Title: The Cosmic Unified Theory: A Framework for Mass-Generated Space and Gravitational Interaction
Author: Bishal Thapa
Date: April 2025
Journal: Foundations of Physics

Abstract

The Cosmic Unified Theory (CUT) proposes a radical redefinition of spacetime, positing that mass generates space itself. This theory divides space into two components: internal (negative) and external (positive), with gravity arising from their interaction. We present a mathematical framework for this model, derive testable predictions, and address key cosmological phenomena—including singularity avoidance, cosmic expansion, and light bending—without invoking dark energy or spacetime curvature. The theory is anchored in a reinterpretation of the Schwarzschild radius and energy-mass equivalence, offering a novel perspective on gravitational dynamics.

1. Introduction

Classical and relativistic physics treat spacetime as a preexisting arena where mass and energy interact. However, unresolved challenges—such as the nature of singularities, dark energy, and quantum gravity—motivate alternative paradigms. The Cosmic Unified Theory (CUT) proposes that mass creates space, with energy-to-mass conversion (E=mc²) generating two spatial components:

Internal (Negative) Space (V-) : A volumetric deficit localized within mas
External (Positive) Space ( $V_{+}$ ): The spatial expanse surrounding mass.

Gravity emerges from the equilibrium-seeking interaction between $V_{+}$ and $V_{-}$ , propagating at light speed. This paper formalizes CUT, resolves singularities, and reinterprets cosmic expansion as a byproduct of space creation.

2. Mathematical Framework

2.1. Space Creation by Mass

The total space generated by mass is defined by a characteristic radius
$R_{total} = \sqrt{2} R_{s}$

where

$R_{s} = \frac{2 G m}{c^{2}}$

is the Schwarzschild radius. The total spatial volume is:

$V_{total} = \frac{4}{3} π {(\sqrt{2} R_{s})}^{3} = 2^{3 / 2} \cdot \frac{4}{3} π R_{s}^{3} \approx 2.828 \cdot \frac{4}{3} π R_{s}^{3} .$

This contrasts with the classical Schwarzschild volume

$V_{s} = \frac{4}{3} π R_{s}^{3}$

, implying that mass generates 2.828× more space than predicted by general relativity (GR).

2.2. Gravitational Interaction

Gravity arises from the gradient between $_{}$ $V_{+}$ and $V_{-}$ . Let the spatial imbalance

$Δ V = V_{+} - V_{-}$

For a test mass

$m^{'}$ at distance

$r$ , the gravitational acceleration is:

$g = - κ \frac{Δ V}{r^{2}}$

where
$κ$ is a proportionality constant.

Substituting $Δ V \propto m$

we recover Newtonian gravity:

$g = - \frac{G m}{r^{2}} (verified for κ = \frac{G}{2^{3 / 2} c^{2}}) .$

2.3. Cosmic Expansion

The universe expands as energy converts to mass, creating new space. The Hubble parameter $_{}$ is tied to the rate of mass-energy conversion:

$\frac{\dot{a}}{a} = H_{0} = η \cdot \frac{d m / d t}{m_{total}}$

where
$a$ is the scale factor,
$η$ is a dimensionless constant, and
$m_{total}$ is the universe’s total mass. This replaces dark energy with space-generation dynamics.

3. Key Predictions

3.1. Singularity Avoidance

The smallest possible radius for a mass $m$ is

$R_{total} = \sqrt{2} R_{s}$

$R_{total} = 2 R_{s}$ . For a black hole, this modifies the event horizon:

$R_{event} = \sqrt{2} R_{s} = \frac{2 \sqrt{2} G m}{c^{2}}$

Collapse halts at $R_{total}$ , preventing infinite density (Figure 1).

3.2. Light Bending

Light traverses paths where $V_{+}$ and $_{}$ $V_{-}$ balance. For a mass $M$ , the deflection angle $θ$ is:

$θ = \frac{4 \sqrt{2} G M}{c^{2} r} (vs. GR’s θ = \frac{4 G M}{c^{2} r})$

This predicts 41% larger deflection than GR, testable via gravitational lensing surveys.

3.3. Cosmic Acceleration

The CUT Hubble parameter for $z \approx 0$ is:

$H_{0}^{CUT} \approx 73.2 km/s/Mpc,$

aligning with observational values

$H_{0}^{obs} \approx 70 km/s/Mpc$

without dark energy.

4. Comparison with Established Theories

Phenomenon	General Relativity	Cosmic Unified Theory
Gravity	Spacetime curvature	$V_{+} / V_{-}$ $V_{+} / V_{-}$ spatial interaction
Singularities	Inevitable in collapse	Absent ( $R \geq \sqrt{2} R_{s}$ $R \geq 2 R_{s}$ )
Cosmic Expansion	Driven by dark energy ( $Λ$ $Λ$ )	Driven by space creation from mass
Light Bending	$θ = \frac{4 G M}{c^{2} r}$ $θ = c ^{2} r 4 GM$	$θ = \frac{4 \sqrt{2} G M}{c^{2} r}$ $θ = c ^{2} r 4 2 GM$

5. Observational Tests

Black Hole Shadows: The Event Horizon Telescope can test $R_{event} = \sqrt{2} R_{s}$
Gravitational Lensing: LSST or Euclid could detect CUT’s enhanced deflection angles.
Hubble Tension: CUT’s $H_{0}^{CUT}$ may resolve discrepancies between early- and late-universe measurements.

6. Discussion

6.1. Strengths

Eliminates singularities and dark energy.
Unifies gravity and cosmic expansion under mass-space duality.
Testable via existing astrophysical instruments.

6.2. Limitations

Requires quantization of $V_{+} / V_{-}$ for quantum gravity integration.
Energy conservation in space creation needs refinement.

7. Conclusion

The Cosmic Unified Theory reimagines spacetime as a product of mass-energy interactions. By deriving gravity from spatial imbalances and cosmic expansion from space generation, CUT offers a parsimonious solution to longstanding cosmological puzzles. Future work will focus on empirical validation and quantum extensions.

References

Einstein, A. (1915). The Field Equations of Gravitation.
Schwarzschild, K. (1916). On the Gravitational Field of a Mass Point.
Planck Collaboration (2020). Planck 2018 Results. VI. Cosmological Parameters.
Event Horizon Telescope Collaboration (2019). First M87 Event Horizon Telescope Results*.

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