Early Universe Plasma Separation and the Creation of a Dual Universe

The Planck Legacy recent release revealed a closed and positively curved early universe with a confidence level greater than 99%. In this study, the Friedmann–Lemaîtree– Robertson–Walker (FLRW) metric is enhanced to model early universe plasma, incorporating its reference curvature radius upon the emission of the cosmic microwave background (CMB) and the reference scale factor of the energy flux. The universe evolution from early plasma is modelled utilising quantised spacetime worldlines, where they revealed both positive and negative solutions implying that matter and antimatter in the plasma could be separated by electromagnetic fields and evolved in opposite directions as distinct sides of the universe, corroborating the CMB dipole anisotropy. The model indicates a nascent hyperbolic expansion is followed by a first phase of decelerating expansion during the first ~10 Gyr, and then, a second phase of accelerating expansion. The model theoretically resolves the tension in Hubble parameter measurements, with a predicted density at the phase transition of ~1.16. Further, it predicts a final time-reversal phase of rapid spatial contraction leading to a Big Crunch, signalling a cyclic universe. Simulations of the quantised spacetime continuum flux through its travel along the predicted worldlines demonstrated the fast-orbital speed of stars resulting from an external momentum exerted on galaxies via the spatial curvature through imaginary time dimension. These findings indicate that early universe plasma could be separated and evolved into distinct sides, collectively and geometrically influencing the universe evolution.


INTRODUCTION
Advances in cosmology and astronomical observations over the last two decades have revealed many inconsistencies with the standard model of cosmology of a spatially flat universe, the lambda cold dark matter model (ΛCDM). The recent Planck Legacy (PL18) release indicated the existence of an enhanced lensing amplitude in the CMB, which is higher than that estimated by ΛCDM. This endorses a closed and positively curved early universe with a confidence level more than 99% (Aghanim et al., 2020;Di Valentino, Melchiorri and Silk, 2020). Besides, the observed gravitational lensing by substructures of several galaxy clusters is an order of magnitude more than that estimated by ΛCDM (Meneghetti et al., 2020;Umetsu, 2020). Furthermore, the well-known 120 orders of magnitude discrepancy between the estimated vacuum energy density by ΛCDM for a flat accelerated expanding universe and the energy cutoff calculations of the vacuum energy density by the quantum field theory (QFT) (Rugh and Zinkernagel, 2000). Therefore, this evidence endorses a spatially curved universe in spite of the spacetime flatness of the local/present universe.
The early universe was composed of hot and opaque plasma at thermal equilibrium and highest density (Weinberg, 1972;Holcomb and Tajima, 1989), whereas the expansion of the closed early universe reduced universe's density and increased its entropy. In contrast with the ΛCDM assumption of antimatter elimination, the matter and antimatter in the plasma could be separated by electromagnetic fields (Klein, 1966(Klein, , 1971 due to the plasma drift phenomenon, consequently, evolving in opposite directions. This scenario corresponds the CMB dipole anisotropy and the quantum electrodynamics theory (QET), where advanced measurements of the fine structure of hydrogen and antihydrogen atoms were found to be consistent with predictions of QET with a precision of 2%, including the Lamb shift feature (Ahmadi et al., 2020). These measurements corroborate the concept of identical matter and antimatter apart of their opposite charge and spin, which can undermine the elimination assumption. Sings of plasma separation or a significant predominant event might be observed as the associated noise surrounding the measured gravitational waves (Creswell et al., 2017). Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 17 December 2020 doi:10.20944/preprints202005.0250.v8 In 2020, Riess found that the expansion of the universe is faster than ΛCDM estimations with the disagreement between measurements taken from the early universe based on the CMB and the present universe using the type Ia supernovae distanceredshift method is four to six standard deviations (Riess, 2020), while Ryskin demonstrated that the vacuum energy cannot be inducing this accelerated expansion (Ryskin, 2020). Further, ΛCDM assumes a homogeneous and isotropic universe on large scales. Although this assumption could be consistence with the early universe, the observed voids and galaxy filaments indicate an anisotropic universe (Albert Robson, 2019). Besides, the universe expanding rate is observed to vary depending on the direction while precise measurements of the fine structure constant over multiple directions in several studies revealed it varies with time and across a specific axis (Uzan, 2011;Wilczynska et al., 2020). This indicates a strong anisotropy at a five-sigma confidence level (Migkas et al., 2020). Therefore, emerging evidence supports a growing need for profound adjustments to ΛCDM or new physics (Lusso et al., 2019).
In this study, an alternative cosmological model of a closed early universe is considered. The universe evolution from the early universe plasma is modelled utilising quantised spacetime continuum worldlines. The paper is organised as follows. Section 2 presents the plasma modelling, its boundary contribution and the derivation of the quantised worldlines. Sections 3 discusses the universe evolution and its expansion rate while Section 4 simulates the curvature of the universe and the spiral galaxy orbital speed. Section 5 summarises the outcomes and conclusions. Finally, Section 6 suggests future works.

Mathematical Model
In addition to the PL18 evidence of a positively curved early universe, the closed finite universe can provide an agreement with the CMB anisotropy observations (Efstathiou, 2003) and could explain the quantum entanglement (QE), where the energy of the finite universe is conserved, thus cosmic conservation governs the total spin of a pair of particles to be conserved regardless of their locations. Otherwise, unpreserved total spin breaks energy conservation of the finite closed universe (Al-Fadhli, 2020b).
The measured gradual variation in the finestructure 'constant' (Donoghue, 2003;Uzan, 2011;Wilczynska et al., 2020) can be a result of the evolution of the universe's density due to its expansion, which affects the travel speed of light. These measurements may reveal that the presumed fundamental constants might be dependent on other universe properties.
According to Mach's principle, Schrödinger in 1925 pointed to the reliance of the Newtonian gravitational 'constant' on the distribution of universe's masses and the universe's radius of curvature while Dirac in 1938 proposed its correlation to the universe's age (Dirac, 1938), i.e., and could be functions of the conformal time .
Alternatively, this study sought a fundamental constant relying on the energy conservation law, as it is a firm fundamental law within a closed system (closed universe). Because of the spacetime curving nature according to general relativity (GR), a new constant is defined as spacetime continuum modulus of deformation/curvature . Spacetime is regarded as a continuum having a dual quantum nature that it curves as waves and, travels as quantum particles at the speed of light; where the latter is justified due to the energy flux from early universe plasma into space at the speed of light creating 'spacetime continuum', 'quintessence', 'vacuum energy', or 'darknesses'. Recent findings regarding light polarization from the CMB support the existence of an exotic substance through space causing these measured polarizations (Minami and Komatsu, 2020). This corroborates the concept of spacetime continuum quantum duality. By using Einstein field equations, =(stress/strain) in ( / 2 ) is expressed as where the stress is signified by the stress-energy tensor of trace , while the strain is signified by the Ricci curvature tensor as the change in curvature divided by ℛ = 1/ 2 , the scalar of the preexisting curvature, and is the universe curvature radius. According to the theory of elasticity, the modulus times the volume equals the internal energy of reversible systems (Landau, 1986). Thus, could represent the internal energy density of the space (vacuum energy density).
is proportional to the fourth-order of , resembling the QFT energy cut-off prediction of the vacuum energy density (Rugh and Zinkernagel, 2000). Further, because the modulus is a constant (Landau, 1986), Eq. (1) confirms the reliance of on the universe curvature radius . By incorporating the background/pre-existing universal curvature as function of the conformal time represented by the scalar curvature ℛ while is utilised to maintain the compatibility of the extended Einstein-Hilbert action as where is the Ricci scalar curvature, ℒ is the Lagrangian density and is the determinant of the metric tensor .
The derivations of the extended action are given in (Al-Fadhli, 2020a) as The extended field equations in Eqs.
(3) consist of the conformally transformed Einstein field equations and the boundary term, in addition to the energy-stress term on the right-hand side; where ̂= + 2 ̅ = + 2ℛ /ℛ is the conformal transformation of the metric tensor due to the fact that Einstein spaces are a subclass of the conformal space (Kozameh et al., 1985).
is the extrinsic curvature tensor and ̂ denotes the conformally transformed induced metric tensor on the spacetime boundary manifold. The conformal transformation can describe the tidal distortion of gravitational waves in the absence of matter (Penrose, 2005) and the galaxy rotation curve as it accounts for the universe curvature evolution over the universe's age. The boundary tensor/term is only significant at the high-energy limit such as in black holes (Dyer and Hinterbichler, 2009) and the early universe, and can remove the singularities from the theory.

Early Universe Plasma Model
The FLRW metric is the standard cosmological metric model, which assumes an isotropic and homogenous universe (Ellis and van Elst, 1998;Lachì Eze-Rey and Luminet, 2003), where the isotropy and homogeneity of the early universe plasma based on the CMB are consistent with this metric model. The PL18 release revealed a closed and positively curved early universe. Therefore, the plasma reference radius of curvature upon the emission of the CMB and the corresponding early universe scale factor of the energy flux as shown in Figure 1 at the reference time are incorporated to enhance the metric model. Thus, the four-dimensional spacetime interval of the enhanced metric is where / is the new dimensionless scale factor and , , are the comoving coordinates. Accordingly, the metric components are No conformal distortion is included in this metric, so its outcomes are comparable with literature. Figure 1 shows the enhanced metric model of the of early universe plasma expansion where , , and are the Hubble parameter, pressure, and density respectively. The equations do not show a conformal distortion as the conformal transformation is not applied in the current study.

Universe Evolution Model
The Friedman equations in Eqs. (7,8) are solved over the imaginary conformal time of one universe life cycle by rewriting Eq. (7) in terms of the imaginary conformal time in its parametric form = − while initiating at the reference imaginary time as Ryden, 2006) and is a function of the imaginary time = . By integrating, the scale factor evolution is 3 is the plasma mass and is the gravitational parameter value at . The constant in Eq. (10) can be written more fundamentally in terms of the modulus representing the vacuum energy density and the universe energy density using Eq.
(1) as /6 . Additionally, the evolution of the imaginary time ( ) can be obtained by integrating the length of the spatial factor contour of one universe life cycle over the expansion speed while initiating at the reference imaginary time with the corresponding spatial factor . Thus, by rewriting Eq. (10) where denotes the reference imaginary time. According to the energy conservation law, the stress-energy tensor divergence vanishes, ∆ , this yields By combining these outcomes, integrating, and then substituting the spatial scale factor rate in Eq. (10) to their outcome, the universe density evolution over the conformal time is where is a constant. According to Eq. (8), the Hubble parameter is dependent on the density; thus, by substituting Eq. (13) to Eq. (8) and initiating the integration at thus, ̇=̈ as By integration, the Hubble parameter evolution is where, = 3 and is the integration constant.
Combining Eqs. (10,(12)(13)(14)(15) in the complex frame results in the quantised hyper-spherical spacetime continuum wave function with respect the reference radius of curvature as the third quantisation: The third quantisation denotes the wave function ⃗⃗⃗⃗ ( ) of the spacetime continuum evolution that simultaneously propagates in space and oscillates in time where / denotes a new dimensionless energy parameter as the ratio of the universe energy density to vacuum energy density. Additionally, under Weyl's quantum phase invariance (gauge invariance) ( ) = ( ) ( ) (Straub, 2006).

Plasma Boundary Contribution
The positive and negative solutions of the quantised spacetime continuum wave function in Eq. (16) imply that matter and antimatter in the plasma are evolving in opposite directions. The plasma drift phenomenon is caused by the presence of the electromagnetic fields (Klein, 1966(Klein, , 1971. In early plasma case consisting of matter and antimatter, the drift phenomenon drives matter and antimatter in opposite directions as they have an opposite electrical charge (Figure 2). For high energy limits, the gravitational contribution of the plasma boundary can be obtained using the boundary term in the extended field equations in Eqs.
(3), where at the reference imaginary time , there is no conformal transformation. Therefore, the induced metric on the plasma hypersphere boundary is given in Eqs. (17) (Pavel Grinfeld, 2013).
The extrinsic curvature tensor is solved utilising the formula = − ⃗⃗⃗ . ∇ ⃗⃗⃗⃗ . Due to the symmetry of the plasma hypersphere, the covariant derivative reduces to the partial derivative as follows The trace of the extrinsic curvature is = = −2/ . The Gaussian curvature (intrinsic curvature) equals one over the square the radius of curvature. Thus, the pre-existing scalar curvature of the plasma boundary at is ℛ = 1/ 2 . On the other hand, the Ricci scalar curvature at can be written as the difference between kinetic and potential energy densities whereby substituting Friedmann equations in Eqs.
By multiplying both sides by the plasma volume and simplifying, the reference radius of curvature is then The reference curvature radius > 0 because any reduction in the plasma volume causes an increase in its pressure, whereas it is the smallest possible radius of the universe.

Spacetime Continuum Worldlines
A chosen mean evolution value of the Hubble parameter of ~70 km•s-1 •Mpc -1 and a phase transition of expansion at universe age of ~10 Gyr are utilised to tune the integration constants of the derived model in Eq. (16) where the predicted energy density at the phase transition is ~1.16. The cosmic evolution of radiation coupled with matter/antimatter according to the quantised wave function model in Eq. (16) is predicted to experience three distinct phases, where due to symmetry, only the positive solution of one universe side is shown in Figure 3.
Firstly, the matter and antimatter sides of the universe expand in opposite directions away from the early universe plasma where they would be blue and red-shifted, corresponding the CMB dipole anisotropy. During the first phase (i.e., the first ~ 10 Gyr), the gradients of the worldlines indicate the expansion is decelerating. The expansion rate is discussed in detail in the next section. Though, in the second phase, the worldlines reverse their directions, with both sides entering a state of free fall towards each other. It is conceivable that both sides of matter and antimatter are free-falling towards each other at gravitational acceleration causing current accelerated expansion. The gradients of worldlines at this phase show an accelerated rate. Hyper-spherical Radius Interestingly, the model predicts a third phase of spatial contraction with a reversal-time arrow that appears after ~ 18 Gyr. In this phase, the universe experiences a contraction, which could be due to a high concentration of matter/antimatter at both sides, leading to the Big Crunch.
The free fall of both sides towards each other at gravitational acceleration can provide a physical explanation of current accelerated expansion while vacuum energy was found to be not accountable for this acceleration (Ryskin, 2020). Further, at the second phase, both sides are getting closer towards each other, which explains the reason behind the current increase in the average temperature of the universe (Chiang et al., 2020) in contrast to the state of cooling down from hot plasma during the first phase.

Evolution of the Hubble Parameter
The Hubble parameter, or the speed of spatial expansion, , and the acceleration ̇ can be determined using Eqs. (15) and (13 in 8), respectively. The predicted speed and acceleration of the spatial expansion are shown in Figure 4. The Hubble parameter, depicted by the blue curve, starts with a hyperbolic expansion at the nascent stages upon plasma separation event where the speed is at its highest value. Then, the speed of expansion decreases during the first ~10 Gyr, due to gravity, until it reaches its minimal value at the phase transition at ~10 Gyr. Next, the Hubble parameter starts to increase in the reverse direction (the negative sign for the speed in the second phase indicates the opposite direction, as shown in Figure 3), which is the result of both sides starting to free-fall towards each other under gravitational acceleration. The Hubble parameter then reaches its zenith as it nears the Big Crunch.
According to the mechanics, the opposite signs of the acceleration (green curve) and the expansion speed in the first phase indicate that the expansion rate is slowing down, while the matching signs in the second phase indicate that the expansion speed is increasing, i.e., accelerated expansion. Additionally, a rectified Hubble parameter, indicated by the orange curve, reflect expansion in the opposite direction during the second phase, so the integration constants are tuned to guide the mean evolution value of the parameter at ~70 km•s -1 Mpc -1 .

Simulation of Spacetime Continuum Curvature
The spacetime worldlines of a single side are simulated based on the derived model in Eq. (16) along with nearby spacetime continuum worldlines corresponding to the early and present universe, as shown in Figure 5. In the early universe, simulations of spacetime worldline evolutions coupled with flat and positive initial curvatures are not equal at any age during the first phase, as shown in Figure 5a. This can reveal that the spacetime is curved similar to the curved surface of a ball, which aligns with early universe positive curvature observation according to PL18 (Di Valentino, Melchiorri and Silk, 2020).
Conversely, for the present accelerated phase of expansion in the reverse direction, the simulation of the evolution of spacetime worldlines coupled with positive initial curvature produce a flat end or flat spacetime, as shown in Figure 5b.  According to the derived model in Eq. (16) shown in Figure 3 and the simulated spacetime curvature in Figure 5, a schematic of a 2D spatial and 1D temporal dimensions is shown in Figure 6a, while radiation only worldlines according to Eq. (16) are predicted to pass from one side to another, which can explain the reason behind observing the CMB light while matter moves much slower than light. Figure 6b shows an approximate apparent topology due to gravitational lensing effects.

Simulation of a Spiral Galaxy
The consistent patterns of the galactic rotation curves observed using precise and independent galactic redshift data have confirmed that hydrogen clouds and outermost stars are orbiting galaxies at speeds faster than those calculated using Newtonian laws. Accordingly, the dark matter hypothesis was introduced to account for the apparently missing galactic mass and explain these fast-orbital velocities (Mannheim and Kazanas, 1989;Sofue and Rubin, 2000). However, no evidence for the existence of dark matter, which is hypothesised to account for the majority of galactic mass, has been observed since its introduction. The failure to find dark matter led to the introduction of new theories such as modified gravity and modified Newtonian dynamics (Chadwick, Hodgkinson and McDonald, 2013;Brouwer et al., 2016;Maeder, 2017;Van Meter, 2018;Milgrom, 2019).
Several recent studies have reported that many galaxies do not contain dark matter (Guo et al., 2019).
This scenario was used to inform galaxy formation simulations using modified Newtonian dynamics without considering the effects of dark matter (Wittenburg, Kroupa and Famaey, 2020). Therefore, it seems that there is no evidence for (or agreement on) the existence or nature of dark matter, and it may not be an essential requirement for galaxy formation.
Alternatively, because the shapes of spiral galaxies are highly similar to vortex shapes, a spiral galaxy can be modelled as a forced vortex, where external momentum is exerted on galaxies by the spacetime continuum curvature along its worldline evolutions. The derived model in Eq. (16)   The simulation shows that the tangential speeds of outer parts of the spiral galaxy are rotating faster in comparison with the rotational speeds of inner parts.
Additionally, the galaxies of the same mass in the present universe were found to rotate faster than they were in the past because of the increase in the external momentum due to the highest spatial curvature at the phase transition. These results agree with the Tully-Fisher relation (Tully and Fisher, 1977). Based on the simulation results, it can be concluded the spacetime continuum curvature along its worldline evolution is responsible for the high speed of galaxies, explaining the effects attributed to dark matter.

Conclusions
In this study, the plasma of the early universe was modelled utilising enhanced FLRW metric. The evolution of the universe from early plasma was model utilising quantised spacetime continuum worldlines. The worldlines revealed two opposite solutions revealing that the universe has two sides: matter and antimatter.
The derived model predicted that a nascent hyperbolic expansion is followed by a phase of decelerating spatial expansion during the first ~ 10 Gyr, followed by a second phase of accelerating Crunch, signifying a cyclic universe. The derived smallest possible reference radius of the early plasma due to its boundary gravitational contributions can reveal the early universe expansion upon emission of the CMB might mark the beginning of the universe from a previous collapse one.

Future Work
The integration constants of the derived model could be fine-tuned based on the astronomical data to accurately estimate the evolution of the universe. The accurate age could be calculated using the derived model in future works.
Funding: This research received no funding.

Acknowledgements: I am grateful to the Preprints
Editor Ms Mila Marinkovic for her rapid and excellent attention in processing the submissions.

Conflicts of Interest:
The author declares no conflict of interest

Appendix A
The Ricci curvature tensor is solved using the Christoffel symbols of the second kind for the extended metric tensor in Eq. (5), which are Firstly, the solved non-zero Christoffel symbols are The − component is Thirdly, the inverse metric tensor is