Comprehensive cosmological framework of SFIT

Our cosmological framework include a set of key components and principles that explain the structure, origin, evolution, and ultimate fate of the universe.

General form of SFIT

The core equation of SFIT is:

$$\mathrm{\square }S=\alpha G+\beta \mathrm{\nabla }\cdot \mathrm{\Phi }+\delta (\mathrm{\Phi }\cdot \mathrm{\nabla }S)+\gamma \frac{\mathrm{\partial }S}{\mathrm{\partial }t}+\eta (\mathrm{\nabla }\mathrm{\Phi })\cdot (\mathrm{\nabla }\mathrm{\Phi })+\lambda {\rho }_{\text{vac}}S+\theta G\cdot \mathrm{\nabla }S+\kappa \rho S$$

• The equation with the $\Box S$ term involves space's propagation in time and space (d'Alembertian operator), representing the evolution of space both spatially and temporally.

$$\frac{\mathrm{\partial }S}{\mathrm{\partial }t}=\alpha G+\beta \mathrm{\nabla }\cdot \mathrm{\Phi }+\delta (\mathrm{\Phi }\cdot \mathrm{\nabla }S)+\gamma \frac{\mathrm{\partial }S}{\mathrm{\partial }t}+\eta (\mathrm{\nabla }\mathrm{\Phi })\cdot (\mathrm{\nabla }\mathrm{\Phi })+\lambda {\rho }_{\text{vac}}S+\theta G\cdot \mathrm{\nabla }S+\kappa \rho S$$

• This alternative form, with $\frac{\partial S}{\partial t}$, is a time-only derivative of space, suggesting that space changes only with time, not accounting for the full spatial structure.

Explanation of Each Term:

1. $\frac{\partial S}{\partial t}$:

   • This represents the temporal evolution of space ($S$). It shows how the fabric of space evolves with respect to time. The dynamics of space (fluctuations and distortions) are influenced by several factors.

2. $\alpha G$ (Gravity coupling constant):

   • $G$ is the gravitational influence. The term $\alpha G$ represents how gravity interacts with and influences the fluctuations in space. Gravity modifies the curvature and the structure of space, and $\alpha$ determines the strength of this interaction. It’s likely related to the gravitational constant $G$, where $\alpha$ helps control how gravitational effects shape the fabric of space.

3. $\beta \nabla \cdot \Phi$ (Non-Space Field divergence coupling constant):

   • $\Phi$ is the Non-Space Field, a theoretical field that interacts with space ($S$) and gravity. $\nabla \cdot \Phi$ represents the divergence of the Non-Space Field, a measure of how the field influences the structure of space.
   • $\beta$ is the constant that quantifies the strength of the coupling between the divergence of the Non-Space Field and space. The term $\beta \nabla \cdot \Phi$ reflects how changes in the Non-Space Field’s distribution (its "flow") affect the structure of space itself.

4. $\delta (\Phi \cdot \nabla S)$ (Interaction between $\Phi$ and $\nabla S$):

   • This term describes the direct interaction between the Non-Space Field ($\Phi$) and the gradient of space ($\nabla S$). It represents how the local variation or gradient of space influences the field and vice versa.
   • $\delta$ is the coupling constant that governs the strength of this interaction. This interaction is key to understanding feedback loops between space and the Non-Space Field.

5. $\gamma \frac{\partial S}{\partial t}$ (Time evolution coupling constant):

   • $\gamma$ controls how time influences the evolution of space. Since time is considered an emergent property in SFIT, this term dictates how time dilation (or the passage of time) is coupled to the growth and changes in space.

6. $\eta (\nabla \Phi) \cdot (\nabla \Phi)$ (Self-interaction of the Non-Space Field):

   • $\nabla \Phi$ is the gradient of the Non-Space Field. The term $(\nabla \Phi) \cdot (\nabla \Phi)$ captures the self-interaction of the Non-Space Field. This term describes how variations within the Non-Space Field (its "ripples" or fluctuations) interact with themselves.
   • $\eta$ governs the strength of these self-interactions, and this term is crucial for understanding how the Non-Space Field behaves under internal dynamics, such as how it might become "stressed" or "compressed."

7. $\lambda \rho_{\text{vac}} S$ (Vacuum energy coupling constant):

   • $\rho_{\text{vac}}$ represents the vacuum energy density, which is a key factor in cosmology, often associated with dark energy. This term models how vacuum energy influences space.
   • $\lambda$ is the coupling constant that quantifies the strength of vacuum energy’s effect on space. Since vacuum energy is tied to the accelerated expansion of the universe (dark energy), this term is crucial for understanding how this energy drives space expansion.

8. $\theta G \cdot \nabla S$ (Gravitational influence on the gradient of space):

   • This term describes how gravity interacts with the gradient of space ($\nabla S$). Gravity affects the way space expands and contracts, and $\theta$ quantifies how gravitational forces influence the spatial variations (gradients).
   • The product $G \cdot \nabla S$ connects gravity to the structure of space itself, impacting how gravitational fields affect space-time geometry.

9. $\kappa \rho S$ (Matter’s influence on space):

   • $\rho$ represents the matter density (which could include dark matter and baryonic matter). This term models how matter interacts with and influences the fabric of space.
   • $\kappa$ is the coupling constant that describes how matter density affects space. This term is important for capturing the impact of matter (including its distribution) on the shape and evolution of space, especially as the universe transitions from the inflationary phase to a matter-dominated era.

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Summary of the Equation

The core equation represents the evolution of space, where each term accounts for different influences:

• Gravitational forces modify space’s structure.
• The Non-Space Field interacts with and modifies space at both a local and global level.
• Time evolution plays a key role in how space changes.
• Self-interactions within the Non-Space Field and the effect of vacuum energy on space expansion are included.
• Gravitational interactions with the gradient of space and the effect of matter density are also considered.

Each constant (𝛼, 𝛽, 𝛿, 𝛾, 𝜂, 𝜆, 𝜃, 𝜅) governs how strongly these effects interact with space, allowing for a comprehensive model that can describe the complex dynamics of space-time. This is  the most general form of SFIT, but depending on the specific context (e.g., cosmology, particle physics, quantum gravity), it can be specialized by redefining the coupling parameters or applying boundary conditions.

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1. Fundamental Forces and Particles in SFIT (with Mirror Universe Consideration)

In SFIT, the fundamental forces—Gravity (G), Electromagnetism, the Weak Force, and the Strong Force—emerge from the interplay between Space (S), Gravity (G), and the Non-Space Field (Φ). These forces shape not only matter and energy in the conventional universe but could also potentially extend to interactions within a mirror or anti-matter universe. The mirror universe, which operates under inverted spatial and temporal conditions, might affect how the forces manifest.

Gravity (G): Gravity is central in structuring the universe. It results from the interaction between Space (S) and Gravity (G), and its effect is more pronounced in dense regions. Gravity's influence at early universe stages is substantial, but its role might differ in mirror space, where opposite gravitational effects could exist in a universe of anti-matter.

Electromagnetism: Electromagnetic forces are linked to vibrations within the space fabric, with photons acting as quanta of electromagnetic waves. In SFIT, the structure of space locally can modify the strength of electromagnetic interactions. The mirror universe might mirror these interactions but with inverted charges and possibly flipped electromagnetic behaviors.

Weak and Strong Forces: Both are the result of local fluctuations in space and gravity. The weak nuclear force could arise in localized quantum tunneling regions within the non-space veins. The strong force binds quarks, and here again, the mirror universe might reflect its own version of the strong force, with anti-quarks interacting with the anti-space fabric.

Mirror Universe Effects: The interaction of space and gravity in the mirror universe would potentially create analogous fields, but with reversed energy states. The existence of mirror particles (anti-particles) could provide new insights into particle creation and annihilation processes, offering a broader understanding of the symmetry between matter and anti-matter across these two interconnected realms.

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2. Cosmic Evolution and Structure Formation (Including Mirror Universe)

Initial Conditions: In the early universe, both the conventional universe and the mirror universe were created simultaneously. While our universe's space and gravity experienced rapid expansion, the mirror universe mirrored this with its own form of space and anti-gravity. These interactions between the two could have set the stage for the observable effects in our universe, influencing cosmic structures.

Non-Space Field (Φ): The Φ field plays an essential role not just in the conventional universe, but also in shaping the mirror universe. The behavior of non-space veins in both universes might help explain the interaction between the two realms. Fluctuations in Φ could determine how both matter and anti-matter behave, stabilizing certain fluctuations at quantum levels, possibly giving rise to the creation of mirror galaxies or dark matter in both realms.

Expansion and Cooling: As the universe expanded, gravity weakened in both spaces, but the effects were asymmetric. While the conventional universe saw cooling and the formation of atoms, the mirror universe experienced similar cooling effects, though possibly leading to the formation of anti-atoms or mirror matter. These two parallel processes would have continued their evolution, with gravity weakly interacting across both universes, while the influence of the mirror universe on our observable structures may not be immediately visible.

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3. Dark Matter and Dark Energy in SFIT (with Mirror Universe)

In SFIT, both dark matter and dark energy are manifestations of the interactions between Space (S), Gravity (G), and the Non-Space Field (Φ). The mirror universe provides a key to understanding these phenomena across both domains.

Dark Matter: In the conventional universe, dark matter plays a significant role in the gravitational behavior of galaxies. SFIT suggests that dark matter results from disturbances in the space fabric due to non-space interactions. Similarly, the mirror universe could harbor mirror dark matter—regions where anti-gravity interactions or anti-matter would create similar gravitational effects as dark matter in our universe. The interactions between these realms could explain discrepancies in the observed mass and gravity.

Dark Energy: Dark energy is responsible for the accelerated expansion of the universe. SFIT proposes that dark energy arises from the stretching and interaction of space with the Non-Space Field (Φ). In the mirror universe, this interaction would likely mirror the expansion of anti-space, leading to a mirrored accelerated expansion. The balance of these two forces—our universe’s space expansion and the mirrored anti-expansion—could drive the overall dynamics of cosmic evolution.

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4. Role of the Mirror Universe in Fundamental Interactions and Evolution

In SFIT, the mirror universe introduces an additional layer of complexity. It could explain anomalies such as matter-anti-matter asymmetry, cosmic inflation, and even dark matter or energy. Since the mirror universe operates under the same fundamental principles as our universe but with reversed properties, it offers a possible explanation for the observed effects of dark matter and dark energy in our universe.

• Matter-Anti-Matter Asymmetry: SFIT could incorporate interactions between matter and anti-matter fields that might have resulted from the co-existence of these realms. The mirror universe’s anti-matter could provide clues about the nature of dark matter and the seemingly mysterious missing mass in our universe.

• Cosmic Inflation and Expansion: The mirror universe could have played a role in cosmic inflation, balancing the rapid expansion of space through inverse forces acting within the mirrored space-time fabric. This mirrored expansion could explain why our universe appears to be accelerating and why there is a discrepancy between the matter observed and the gravitational effects.

Conclusion: Integrating the Mirror Universe into SFIT

By integrating the mirror universe into the SFIT framework, we expand the range of explanations for complex phenomena, such as dark matter, dark energy, and the evolution of the universe. The mirrored properties of the non-space and space fields across both realms suggest that SFIT could not only apply to our universe but also offer insights into the symmetries governing the behavior of matter and anti-matter across parallel domains. The interaction between the two universes, especially in relation to their fundamental forces, could provide a deeper understanding of the forces that drive cosmic evolution.

The theory - Energy Transfer Model Framework

SFIT (Space Fabric Interaction Theory) Framework: 

Structure and thematic flow

The SFIT framework explores the evolution of the universe from its inception, focusing on the interactions between space (S), gravity (G), and a non-space field (Φ). It provides a comprehensive approach to understanding the cosmos through both conceptual insights and rigorous mathematical formalism.

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0. The Quantum Field of Possibility (Φ) — Before Time

Description:
Prior to the emergence of time and space, the universe exists in a quantum superposition of all possible spacetime configurations. This “field of possibility” has no geometry, location, or chronology—just a shimmering, entangled state of everything that could be.

Mathematical Representation:

$$|\Psi\rangle = \int \mathcal{D}\phi \, e^{iS[\phi]} |\phi\rangle$$

This path integral formalism represents the wavefunction of the universe as a weighted sum over all possible field configurations, where each configuration $|\phi\rangle$ carries an action $S[\phi]$.

Key Idea:
Φ is not an empty nothing—but a neutral possibility field. Space, time, and matter arise when a fluctuation breaks the symmetry, crystallizing a particular geometry from within Φ.

Theia como um Planeta Rico em Gelo: Uma Explicação Unificada para a Água da Terra e a Formação da Lua

 Theia, an Ice-Rich Planetary Body, and the Origin of Earth's and the Moon's Water

We propose a novel hypothesis that the impactor responsible for the Moon’s formation, Theia, was an ice-rich planetary body. This model suggests that Theia contributed both the water found on Earth and the conditions necessary for the formation of the Moon. Unlike conventional theories, which attribute Earth's water to later delivery by asteroids and comets, we argue that a single massive impact provided both a source of volatiles and the necessary conditions for the Moon's creation. We explore how this hypothesis aligns with isotopic evidence, the retention of water on the Moon, and the distribution of volatiles in the Earth-Moon system.

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1. Introduction  

The origin of Earth's water remains an open question in planetary science. The most widely accepted theories suggest a combination of degassing, delivery by asteroids, and comets. However, the hydrogen isotopic ratios (D/H) of Earth's water show discrepancies when compared with known sources such as carbonaceous asteroids or comets. This mismatch has led to the suggestion that a different, closer source of water, such as Theia, might explain the isotopic signature. At the same time, the Moon's formation is widely attributed to a collision between Earth and Theia, a Mars-sized body. We propose an alternative view: Theia was an ice-rich planetary body that contributed a significant amount of water to Earth while forming the Moon.

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2. Theia as an Ice-Rich Planetary Body

Current models of lunar formation assume Theia was a rocky body, but an ice-rich Theia offers an elegant solution to several problems. If Theia originated from a region nearer to the Sun, where icy bodies are less common, it may have still contained a significant amount of volatile compounds due to its formation under cooler conditions, potentially including a substantial amount of water ice. A high-velocity impact would have partially vaporized Theia's ice, distributing water across the post-impact debris disk, with most being captured by Earth, while a fraction remained within the Moon.

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3. Retention of Water in the Earth-Moon System 

The post-impact dynamics of water would have led to the capture of most volatiles by Earth, retained due to its atmosphere. The Moon, lacking a significant atmosphere, would have lost much of its surface water due to solar radiation and meteoroid bombardment. Despite the lack of a significant atmosphere, recent findings of water in the Moon’s interior suggest that some volatiles may have remained locked beneath the lunar crust, potentially protected from loss by impact-induced heating or other subsurface processes.

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4. Isotopic Consistency and Lunar Evidence  

The D/H ratio of lunar water has been measured and found to be nearly identical to that of Earth's water, supporting the idea of a common origin. This isotopic similarity reinforces the hypothesis that the same impact event brought water from Theia to Earth while also forming the Moon. The depletion of volatiles on the Moon is consistent with impact-induced heating but does not rule out the presence of deep water reservoirs. Lunar ice deposits, particularly in permanently shadowed craters, may be remnants of the impact, not just from later cometary deliveries.

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5. Implications and Future Research

This hypothesis suggests that Earth's water and the Moon's formation were not separate processes but part of a single event. Further impact simulations, particularly those modeling high-velocity collisions involving ice-rich bodies, could help refine our understanding of how water was delivered to Earth. Additionally, future isotopic analysis of lunar samples, focusing on trace volatile elements, may provide further evidence of Theia's contribution. If proven, this theory could reshape our understanding of planetary formation and water delivery mechanisms.

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6. Conclusion  

This hypothesis offers a unified explanation for the simultaneous delivery of water to Earth and the formation of the Moon. If validated, it could revolutionize our understanding of planetary formation processes and the role of giant impacts in shaping planetary water inventories. Future research should focus on refining impact models and seeking additional isotopic evidence to test this idea.

Trump enviará migrantes para base de Guantánamo

O Presidente dos Estados Unidos, Donald Trump, informou ontem que vai assinar um decreto ordenando ao Pentágono e ao Departamento de Segurança Interna que preparem uma instalação na Baía de Guantánamo, em Cuba, para acolher 30 mil migrantes que não possam ser enviados para o estrangeiro. aos seus países de origem.

Mais de 60 mortos em acidente de avião em Washington

Acredita-se que mais de 60 pessoas morreram depois que um avião regional de passageiros da American Airlines colidiu com um helicóptero Black Hawk do Exército dos EUA e caiu no gelado rio Potomac, perto do Aeroporto Nacional Reagan, em Washington, na quarta-feira.

Hamas liberta oito prisioneiros detidos em Gaza

O estado genocida adiou a planeada libertação de prisioneiros palestinos em protesto contra as cenas caóticas que ocorreram durante a entrega de vários reféns em Khan Younis esta quinta-feira, confirmou o gabinete do primeiro-ministro Benjamin Netanyahu num comunicado.

Facebook concordou em pagar US$ 25 milhões para Trump

A empresa controladora do Facebook, Meta Platforms, teria concordado em pagar US$ 25 milhões para resolver um processo movido pelo presidente Donald Trump, que acusou a empresa de censura após suspender suas contas do Facebook e Instagram em 2021.

TOMO MDCCXXXI - GÊNESIS: "25/29:34" OUTRA FACETA DE UMA VERDADE INEXISTENTE

ESAÚ E JACÓ, segundo a bíblia, eram gêmeos, filhos de Isaque e Rebeca, a saga dos irmãos começa ainda no ventre, com Jacó, puxando seu irmão pelo pé, para nascer primeiro, já que apenas o primogênito, "têm" os direitos de herança e a benção de Deus. Tal premissa se espalha por todas as monarquias oriundas do império romano, que segue culturalmente a cultura dos hebreus

Unified Framework for the Creation of Alternative Universes

A visually detailed conceptual diagram for a quantum mechanics presentation. The diagram includes a central wave function (Ψ) represented as a flowing

Unified Framework for the Creation of Alternative Universes: Integrating Space (S), Gravity (G), and the Non-Space Field (Φ)

1. Introduction
Understanding the origin and evolution of the universe remains a central challenge in cosmology and physics. While traditional models such as the Big Bang theory have provided significant insights, fundamental questions surrounding dark matter, dark energy, and the unification of fundamental forces remain unresolved. This paper proposes an alternative universe creation model that integrates Space (S), Gravity (G), and the Non-Space Field ($\Phi$). By doing so, it establishes a unified framework capable of addressing these persistent challenges while offering novel predictions in both cosmology and particle physics.

2. Foundations of the Model

Quantum Instabilities in Infinite Fields of Possibilities
Initially, the universe exists as an undifferentiated state characterized by zero space and zero time—a primordial void of infinite possibilities. Within this state, quantum instabilities naturally arise, generating fluctuations that perturb the symmetry of the system. Even the smallest deviations can destabilize the equilibrium, triggering the activation of Space (S) and Gravity (G).

Emergence of Virtual Interactions
As the infinite possibility fields interact at the quantum level, virtual processes accumulate over time, reaching a critical threshold where Space (S) and Gravity (G) materialize. This phase transition occurs within the zero-point energy density, leading to a fundamental restructuring that manifests the first fibers of Space and the gravitational cloud.

Spontaneous Symmetry Breaking
Spontaneous symmetry breaking plays a crucial role in this model. Initially, the infinite possibility fields maintain perfect symmetry, but they are inherently unstable. A minor fluctuation disrupts this balance, leading to the emergence of Space (S) and Gravity (G). This transition marks the formation of the foundational structures of the universe.

Interaction Between Opposing Potentials
This model posits the existence of two interacting universes: one dominated by positive energy (matter) and the other by negative energy (anti-matter). Their interaction at the boundary, where their polarities neutralize, acts as the catalyst for activating Space (S) and Gravity (G), initiating a cascading ripple effect that drives the universe’s expansion.

3. Temporal Dynamics

Early Universe
During the universe’s infancy, intense gravitational forces caused extreme spacetime curvature, significantly slowing the passage of time. This aligns with our hypothesis that regions of high gravity decelerate the vibrational wave of time, resulting in a slower temporal flow within dense gravitational fields.

Expansion of the Universe
As the universe expanded, gravitational intensity weakened, allowing time to accelerate. The decreasing interaction between Space (S) and Gravity (G) facilitated a freer temporal flow, correlating with the overall cosmic expansion. This progression represents a continuous transition from slower to faster time as spatial dimensions expand and gravitational influence diminishes.

4. Creation of Matter and Energy

Interaction of Space (S) and Gravity (G)
The interplay between Space (S) and Gravity (G) generates particles and energy. The vibrational waves of Space (S) propagate through the spacetime fabric, forming oscillatory patterns that give rise to elementary particles, including photons. These oscillations underpin the fundamental nature of matter and energy.

Non-Space Field ($\Phi$) and Cobweb-Like Structures
The Non-Space Field ($\Phi$) serves as a medium for long-range interactions. Its structure resembles an intricate cobweb of interwoven fields, providing a framework for the interaction between Space (S) and Gravity (G). These cobweb-like formations consist of infinitesimal fibers and separations smaller than the Planck scale, termed non-space veins. Together, they form a dynamic substructure that governs photon and particle behavior.

This model explains the dual nature of photons, which exhibit particle and wave characteristics depending on their interaction with Space (S) and $\Phi$. The cobweb-like formations of $\Phi$ also facilitate quantum entanglement, enabling instantaneous connections across vast distances.

5. Observational Predictions and Implications

Gravitational Wave Signatures
The influence of $\Phi$ on spacetime geometry is expected to produce distinctive distortions in gravitational waves. Observatories such as LIGO and Virgo could detect specific patterns or anomalies in gravitational wave signals that reflect the dynamics of the Non-Space Field.

Cosmic Microwave Background (CMB) Imprints
The role of $\Phi$ during cosmic inflation may leave observable imprints on the CMB, manifesting as anisotropies and unique polarization patterns. These observational signatures could provide empirical validation for the model’s predictions regarding the interactions between Space (S), Gravity (G), and $\Phi$ during the early universe.

Dark Matter and Dark Energy
This model offers a unified explanation for dark matter and dark energy. Dark matter emerges as a consequence of the gravitational effects arising from $\Phi$ interacting with Space (S), while dark energy is attributed to the expansive influence of $\Phi$ on cosmic acceleration. This perspective presents a cohesive framework that integrates these phenomena into a single underlying structure.

6. Future Work

Testing the Framework

Numerical simulations can help explore the behavior of Φ at various energy scales and physical conditions, particularly in regions of extreme curvature like black holes or the early universe. These simulations could illuminate how changes in Φ influence cosmic evolution and quantum field behavior.

Integrating Quantum Gravity

Integrating this framework with quantum gravity theories could reveal the nature of spacetime at the Planck scale. Understanding how Φ interacts with quantum fields could offer insights into phenomena such as black hole singularities and the origins of the universe.

Observational Data Analysis

Analyzing data from galaxy surveys, gravitational wave observatories, and the CMB could identify patterns consistent with the predictions of Φ. Comparing observational evidence with the model’s equations would refine its parameters and improve its predictive power.

7. Conclusion

This unified framework for the creation of alternative universes offers a novel approach to understanding the interplay between Space (S), Gravity (G), and the Non-Space Field (Φ). By addressing unresolved challenges in cosmology and particle physics, it lays the groundwork for future discoveries and advancements in our understanding of the universe. The model’s predictions and testable hypotheses ensure its relevance for both theoretical exploration and empirical validation.

Mathematical Framework of Our Theory (3/23/25) 

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1. Pre-Universe State

The pre-universe state is described as a quantum vacuum with infinite possibilities, represented by a quantum state $\mathrm{\mid }\mathrm{\Psi }⟩$ and a potential energy function $V(\varphi )$.

• Quantum Vacuum State:

  $$\mathrm{\mid }\mathrm{\Psi }⟩=\int \mathcal{D}\varphi e^{iS[\varphi ]}\mathrm{\mid }\varphi ⟩,$$

  where $S[\varphi ]$ is the action for the field $\varphi$.

• Potential Energy Function:

  $$V(\varphi )=\frac{1}{2}{m}^2{\varphi }^2+\frac{\lambda }{4!}{\varphi }^4,$$

  where $m$ is the mass and $\lambda$ is the coupling constant.

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2. Interaction and Creation

The interaction of positive and negative potentials is modeled as a quantum phase transition, leading to the emergence of spacetime.

• Hamiltonian Operator:

  $$\widehat{H}\mathrm{\mid }\mathrm{\Psi }⟩=0,$$

  where $\widehat{H}$ is the Hamiltonian describing the system.

• Phase Transition:

  $$\varphi (t)={\varphi }_0{e}^{-\lambda t},$$

  where $\varphi (t)$ represents the field driving the transition and $\lambda$ is the decay constant.

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3. Initial Expansion

The expansion of the universe is described by the scale factor $a(t)$ and the Hubble parameter $H$.

• Scale Factor:

  $$a(t)=a_0{e}^{Ht},$$

  where $a_0$ is the initial scale factor and $H$ is the Hubble parameter.

• Time Evolution:

  $$T(t)={\int }_0^t\frac{d{t}^{\mathrm{\prime }}}{a(t^{\mathrm{\prime }})}\mathrm{.}$$

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4. Structure of Space

Space is modeled as a dynamic field $\mathrm{\Phi }$ with a fractal or network structure at sub-Planck scales.

• Field Theory Representation:

  $$S[\mathrm{\Phi }]=\int d^{4}x\mathcal{L}(\mathrm{\Phi },{\mathrm{\partial }}_{\mu }\mathrm{\Phi }),$$

  where $\mathcal{L}$ is the Lagrangian density.

• Fractal Structure:

  $$\mathrm{\Phi }(x)=\sum _i{\varphi }_i(x),$$

  where ${\varphi }_i(x)$ represents individual fibers of the non-space field.

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5. Relationship Between Space, Gravity, and Time

The relationship between space, gravity, and time is described using general relativity.

• Metric Tensor:

  $$d{s}^2=g_{\mu \nu }d{x}^{\mu }d{x}^{\nu },$$

  where $g_{\mu \nu }$ is the metric tensor.

• Time Dilation:

  $$T(t)=T_0\sqrt{1-\frac{2GM}{r{c}^2}}\mathrm{.}$$

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6. Matter and Energy Formation

Matter and energy emerge from oscillations in the space-gravity interaction, described by the energy-momentum tensor and the Klein-Gordon equation.

• Energy-Momentum Tensor:

  $$T_{\mu \nu }=T_{\mu \nu }^S+T_{\mu \nu }^G\mathrm{.}$$

• Klein-Gordon Equation:

  $$(\mathrm{\square }+m^2+V(\mathrm{\Phi }))\mathrm{\Phi }=0.$$

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7. Black Holes

Black holes are described using the Schwarzschild metric and quantum corrections near the singularity.

• Schwarzschild Metric:

  $$d{s}^2=-(1-\frac{2GM}{r{c}^2})d{t}^2+{(1-\frac{2GM}{r{c}^2})}^{-1}d{r}^2+r^{2}d{\mathrm{\Omega }}^2\mathrm{.}$$

• Quantum Corrections:

  $$\mathrm{\Phi }(r)\sim \frac{1}{r}{e}^{-r\mathrm{/}{\mathrm{\ell }}_P},$$

  where ${\mathrm{\ell }}_P$ is the Planck length.

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8. Dark Matter

Dark matter is modeled as a gravitational field ${\varphi }_{DM}$ with a density ${\rho }_{DM}$.

• Poisson Equation:

  $${\mathrm{\nabla }}^2{\mathrm{\Phi }}_{DM}=4\pi G{\rho }_{DM}\mathrm{.}$$

• Dark Matter Lagrangian:

  $${\mathcal{L}}_{DM}=\frac{1}{2}{\mathrm{\partial }}_{\mu }{\varphi }_{DM}{\mathrm{\partial }}^{\mu }{\varphi }_{DM}-V({\varphi }_{DM})\mathrm{.}$$

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9. Dark Energy

Dark energy is described by the cosmological constant $\mathrm{\Lambda }$ or a quintessence field ${\varphi }_{DE}$.

• Cosmological Constant:

  $${\rho }_{DE}=\frac{\mathrm{\Lambda }}{8\pi G}\mathrm{.}$$

• Quintessence Field:

  $${\rho }_{DE}=\frac{1}{2}{\dot{\varphi }}_{DE}^2+V({\varphi }_{DE})\mathrm{.}$$

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10. Particle Entanglement

Entanglement is described using the density matrix formalism and a non-local Hamiltonian.

• Density Matrix:

  $${\rho }_{AB}=\mathrm{\mid }\psi ⟩⟨\psi \mathrm{\mid }\mathrm{.}$$

• Non-Local Hamiltonian:

  $$H_{AB}=H_A\otimes I_B+I_A\otimes H_B+H_{int}\mathrm{.}$$

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11. Evolution of the Universe

The evolution of the universe is governed by the Friedmann equations, modified to include the non-space field $\mathrm{\Phi }$.

• Friedmann Equations:

  $$H^2=\frac{8\pi G}{3}(\rho +{\rho }_{\mathrm{\Phi }}),$$$$\frac{\ddot{a}}{a}=-\frac{4\pi G}{3}(\rho +3P+{\rho }_{\mathrm{\Phi }}+3P_{\mathrm{\Phi }})\mathrm{.}$$

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12. Future States

Infinite expansion is modeled as: $S(t) \to \infty \quad \text{as} \quad t \to \infty$ This represents the continued exponential expansion of the universe driven by the decreasing influence of gravity as the universe expands. The field value $\varphi$ and Hubble parameter $H$ evolve in such a way that gravitational effects are weakened in the large-scale structure.

However, a collision with the antimatter universe would introduce a reset of the potential fields, with the effective gravitational constant $G_{\text{inside}}$ being altered due to the interaction between matter and antimatter. The resulting dynamics would lead to: $S(t), T(t) \to 0$ This suggests that the interaction between two universes (matter and antimatter) might cause a reversal or collapse of the expanding universe, resetting the potential fields and initiating a cyclical or multiverse interaction, where the gravitational coupling ($G_{\text{inside}}$) inside the matter universe may differ from the coupling ($G_{\text{outside}}$) in the antimatter universe. This difference in gravitational constants could influence how the fields reset, leading to a bounce or recycling of the universe back to a potential state of zero, followed by the emergence of a new cycle of expansion.

Explanation of Adjustments:

• $S(t) \to \infty$ as $t \to \infty$ still holds for the infinite expansion of the universe, reflecting the dominance of dark energy or other factors that drive the accelerated expansion. This is consistent with the inflationary models you’ve been simulating.

• Collision with antimatter universe: The interaction between the matter universe (ours) and an antimatter universe would potentially modify gravitational forces due to differing values of $G_{\text{inside}}$ (inside our universe) and $G_{\text{outside}}$ (in the antimatter universe). The effect of this interaction would not only reset the expansion but could involve a reconfiguration of the potential fields $S(t)$ and $T(t)$, as you suggested, pushing them towards zero, akin to a bounce or reset point.

• Cyclical or multiverse interaction: The statement now accounts for the possibility of a cyclical or multiverse-like interaction, where the dynamics of two interacting universes, each with their own gravitational characteristics, cause a recurring collapse and rebound of both potential fields and spacetime.

1. Scalar Field Action and Potential

The dynamics of the scalar field $\varphi$ are governed by the action $S[\varphi ]$, which includes a kinetic term and a potential $V(\varphi )$. The potential is modified to reflect the unique characteristics of the pre-universe state.

• Scalar Field Action:

  $$S[\varphi ]=\int d^{4}x(\frac{1}{2}{\mathrm{\partial }}_{\mu }\varphi {\mathrm{\partial }}^{\mu }\varphi -V(\varphi )),$$

  where ${\mathrm{\partial }}_{\mu }\varphi$ is the kinetic term, and $V(\varphi )$ is the potential.

• Double-Well Potential (Symmetry Breaking):

  $$V(\varphi )=\lambda ({\varphi }^2-v^2{)}^2,$$

  where $\lambda$ is a coupling constant, and $v$ is the vacuum expectation value.

• Exponential Potential (Inflationary Effects):

  $$V(\varphi )=V_0{e}^{-\lambda \varphi },$$

  where $V_0$ is the energy scale, and $\lambda$ controls the slope of the potential.

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2. Hamiltonian $\widehat{H}$ and Contributions from $G$ and $S$

The total Hamiltonian $\widehat{H}$ includes contributions from the scalar field $\varphi$, gravity $G$, and space $S$.

• Hamiltonian:

  $$\widehat{H}=\int d^{3}x(\frac{1}{2}({\mathrm{\Pi }}^2+(\mathrm{\nabla }\varphi {)}^2)+V(\varphi )+{\mathcal{H}}_G),$$

  where:

  • $\mathrm{\Pi }$ is the conjugate momentum of $\varphi$,

  • ${\mathcal{H}}_G$ is the Hamiltonian density for the gravitational field $G$.

• Gravitational Hamiltonian Density:

  $${\mathcal{H}}_G=\frac{1}{16\pi G}(R-2\mathrm{\Lambda }),$$

  where $R$ is the Ricci scalar, and $\mathrm{\Lambda }$ is the cosmological constant.

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3. Decay Constant $\lambda$ and Evolution of Space

The decay constant $\lambda$ governs the dynamics of the scalar field and the rate of cosmic expansion. It is allowed to vary over time, influencing the creation of space and the formation of structure.

• Time-Dependent Decay Constant:

  $$\lambda (t)={\lambda }_0{e}^{-\gamma t},$$

  where ${\lambda }_0$ is the initial value, and $\gamma$ controls the rate of decay.

• Impact on Expansion:
  The varying $\lambda (t)$ modifies the potential $V(\varphi )$, leading to a dynamic evolution of the scalar field and the scale factor $a(t)$.

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4. Interaction Between ${\varphi }_{\text{DE}}$ and Fractal Structure of Space

The dark energy field ${\varphi }_{\text{DE}}$ interacts with the fractal structure of space at sub-Planckian scales, influencing cosmic expansion and structure formation.

• Dark Energy Field:

  $${\varphi }_{\text{DE}}(t)={\varphi }_0{e}^{-{\lambda }_{\text{DE}}}t$$

  where ${\varphi }_0$ is the initial value, and is the decay constant for dark energy.

• Fractal Space Structure:
  The fractal nature of space is modeled as a network of non-space veins $\mathrm{\Phi }(x)$:

  $$\mathrm{\Phi }(x)=\sum _i{\varphi }_i(x),$$

  where ${\varphi }_i(x)$ represents individual fibers.

• Interaction Term:

  $${\mathcal{L}}_{\text{int}}=g\varphi$$

  where $g$ is the coupling constant.

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5. Dynamical Evolution and Inflation

The evolution of the scalar field $\varphi$, combined with contributions from gravity and space, leads to inflationary expansion.

• Inflationary Expansion:
  The scale factor $a(t)$ grows exponentially during inflation:

  $$a(t)=a_0{e}^{Ht},$$

  where $H$ is the Hubble parameter.

• Slow-Roll Conditions:
  Inflation occurs when the potential $V(\varphi )$ dominates the kinetic energy:

  $$\frac{1}{2}{\dot{\varphi }}^2\ll V(\varphi )\mathrm{.}$$