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A Unified Field Perspective on Gravitational Expansion and the Emergent Dark Field Framework


Abstract

This paper presents a novel theoretical framework that draws an analogy between gravitational and electromagnetic interactions, suggesting a unified approach to explain cosmic phenomena such as Hubble expansion, dark energy, dark matter, galactic rotation curves, and cosmic microwave background (CMB) anisotropies. A new concept termed the "dark field" is introduced as the gravitational analog of the magnetic field, resulting from mass currents in spacetime. A derived force equation, F = p × d, is proposed to govern cosmic-scale expansion, paralleling the Lorentz force in electromagnetism.


1. Introduction

The conventional treatment of gravitation and cosmic expansion considers phenomena such as Hubble flow, dark matter, and dark energy as distinct and unconnected. This work introduces a unified theory based on analogical reasoning between gravitational and electromagnetic interactions:


Mass m : Electric charge q


Gravitational field g : Electric field E


Dark field d : Magnetic field B


Leading to a gravitational Lorentz-like force:

F = mg + mv × d


2. Derivation of Cosmic Expansion Law

Starting from the postulate:

F = p × d (where p = mv)


Removing mass and integrating over time yields:

a = v × d

=> v = s × d


Assuming |d| = H(t), we retrieve Hubble's Law:

v = Hs


3. Physical Interpretation

The presence of mass universally implies that spacetime expands isotropically. The expression F = mv × d suggests that mass-induced expansion behaves similarly to electromagnetic induction, with the dark field arising from mass fluxes in spacetime.


4. Applications


4.1 Big Bang and Dark Energy

Initial gravitational conditions induced large-scale expansion post-Big Bang. Dark energy is interpreted as reactive force from induced expansion.


4.2 Dark Matter Interpretation

The dark field replaces the need for unseen mass, acting as a feedback force on moving mass analogous to magnetic induction.


4.3 Void Formation

Cosmic web structures emerge due to anisotropic expansion reinforced by aligned mass flows.


4.4 Orbital Stability

Stable multi-body systems (e.g., Earth-Moon-Jupiter) are explained via damping from dark field feedback.


4.5 Galactic Rotation Curves

Flat velocity profiles are accounted for by mutual induction effects between gravitational and dark fields.


4.6 Accelerating Expansion

From a = v × d, cosmic acceleration is a natural outcome:

F = GMm / r^2 = ma = m(v × d)

=> a = v × d


4.7 CMB Anisotropies

Slight asymmetries in dark field distribution explain small temperature fluctuations in the CMB.


5. Mathematical Refinement

A generalized form is given by:

dp/dt = ma + v (dm/dt) = mv × D


Integration with constant mass:

v = s × D


With corrections:

v = s × D - ∫(v/m) dm - ∫ s · (dD/dt)


6. Field Equations Analogous to Maxwell’s Equations

Gravitational and dark fields are expressed analogously:


Differential Form:

∇ · g = ρ / ε

∇ · d = 0

∇ × g = -∂d/∂t

∇ × d = μJ + εμ ∂g/∂t


Integral Form:

∮ g · dl = -d/dt ∬ d · dA

∮ d · dl = ∬ J · dA + d/dt ∬ g · dA


7. Reversing Hubble’s Law

From F = H p:

v × d = s · (dH/dt) + H v


Providing refinements to cosmological evolution equations.


8. Conclusion

This framework posits that gravitational expansion (dark field dynamics) is the dual of gravitational attraction, similar to the electric-magnetic interplay in electromagnetism. It provides a consistent explanation across diverse cosmological phenomena without requiring separate entities for dark energy or dark matter. The analogy with Maxwell’s equations offers a simplified model of the universe—potentially forming a new paradigm: Spatiophysics.


References

(To be completed with relevant literature from general relativity, electromagnetism, Hubble's law, and recent cosmological data.)