Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 April 2021 doi:10.20944/preprints202005.0250.v9 On Spacetime Quantum Duality and Bounce Cosmology of a Dual Universe Mohammed. B. Al-Fadhli1* 1College of Science, University of Lincoln, Lincoln, LN6 7TS, UK. *Correspondence: [email protected]; [email protected] Abstract: The recent Planck Legacy release confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra, which endorses the positive curvature of the early Universe with a confidence level exceeding 99%. In this study, the pre-existing curvature is incorporated to extend the field equations where the derived wave function of the Universe is utilized to model Universe evolution with reference to the scale factor of the early Universe and its radius of curvature upon the emission of the CMB. The wave function reveals both positive and negative solutions, implying that matter and antimatter of early Universe plasma evolve in opposite directions as distinct Universe sides. The wave function indicates that a nascent hyperbolic expansion is followed by a first phase of decelerating expansion away from early plasma during the first ~10 Gyr, and then, a second phase of accelerating expansion in reverse directions, whereby both Universe sides free-fall towards each other under gravitational acceleration. Simulations of the predicted conformal curvature evolution demonstrate the fast orbital speed of outer stars owing to the external fields exerted on galaxies as they travel through conformally curved space-time. Finally, the wave function predicts an eventual time-reversal phase comprising rapid spatial contraction that culminates in a Big Crunch, signalling a cyclic Universe. These findings reveal that early plasma could have separated and evolved into distinct sides that collectively and geometrically influencing the Universe evolution, physically explanting the effects attributed to dark matter and energy. Keywords: Accelerated Expansion; Fast orbital speed of outer stars; Duality; Antimatter. 1. INTRODUCTION Bounce cosmology provides an alternative view The Planck Legacy PL18 release confirmed the of the Universe, in which our Universe expanded existence of an enhanced lensing amplitude in the from a hot and very dense state of a previous collap- power spectra of the CMB [5]. Notably, it is more than sed Universe [1]. This cosmology is free from the that estimated by the lambda cold dark matter model singularity problem and offers a clearer view of the (ΛCDM), which endorses the positive curvature of early Universe. However, the null-energy condition the early Universe with a confidence level more than is generally violated by the conjectured bounce of re- 99% [5,6]. Besides, the observed gravitational lensing expansion in several modified gravity theories [2]. by substructures of several galaxy clusters is an order Alternatively, this bounce could be realized through other scenarios, such as the phenomenon of plasma of magnitude higher than that estimated by the drift in the presence of electromagnetic fields. In this ΛCDM [7,8]. This endorses a curved Universe despite sense, matter and antimatter in early Universe of the present/local space-time flatness. plasma could be separated by primordial electro- The presumed concepts of dark energy, dark magnetic fields upon the emission of the cosmic matter, and antimatter early elimination are being microwave background (CMB), thereby evolving in challenged by new observations and measurements. opposite directions owing to their opposite spin and Riess in 2020 found the Universe expansion is faster charge. The plasma separation until and under the than the ΛCDM estimates [9] while Ryskin showed right conditions would allow the collapsed state to that vacuum energy cannot be causing the acceler- achieve thermal equilibrium while the gravitational ated expansion [10]. In addition, external field effect contributions of early Universe plasma boundary that influence galactic rotation curves were detected could realize a singularity-free paradigm. Signs of the at up to 8σ to 11σ, challenging traditional dark matter plasma separation or a significant predominant event concepts [11]. Additionally, advanced measurements might be observed as associated noise surrounding of the fine structure of hydrogen and antihydrogen the measured gravitational waves [3]. Additionally, atoms were found to be consistent with Quantum the magnetic fields that presently pervade the Electrodynamics Theory predictions at a margin of Universe at all probed scales favour a primordial 2%, including the Lamb-shift feature, undermining origin of this kind [4]. elimination assumptions [12]. 1 © 2021 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 April 2021 doi:10.20944/preprints202005.0250.v9 Accordingly, a closed early Universe model is is consistent with Mach’s principle, the reliance of the considered in this study to approach the problems of small structure on the larger structure. Schrödinger in accelerated expansion and fast orbital speed of stars 1925 pointed to the reliance of 퐺푡 on the distribution from a new perspective. The closed finite Universe of Universe’s masses and the Universe’s radius while can provide an agreement with the CMB anisotropy Dirac in 1938 proposed its correlation to the age of the observations [13] and could explain the quantum Universe [16]. The evolution in 퐺푡 can be endorsed entanglement, where the total Universe energy is by the measured gradual evolution in the fine- finite; thus, cosmic conservation preserves the total structure ‘constant’ [17–19], which can reveal that the spin of a pair of particles regardless of their locations presumed fundamental constants may rely on other [14]. The pre-existing curvature is considered to properties of the Universe. extend the field equations and the evolution of the On the other hand, 퐸퐷 is in terms of energy Universe from early plasma is modelled by utilising density and represents the continuum’s resistance to the Universe wave function. This paper is organised deformation [20]. Eq. (1) shows 퐸퐷 is proportional to as follows. Section 2 presents the extended field the fourth-power of the speed of light, which, in turn equations. Sections 3 and 4 discuss the Universe directly proportional to the frequency; in accordance model, its evolution, and its minimal radius while with the frequency cut-off predictions of the vacuum Section 5 presents the spiral galaxy simulation under energy density in the Quantum Field Theory [21]; external fields. Finally, section 6 concludes this work thus, 퐸퐷 can characterize space-time continuum’s and suggests future works. resistance to curvature and could represent vacuum energy density. Further, the inverse proportionality 2. Extended Field Equations for the Curved in Eq. (1) could explain galaxy formation without Early Universe involving dark matter where 퐺푡 was larger in value The recent PL18 release revealed a positive early at the early Universe. Galaxy formation has been Universe curvature, that is, is evidence of a pre- simulated using modified Newtonian gravity [22]. existing or background curvature. To consider this By incorporating the pre-existing/background pre-existing curvature and its evolution over cosmic curvature as a function of cosmic time and complying with the law of energy conservation, the Einstein– time, 푡, a modulus of spacetime deformation, 퐸퐷, is utilized. Spacetime is regarded as a continuum with Hilbert action can be extended to 퐸퐷 푅 a dual quantum nature, that it curves as waves 4 푆 = ∫ [ + ℒ푀] √−푔 푑 푥 (2) according to General Relativity while fluxing as 2 ℛ quantum energy particles; where the latter is justified where 푅 and ℛ are the Ricci and the pre-existing because the energy flux from early Universe plasma scalar curvatures respectively, ℒ푀 is the Lagrangian into space at the speed of light creating a ‘spacetime density and 푔 is the determinant of the metric 푔푢푣. continuum’ or ‘vacuum energy’. This concept of The indistinctive variation in the action yields spacetime quantum duality can be corroborated by 훿푅 −푔 훿ℛ −푔푅 훿 −푔푅 퐸퐷 √ √ √ 4 [ ( − 2 + )] 푑 푥 recent findings regarding the polarization of light 2 ℛ ℛ ℛ 훿푆 = ∫ 푅 from the CMB, which indicated the possible existence (3) 4 of an exotic substance throughout space that causes + [훿ℒ푀√−푔 + 훿√−푔ℒ푀] 푑 푥 ( ) these measured polarizations [15]. By using the trace- reversed Einstein field equations, the modulus of the By differentiating the determinant according to the 휇휈 Jacobi's formula as 훿√−푔 = −√−푔 푔휇휈훿푔 /2 where continuum, 퐸퐷 = (stress/strain), is expressed as the variation in the metric times the inverse metric, 4 푇 − 푇푔 /2 c 휇 휇휈 휇휈 푔휇휈 푔 = 훿 , yields 푔휇휈 훿푔 + 푔 훿푔휇휈 = 0, while the 퐸퐷 = = 2 (1) 휇휈 휈 휇휈 휇휈 푅휇휈/ℛ 8π퐺푡푟푡 휇휈 variation in the scalar curvature, 푅 = 푅휇휈푔 , is 훿푅 = 휇휈 푢푣 where the stress is signified by the stress-energy 푅휇휈훿푔 + 푔 훿푅휇휈 [23]. Thus, Eq. (3) is expressed as tensor, 푇휇휈, of trace, 푇, while the strain is signified by 퐸퐷 [ (푅 훿푔휇휈 + 푔휇휈훿푅 )] √−푔 푑4푥 2ℛ 휇휈 휇휈 the Ricci curvature tensor, 푅휇휈 , as the change in 2 퐸 푅 curvature divided by ℛ = 1/푟푡 , the scalar of the − [ 퐷 (ℛ 훿푔휇휈 + 푔휇휈훿ℛ )] −푔 푑4푥 2 휇휈 휇휈 √ pre-existing curvature, 푟 is the Universe’s radius of 2ℛ 푡 훿푆 = ∫ (4) 퐸퐷푅 휇휈 4 curvature and 푔휇휈 is the metric tensor. According to − [ 푔 훿푔 ] √−푔 푑 푥 4ℛ 휇휈 the theory of elasticity, 퐸퐷 is a constant; therefore, ℒ푀 Eq. (1) shows an inverse proportionality between the + [훿ℒ − 푔 훿푔휇휈] √−푔 푑4푥 푀 2 휇휈 ( ) gravitational ‘constant‘, 퐺푡, and 푟푡, where 퐺푡 follows the inverse square law with respect to the Universe’s The lambda/pressure is not considered, which could radius as a function of cosmic time. This relationship be implicitly incorporated into stress-energy tensors. 2 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 April 2021 doi:10.20944/preprints202005.0250.v9 By considering the first boundary term in Eq.