zero-energy attachment space without the Higgs field as follows.

Detachment space is the space precursor of the reverse Higgs field. Unlike the conventional model, detachment space actively couples to massive particle. Under spontaneous symmetry breaking, the coupling of massive particle to zero-energy detachment space produces the transitional nonzero-energy reverse Higgs field-particle composite which under spontaneous symmetry restoring produces massless particle on zero-energy detachment space without the longitudinal component without the reverse Higgs field as follows.

For the electroweak interaction in the Standard model where the electromagnetic interaction and the weak interaction are combined into one symmetry group, under spontaneous symmetry breaking, the coupling of the massless weak W, weak Z, and electromagnetic A (photon) bosons to zero-energy attachment space produces the transitional nonzero-energy Higgs fields-bosons composites which under partial spontaneous symmetry restoring produce massive W and Z bosons on zero-energy attachment space with the longitudinal component without the Higgs field, massless A (photon), and massive Higgs boson as follows.

massless WZ + zero-energy WZ attachment space + massless A + zero-energy A attachment space A → spontaneous symmetry breaking [ the transitional nonzero-energy WZ Higgs field − WZ composite ] + [ nonzero-energy A Higgs field − A composite ] → partial spontaneous symmetry restoring massive WZ with the longitudinal component on attachment space without the Higgs field + massless A + the nonzero energy massive Higgs boson (26)

In terms of mathematical expression, the conventional permanent Higgs field model and the transitional Higgs field model are identical. The interpretations of the mathematical expression are different for the permanent Higgs field model and the transitional Higgs field model. The transitional Higgs field model avoids the cosmological problem in the permanent Higgs field model.

In the Higgs mechanism, gauge bosons are assumed to be massless originally. Elementary fermions (leptons and quarks) can be assumed to be massive originally. However, the observed neutrinos are nearly massless and left-handed only. The paper posits that the left handed became massless through the reverse Higgs mechanism. For the symmetrical massive left handed neutrinos and right-handed neutrinos under spontaneous symmetry breaking, the coupling of the massive left handed neutrinos and the massive right handed neutrinos to zero-energy detachment space produces the transitional nonzero-energy reverse Higgs fields-neutrinos composites which under partial spontaneous symmetry restoring produce massless left handed neutrinos on zero-energy detachment space without the longitudinal component without the reverse Higgs field, massive right-handed neutrinos (dark matter), and the massive reverse Higgs boson as follows.

massive ν L + zero energy ν L detachment space + massive ν R + zero-energy ν R detachment space → spontaneous symmetry breaking [ the transitional nonzero-energy ν L reverse Higgs field − ν L composite ] + [ nonzero-energy ν R reverse Higgs field − ν R composite ]

→ partial spontaneous symmetry restoring massless ν L without the longitudinal component on detachment space without the Higgs field + massive ν R + the nonzero energy massive reverse Higgs boson (27)

As described in the previous paper [

The combination of n units of attachment space as 1 and n units of detachment space as 0 brings about three different spaces: binary partition space, miscible space, or binary lattice space as below.

( 1 ) n + ( 0 ) n → combination ( 1 ) n ( 0 ) n , ( 1 + 0 ) n or ( 1 0 ) n attachment space detachment space binary partition space , miscible space , binary lattice space (28)

Binary partition space, (1)_{n}(0)_{n}, consists of two separated continuous phases of multiple quantized units of attachment space and detachment space, and it is the space structure for wave-particle duality in quantum mechanics. In miscible space, (1 + 0)_{n}, attachment space is miscible to detachment space, and there is no separation of attachment space and detachment space, and it is the space structure for miscible mass-energy in relativity. Binary lattice space, (1 0)_{n}, consists of repetitive units of alternative attachment space and detachment space, and it is the space structure for virtual particles in quantum field theory.

An object in binary partition space (1)_{n}(0)_{n} has both movement and rest at the same time, resulting in wave-particle duality for movement-rest duality in quantum mechanics. An object in binary partition space cannot be completely at movement (zero momentum) or completely at rest (zero distance), resulting in the uncertainty principle as follows.

σ x σ p ≥ ℏ 2 (29)

where x is position and p is momentum. The interference to binary partition space collapses binary partition space, resulting in miscible space as follows.

( 0 ) n ( 1 ) n → collapse ( 0 + 1 ) n binary partition space miscible space (30)

In miscible space, attachment space is miscible to detachment space, resulting in miscible mass and energy where attachment space for mass provides zero speed for rest mass m_{0}, while detachment space for energy provides the speed of light for kinetic energy. The total energy is the combination of both as follows.

E = K + m 0 c 2 = γ m 0 c 2 (31)

where γ = 1 / ( 1 − v 2 / c 2 ) 1 / 2 is the Lorentz factor for time dilation, m_{0} is rest mass, E is the total energy, and K is the kinetic energy. Binary lattice space, (1 0)_{n} is the space structure for virtual particles in quantum field theory which will be described in the next section.

The seven steps in the cyclic universes model are 1) the formation of positive-mass and negative-mass dual 11D4d membrane-antimembrane universes from the zero-mass inter-universal void, 2) the transformation of the 11D4d membrane-antimembrane dual universes to the 10D4d string-antistring dual universes and dual external dual gravities, 3) the transformation from the string-antistring dual universes to the particle-antiparticle dual universes, 4) the transformation of the positive-mass 10D4d universe into the positive-mass 4D universe, and the transformation of the other three universes into the hidden oscillating dimension number universes from 10D to 5D, 5) the transformation of all four universes into the 4D universes, 6) the positive-mass 4D universe and the three hidden oscillating dimension number from 5D to 10D, and 7) the return to the 10D4d particle-antiparticle universes (the step 3) as in

1) the formation of the positive-negative-mass 11D4d membrane-antimembrane dual universes

In the cyclic universes model, the universes start with the positive-mass 11D4d membrane-antimembrane universe and the negative-mass 11D4d membrane-antimembrane universe derived from the zero-mass inter-universal void. The mass sum of the dual universes is zero. The zero-mass inter-universal void and the dual universe are reversible, so the dual universe can reverse back to the zero-mass inter-universal void. The inter-universal void contains only detachment space to prevent irreversible inter-universal collision, while the dual universes contain only attachment space without kinetic energy. These 11D dual universes are the universes with the oscillating spacetime dimension number, and start the process of oscillation between 11D and 11D through 10D and between 10D and 10D through 4D.

2) the transformation of the 11D4d membrane-antimembrane dual universes to the 10D4d string-antistring dual universes and dual external gravities

As described in Section 3.1.1., the transformation of the 11D membrane produces the 10D string and the external gravity. The results are the positive-mass 10D4d string-antistring universe, the positive-mass external gravity, the negative-mass 10D4d string-antistring universe, and the negative-mass external gravity. These four universes are separate, and have equal energy. The 10D4d string-external gravity and the 11D4d membrane are reversible.

3) the transformation from the string-antistring dual universes to the particle-antiparticle dual universes

Since string exists only in 10D, so any further transformation of D to lower than 10 cannot be string. As a result, to transform lower than 10, string-antistring is converted into particle-antiparticle. The results are the positive-mass 10D4d particle-antiparticle universe, the positive-mass 10D4d external gravity, the negative-mass 10D4d particle-antiparticle universe, and the negative-mass 10D4d external gravity. Particle-antiparticle and string-antistring are reversible.

4) the transformation of the positive-mass 10D4d particle-antiparticle universe into the positive-mass 4D universe, and the transformation of other three universes into the hidden oscillating dimension number universes from 10D to 5D

The positive-mass 10D particle-antiparticle universe is transformed into the positive-mass 4D universe to produce the 4D standard model particles. Under the oscillating spacetime dimension number, the negative-mass 10D particle-antiparticle, the positive-mass external gravity, and the negative-mass external gravity are transformed into the hidden oscillating dimension number universes from 10D to 5D.

4a) the formation of the positive-mass 4D particle-antiparticle universe

The formation of the positive-mass 4D particle-antiparticle universe includes the inflation and followed by the Big Bang. The inflation involves the VSLD transformation from 10D4d to 4D10d, because from Equation (13), the rest mass M_{0} of 4D10d is M 0 , 10 = M 0 , 4 / α 2 ( 10 − 4 ) ≈ 137 12 times of the rest mass of 10D4d, resulting in the inflation for the rapid expansion

The Big Bang involves the entrance of detachment space from the inter-universal void to the positive-mass universe. Detachment space introduces massless particles and kinetic energy for the cosmic expansion, and forms the three spaces with attachment space. The Big Bang consists of the two steps. In the first step, all particles are converted into massless particles by detachment space for the reverse Higgs field as in Equation (25). The second step involves the partial conversion of massless particles into massive particles by attachment space for the Higgs field to produce massless particles, massive particles, and the Higgs boson as in Equations (26) and (27) for the standard model. The emergence of detachment space starts kinetic energy which causes the cosmic expansion as the Big Bang.

the inflation and the Big Bang ( detachment space + partial attachment space ) 10D4d → theinflation 4D10d → detachment space ( reverse Higgs field ) massless particles → partial attachment space ( Higgs field ) massive particles , massless particles , Higgs boson (32)

4D10d particle was sliced into six different particles: 4D9d, 4D8d, 4D7d, 4D6d, 4D5d, and 4D4d equally by mass. Baryonic matter is 4D4d, while dark matter consisted of the other five types of particles (4D9d, 4D8d, 4D7d, 4D6d, and 4D5d) as follows.

10D4d → cosmic inflation 4D10d → the slicing baryonic matter ( 4D4d ) + dark matter ( 4 D 5 d , 4 D 6 d , 4 D 7 d , 4 D 8 d , 4 D 9 d ) (33)

As a result, the mass ratio of dark matter to baryonic matter is 5 to 1. At observed 68.6% dark energy [

As described in Section 3.2.2., the space structure with both attachment space and detachment produces binary partition space (1)_{n}(0)_{n} for wave-particle duality in quantum mechanics, miscible space (1 + 0)_{n} for miscible mass-energy in relativity, and binary lattice space (1 0)_{n} for virtual particles in quantum field theory. Binary lattice space is derived from the slicing of mass dimensions by detachment space as described by Bounias and Krasnoholovets [_{n} for virtual particles in quantum field theory. For an example, the slicing of 10d particle into 4d particle is as follows.

1 10 → slicing 1 4 ∑ d = 5 10 ( 0 4 1 4 ) n , d 10 d particle 4d core particle binary lattice space (34)

where 1 is attachment space, 0 is detachment space, 1_{10} is 10d particle, 1_{4} is 4d particle, d is the mass dimension number of the dimension to be sliced, n as the number of slices for each dimension, and (0_{4} 1_{4})_{n} is binary lattice space with repetitive units of alternative 4d attachment space and 4d detachment space. For 4d particle starting from 10d particle, the mass dimension number of the dimension to be sliced is from d = 5 to d = 10. Each mass dimension is sliced into infinite quantized units (n = ∞) of binary lattice space, (0_{4} 1_{4})_{∞}. For 4d particle, the 4d core particle is surrounded by 6 types (from d = 5 to d = 10) of infinite quantized units of binary lattice space. Such infinite quantized units of binary lattice space represent the infinite units (n = ∞) of separate virtual orbitals for virtual particles in a gauge force field, while the dimension to be sliced is “mass dimensional orbital” (DO), representing a type of gauge force field. In addition to the six DO’s for gauge force fields from d = 5 to d = 10, the weak internal gravity appears as the seventh DO at d = 11. As a result, there are seven mass dimensional orbitals as in

The seven mass dimensions are arranged as F_{5} B_{5} F_{6} B_{6} F_{7} B_{7} F_{8} B_{8} F_{9} B_{9} F_{10} B_{10} F_{11} B_{11}, where F_{d} and B_{d} are mass dimensional fermion and mass dimensional boson, respectively. Under the varying supersymmetry dimensional (VSD) transformation, the mass of mass dimensional fermion and the mass of mass dimensional boson are related to each other with three simple formulas as the follows.

M d , B = M d,F / α d (35)

M d + 1,F = M d,B / α d + 1 (36)

M d + 1,B = M d , B / α d + 1 2 , (37)

where d is the mass dimension number, F is fermion, and B is boson. Each dimension has its own α_{d}, and all α_{d}’s except α_{7} (α_{w}) of the seventh dimension (weak interaction) are equal to α, the fine structure constant of electromagnetism.

As shown in the previous paper “Split Membrane 11D Spacetime = 1D Eleventh Dimension Interval Space + 6D Rishon Space + 3D Higgs Space + 1D Einstein Time: Cosmology” [

The Periodic Tableof Elementary Particles

The periodic table of elementary particles [

matter neutrinos) and the seven auxiliary mass dimensions (a’s) for unstable leptons (muon and tau) and quarks (d, u, s, c, b, and t) as in

In the periodic table of elementary particles, the five dark matter particles are derived from Equation (33). Without electromagnetism at d = 5, dark matter does not have charge particle, and has to be neutrinos. Initially derived from Equation (33) and the symmetry between dark matter and baryonic matter, there were five dark matter massive right-handed neutrinos and one baryonic matter massive left-handed neutrino. Through the reverse Higgs mechanism as Equation (27), the left-handed neutrino becomes massless, while the right-handed neutrinos as sterile dark matter neutrinos remain massive. The reverse Higgs boson was observed [

As sterile neutrinos, dark matter does not react with baryonic matter possibly except baryonic neutrinos. A new observation of Excess Electronic Recoil Events in XENON1T indicates an excess over known backgrounds is observed below 7 keV, rising towards lower energies and prominent between 2 - 3 keV which enables the most sensitive searches for solar axions, an enhanced neutrino magnetic moment using solar neutrinos, and bosonic dark matter [_{DM} and massless ν_{BM} to produce boson B_{5} at 3.7 keV (

massive ν DM + massless ν ¯ BM → boson B 5 at 3.7 keV (38)

All neutrinos and electron as well as gauge bosons are in the principal mass dimensions. All quarks and unstable leptons are in the auxiliary mass dimensions. The three generations of baryonic matter lepton-quark is the maximum generations allowed for the seven principal dimensions and the seven auxiliary dimensions.

d | a = 0 | a = 0 | 1 | 2 | 1 | 2 | 3 | 4 | 5 | a = 0 |
---|---|---|---|---|---|---|---|---|---|---|

Stable Baryonic Matter Leptons | Dark Matter Leptons | Unstable Leptons | Quarks | Bosons | ||||||

5 | ν_{e} | ν_{DM5} | B_{5} = A electromagnetism | |||||||

6 | e | ν_{DM6} | B_{6} = g* strong (basic gluon for quarks) | |||||||

7 | ν_{μ} | ν_{DM7} | μ_{7 } | τ_{7 } | d_{7}/u_{7} | s_{7} | c_{7} | b_{7} | t_{7} | B_{7} = Z0 L left-handed BM weak |

8 | ν_{τ} | ν_{DM8} | μ_{8} (absent) | b_{8} (absent) | t_{8} | B_{8} = Z0 R right-handed DM weak | ||||

9 | ν'_{τ} (high-mass ν_{τ} ) | ν_{DM9} | B_{9} = dark matter repulsive force | |||||||

10 | B_{10} = particle-antiparticle asymmetry | |||||||||

11 | gravitino | B_{11} = gravity |

B_{d} | M_{d} | GeV (calculated) | Gauge boson | Interaction |
---|---|---|---|---|

B_{5} | M_{e}α | 3.7 × 10^{−6} | A = photon | Electromagnetic |

B_{6} | M_{e}/α | 7 × 10^{−2} (70.02 MeV) | g* = basic gluon | Strong |

B_{7} | M Z = M B6 / α w 2 | 91.1876 (given) | Z_{L} | weak (left) for baryonic matter_{ } |

B_{8} | M_{7}/α^{2} = M_{Z}/α^{2} | 1.71 × 10^{6} | Z_{R} | weak (right) for dark matter_{ } |

B_{9} | M_{8}/α^{2} = M_{Z}/α^{4} | 3.22 × 10^{10} | dark matter repulsive force_{ } | |

B_{10} | M_{9}/α^{2} = M_{Z}/α^{6} | 6.04 × 10^{14} | particle-antiparticle asymmetry_{ } | |

B_{11} | M_{10}/α^{2} = M_{Z}/α^{8} | 1.13 × 10^{19} | G_{ } | gravity |

Gauge Bosons

In the periodic table of elementary particles, the given observed masses are the mass of electron for F_{6} and the mass of Z boson for B_{7}. From Equations (35), (36) and (37), α_{w}= α_{7} = α of week interaction = (M_{B6}/M_{B7})^{1/2} = (M_{F6}/α/M_{B7})^{1/2} = (M_{e}/α/M_{Z})^{1}^{/2} = 0.02771. Therefore, the masses of gauge bosons are as in

The lowest energy gauge boson (B_{5}) at d = 5 is the Coulomb field for electromagnetism. The second gauge lowest boson (B_{6}) at d = 6 is basic gluon (g* = 70 MeV ≈ one half of pion) is the strong force as the nuclear force in the pion theory [_{6} is denoted as basic gluon, g*. At short enough distances (shorter than the nucleon radius) or high enough energies, gluons emerge to confine fractional charge quarks. Fractional charge quarks are confined by gluons in QCD (quantum chromodynamics). No isolated fractional charge quark is allowed, and only collective integer charge quark composites are allowed. In general, collective fractional charges are confined by the short-distance confinement force field where the sum of the collective fractional charges is integer [

The third lowest boson (B_{7}) at d = 7 is Z_{L} for the left-handed weak interaction among leptons and quarks. Spontaneous symmetry breaking produces massive weak bosons, massless photon and the Higgs boson as Equation (27). Massive weak bosons produce short-distance interaction. B_{8} at d = 8 is Z_{R} for the right-handed weak interaction among dark matter neutrinos as dark matter neutrino oscillation. The symmetry between Z_{R} and Z_{L} provides the neutrino oscillation for both baryonic matter neutrinos [

B_{9} as the gauge boson represents dark matter repulsive force. The condensed baryonic gas at the critical surface density (derived from the acceleration constant a_{0} in MOND [

B_{10} at d = 10 is for the gauge boson for particle-antiparticle asymmetry to provide the slight excess of particle in particle-antiparticle at the Big Bang, while B_{8} has particle-antiparticle symmetry. (B_{9} emerged long after the Big Bang.) As a result, the excess of particle is α^{4} (2.8 × 10^{−9}) per particle-antiparticle (photon) for the ratio between B_{8} and B_{10}. Since baryonic matter is 1/6 of dark matter and baryonic matter from Equation (33), the baryonic matter excess is 4.7 × 10^{−10} which is in a good agreement with 6 × 10^{−10} for the ratio of the numbers between baryonic matter and photons in the Big Bang nucleosynthesis [

B_{11} is for gravity. F_{11} (8.275 × 10^{16} GeV) relates to spin 3/2 gravitino, while B_{11} (1.134 × 10^{19} GeV) relates to spin 2 graviton. In supersymmetry, gravitino and graviton mediate the supersymmetry between fermion and boson in space dimension and gravitation. There are 11 space dimensions in the 11 spacetime dimensional membrane. As a result, the supersymmetry involves 11 F_{11} + B_{11}, which is equal to 1.225 × 10^{19} GeV in excellent agreement with the Planck mass (1.221 × 10^{19} GeV) derived from observed gravity as (ћc/G)^{1/2} where c is the speed of light, G is the gravitational constant, and ħ is the reduced Planck constant.

Leptons and Quarks

The seven dimensional orbitals are the base for the periodic table of elementary particles [

4b) the formation of the hidden oscillating dimension number universes from 10D to 5D

The negative-mass 10D particle-antiparticle, the positive-mass external gravity, and the negative-mass external gravity are transformed into the hidden oscillating dimension number universes from 10D to 5D.

10 D 4 d → 9 D 5 d → 9 D 4 d → 8 D 5 d → 8 D 4 d → 7 D 5 d → 7 D 4 d → 6 D 5 d → 6 D 4 d → 5 D 5 d → 5 D 4 d (39)

From Equation (19), under the VSLD transformation and the VSD transformation, the three universes expand through the increasing rest mass and the translation-fractionalization from 10D4d to 5D4d. To the positive-mass 4D universe, the three universes from 10D to 5D are hidden, because as mentioned in Section 3.1.2., particles with different space-time dimensions and different speeds of light are transparent and oblivious to one another to avoid the violation of causality due to differences in the speed of light. During this time, the positive-mass 4D universe expands normally.

5) the transformation of all four universes into the 4D universes

When all four universes become 4D, the three other universes become dark energy as a part of the positive-mass 4D universe.

5D4d → 4D5d → 4D4d (40)

The result is the accelerating expansion. Since the other three universes have no detachment space to produce kinetic energy, dark energy is inert as the inert cosmological constant. As these three universes can take the form of a cosmological constant, the field equations are modified to

R μ ν − 1 2 R g μ ν + Λ g μ ν = 8 π G c 4 ( T μ υ + + T μ υ − + C μ υ ) (41)

where R_{μν} is the Ricci curvature tensor, R is the scalar curvature, g_{μν} is the metric tensor, Λ is the cosmological constant, G is Newton’s gravitational constant, c is the speed of light in vacuum, T μ υ + is the positive stress-energy tensor for the positive-mass universe, T μ υ − is the positive-negative stress-energy tensor for negative-mass universe, negative-mass external gravity, and positive-mass external gravity, and C_{μν} is the creation tensor for negative-mass universe, negative-mass external gravity, and positive-mass external gravity.

The ratio of the time periods for the transformations from D → D - 1 is proportional to ln of the total number of particles (Equation (22)) to be transformed from D → D - 1 for the exponential growth with time as in

The maximum dark energy is 75% for the three out of the four universes, when the spacetime numbers of all particles are 4. The observed % of dark energy is 68.6, and our universe is 13.8 billion-year old [

6) the positive-mass 4D universe and the three hidden oscillating dimension number universes from 5D to 9D

The three oscillating universes from 5D to 10D again become the hidden universes.

4 D 4 d → 5 D 4 d → 5 D 5 d → 6 D 4 d → 6 D 5 d → 7 D 4 d → 7 D 5 d → 8 D 4 d → 8 D 5 d → 9 D 4 d → 9 D 5 d (42)

They contract by the decreasing rest mass and the translation-condensation. The positive-mass 4D universe contracts through gravity. Through symmetry, all four universes contract synchronically and equally.

7) the return to the 10D4d particle-antiparticle universes (step 3)

Eventually, the oscillating universes return to the original 10D. The positive-mass 4D universe reaches the Big Crush to lose all detachment space to become 4D10d, and followed by the deflation to transform into 10D4d. The four universes return to the step 3.

From the step 3, the universes can undergo another cycle of the particle-antiparticle universes, or can reverse to the step 2 for the string-antistring dual universes, to the step 1 for the membrane-antimembrane dual universes, and ultimately, to the zero-mass inter-universal void.

As mentioned in the previous section, with positive mass dark matter, the Navarro-

10D → 9D | 9D → 8D | 8D → 7D | 7D → 6D | 6D → 5D | 5D → 4D | |
---|---|---|---|---|---|---|

ratio of total numbers of particles | 1 | α^{−2 } | α^{−4} | α^{−6} | α^{−8} | α^{−10} |

ratio of ln (total number of particles) | 0 | −2lnα | −4lnα | −6lnα | −8lnα | −10lnα |

ratio of periods in time | ~0 | 1 | 2 | 3 | 4 | 5 |

percentages of periods in time | ~0 | 6.7 | 13.3 | 20 | 26.7 | 33.3 |

Frenk-White (NFW) profile [

Another unsolved problem is central supermassive black hole (SMBH) that is located in most massive galaxies. Its origin remains unclear because the greatest difficulty to any theory of SMBH formation has been the observation of very massive (M ≈ 10^{9} M_{⊙}) quasars with SMBH already in place by z ≈ 7, when the universe is just ≈ 800 Myr old long before any stars could grow big or old enough to collapse under their own mass, explode in a supernova and form a black hole [

A new unsolved problem is the recent discovery of a cold, massive, rotating disk galaxy (the Wolfe Disk) 1.5 billion years after the Big Bang [

In this paper, dark matter with and without repulsive force provides an answer to all three unsolved problems, and explains protogalaxy evolution and galaxy evolution. This paper proposes that the condensed baryonic gas at the critical surface density induces the creation tensor for dark matter repulsive force to transform dark matter in the region into repulsive dark matter repulsing one another. Repulsive dark matter removes the DM (dark matter) core-cusp, and provides stabilities for SMS and large protogalaxy before the formation of a large galaxy. Without repulsive dark matter, the universe would have been filled with “train wrecks” without large galaxy structures.

Protogalaxy evolution consists of six steps: 1) Small Core-Cusp Protogalaxy (BM-DM core cusp-halo), 2) Large Core-Cusp Protogalaxy (BM-DM core cusp-halo), 3) Streaming Protogalaxy (streaming BM core-static BM shell-DM halo), 4) SMBH Protogalaxy (central SMBH-streaming BM core-static BM shell-DM halo). 5) Bulge Protogalaxy (central SMBH-bulge-streaming BM core-static BM shell-DM halo), and 6. Protogalaxy Termination (central SMBH-bulge-combined BM shell-DM halo) as

1) The Small Core-Cusp Protogalaxy Step

Quantum fluctuations in the matter distribution were created in the first fraction of a second during an inflationary period. Gravitational instability grew these fluctuations over time. Baryonic matter and dark matter without dark matter repulsive force were initially well mixed. Dark halos emerged as gravitationally bound regions of matter that have decoupled from the cosmic expansion and collapsed. Dark matter haloes were formed as in N-body collisionless dark matter simulations. They followed the NFW profile where the highest density is at the center as the core cusp [

2) The Large Core-Cusp Protogalaxy Step

Dark matter halo structure formation is bottom-up merge with small dark matter haloes forming first. The baryonic gas content can contract together with the dark matter only in dark halos above the cosmological Jeans mass, MJ ≈ 10^{4} M_{⊙}[(1 + z)/11]^{3/2}, in which the gravity of dark matter can overwhelm thermal gas pressure [

3) The Streaming Protogalaxy Step

The condensed baryonic gas at the critical surface density (derived from the acceleration constant a_{0} in MOND [

4) The SMBH Protogalaxy Step

Primordial halos expose to highly supersonic baryon streaming motions [^{7} - 10^{8} M_{⊙} that trigger rapid atomic cooling and catastrophic baryon collapse to start forming SMSs at central infall rates of up to ≈1 M_{⊙} yr^{−}^{1} in the atomically cooled protogalaxies [^{5} M_{⊙} undergoes direct collapse black hole (DCBH) without supernova to produce the central SMBH [

5) The Bulge Protogalaxy Step

The incoming streaming baryons during the protogalaxy collapse accelerated the growth of the SMBH. Eventually, the radiation from the SMBH reduced greatly the streaming motion of the incoming streaming baryons, and the SMBH was decoupled from the streaming BM core as described by Joseph Silk, Martin Rees, and Andrew King [

6) The Protogalaxy Termination Step

Eventually, without streaming, the streaming BM core and the static BM shell were combined into the combined region, resulting in the SMBH-bulge-combined BM shell (streaming BM core + the static BM shell)-DM halo. The protogalaxy termination means the end of the protogalaxy collapse. The protogalaxy termination step started galaxy evolution when the star formation in the combined region in a large galaxy became active.

Elliptical galaxies are mildly flattened, and are mainly supported by the random motions of their stars. Spiral galaxies, on the other hand, have highly flattened disks that are mainly supported by rotation of their stars. Most elliptical and spiral galaxies have both with the ellipsoidal component called the bulge. Irregular galaxies do not have definite shape and the bulge. In this paper, the morphology of galaxies is derived from the monolithic heterogeneous protogalaxy collapse which produced both SMBH and galaxies. Essentially as described in this section, the protogalaxies with the small DM core cusp produced elliptical galaxies, the protogalaxies with the large DM core cusp produced spiral galaxies, and the protogalaxies with the very large DM core cusp produced irregular galaxies.

1) The Formation of Elliptical Galaxy

The progenitor of elliptical galaxy is the protogalaxy with small DM core cusp and large BM shell. The ejection of dark matter from a small DM core cusp resulted in a small empty core which was filled by the streaming baryons to form a small streaming BM core surrounded by a large static BM shell. In terms of star formation, the normal star formation took place only in the large BM shell, while the SMS and DCBH formation took place only in the small streaming BM core. The large amount of baryon gas was depleted by the star formation in the large static BM shell. The stars are in random orbits around the center. The protogalaxy collapse caused the slight flattering of the protogalaxy into elliptical shape whose lengths of major axes are proportional to the relative sizes of the DM core cusp. The early large consumption of gas by the star formation in the large static BM shell depleted large amount of baryon gas, so elliptical galaxies now have very few young stars.

During the early universe, large protogalaxies accreted the surrounding small and medium protogalaxies, and turned them into metal-poor globular clusters without external dark matter haloes [

2) The Formation of Spiral Galaxy and Barred Spiral Galaxy

The progenitor of spiral galaxy is the protogalaxy with large DM core cusp and small BM shell. The ejection of dark matter from a large DM core cusp resulted in a large empty core which was filled by the streaming baryons to form a large streaming BM core surrounded by a small static BM shell. During the protogalaxy collapse, the streaming baryons initially formed a dense cloud at the center of the streaming BM core. The infalling streaming baryons toward the dense cloud at the center produced the rotational baryon cloud due to the conservation of angular momentum, similar to the rotational cloud during the collapse of the cloud. Eventually, the whole streaming BM core and then the whole protogalaxy became rotational. (In the progenitor of elliptical galaxy, the streaming BM core was too small to rotate the whole protogalaxy.) The stars orbit around the center.

After the termination of protogalaxy collapse, the collapsed protogalaxy consisted of central SMBH-bulge-combined BM shell-DM halo. After the end of the protogalaxy, the protogalaxy underwent differential rotation with the increasing angular speeds toward the center. After few rotations, the protogalaxy turned into the spiral structure consisting of the center disk with the pre-existed bulge-SMBH at the center and the attached spiral arms. The arms consisted of the low density gas regions and the high density gas regions. The high density gas regions hindered the rotational movement of the low baryon gas, so the low baryon gas formed the large high density regions behind the high density gas regions. After few rotations, all large high density regions coalescent into few major arms at the minimum rotational velocities as the high density waves described in the density wave theory by C. C. Lin and Frank Shu [

Without the early large depletion of baryon gas in the small BM shell and with the radiation from SMBH and stars to retard the star formation rate, spiral galaxies

and barred spiral galaxies now have many young stars and large amounts of interstellar gas. The stars form in the spiral arms much later than in the bulge and the bar, so they are many young stars in the spiral arms. The lengths of the spiral arms are proportional to the relative sizes of the DM core cusp as the lengths of major axes proportional to the relative sizes of the DM core cusp in elliptical galaxies.

3) The Formation of Irregular Galaxy

If the size of the DM core cusp was very large, the streaming dark matter in the DM core cusp streamed outward, and not enough baryonic matter particles from the BM-DM halo streamed inward to form SMS. Eventually, the protogalaxy became fragmented, resulting in irregular galaxy.

In summary, this paper modifies the Farnes’ unifying theory of dark energy and dark matter which are negative-mass to be created continuously from the negative-mass universe in the positive-negative mass universe pair. The first modification explains that observed dark energy is 68.6% greater than 50% for the symmetrical positive-negative mass universe pair. This paper starts with the proposed positive-negative-mass 11D universe pair (without kinetic energy) which is transformed into the positive-negative mass 10D universe pair and the external dual gravities as in the Randall-Sundrum model, resulting in the four equal and separate universes consisting of the positive-mass 10D universe, the positive-mass massive external gravity, the negative-mass 10D universe, and the negative-mass massive external gravity. The positive-mass 10D universe is transformed into 4D universe (home universe) with kinetic energy through the inflation and the Big Bang to create positive-mass dark matter which is five times of positive-mass baryonic matter. The other three universes without kinetic energy oscillate between 10D and 10D through 4D, resulting in the hidden universes when D > 4 and dark energy when D = 4, which is created continuously to our 4D home universe with the maximum dark energy = 3/4 = 75%. In the second modification to explain dark matter in the CMB, dark matter initially is not repulsive. The condensed baryonic gas at the critical surface density induces dark matter repulsive force to transform dark matter in the region into repulsive dark matter repulsing one another, corresponding to the Farnes’ repulsive dark matter. In this way, a galaxy actually started with a dark matter core-cusp without repulsive dark matter. The removal of the core cusp by repulsive dark matter afterward solves many difficult problems in protogalaxy and galaxy evolutions.

Protogalaxy evolution consists of six steps: 1) small core-cusp protogalaxy (BM-DM core cusp-halo), 2) large core-cusp protogalaxy (BM-DM core cusp-halo), 3) streaming protogalaxy (streaming BM core-static BM shell-DM halo), 4) SMBH protogalaxy (central SMBH-streaming BM core-static BM shell-DM halo), 5) bulge protogalaxy (central SMBH-bulge-streaming BM core-static BM shell-DM halo), and 6) protogalaxy termination (central SMBH-bulge-combined BM shell-DM halo) as ^{7} - 10^{8} M_{⊙} that triggered rapid atomic cooling and catastrophic baryon collapse, resulting in the supermassive star (SMS) formation in the atomically-cooled streaming BM core. The collapse of the SMS at a few 10^{5} M_{⊙} produced the DCBH for the central SMBH. The bulge was generated in the streaming BM core surrounding the SMBH afterward. During and after the protogalaxy collapse, the star formations produced different types of galaxies (elliptical, spiral, barred spiral, and irregular). Essentially, the protogalaxies with the small DM core produced elliptical galaxies, the protogalaxies with the large DM core produced spiral-barred spiral galaxies, and the protogalaxies with the very large DM core produced irregular galaxies.

According to the theoretical calculation, the calculated percentages of dark energy, dark matter, and baryonic matter are 68.6 (as an input from the observation), 26, and 5.2, respectively, in agreement with observed 68.6, 26.5, and 4.9, respectively, and dark energy started in 4.33 billion years ago in agreement with the observed 4.71 ± 0.98 billion years ago. In conclusion, the modified Farnes’ unifying theory reinterprets the Farnes’ equations, and is a unifying theory of dark energy, dark matter, and baryonic matter in the positive-negative mass universe pair. The unifying theory explains protogalaxy and galaxy evolutions in agreement with the observations.

The author declares no conflicts of interest regarding the publication of this paper.

Chung, D.-Y. (2020) A Unifying Theory of Dark Energy, Dark Matter, and Baryonic Matter in the Positive-Negative Mass Universe Pair: Protogalaxy and Galaxy Evolutions. Journal of Modern Physics, 11, 1091-1122. https://doi.org/10.4236/jmp.2020.117069