TITLE:
The Evolution of the Universe Based on Principal Bundle Geometry
AUTHORS:
Bi Qiao
KEYWORDS:
Generalized Gauge Transformation, Dark Matter, Dark Energy, Einstein Equation, Universal Evolution
JOURNAL NAME:
Journal of Modern Physics,
Vol.16 No.4,
April
14,
2025
ABSTRACT: This paper proposes a novel geometric framework for unifying dark matter, dark energy, and cosmic evolution through a modified gauge-theoretic approach. By introducing a scalar function
γ(
x
)=tanh(
kx
)
, where
x=
a
a
0
(with
a
as the local “absolute acceleration” and
a
0
≈
10
−8
cm/s² a reference scale), we construct an extended principal bundle
P
˜
=P×ℝ
and redefine the connection form as
ω
˜
=
ω
G
+dγ
, ensuring curvature invariance while modulating gravitational sources. In the Newtonian limit, the field equation simplifies to
γ
∇
2
ϕ=−4πρ
, revealing
γ
’s role in scaling gravitational effects. Distinctively, dark matter and dark energy emerge as geometric consequences of spacetime curvature rather than exotic components:
γ→1
restores standard gravity at small scales,
0<γ<1
enhances gravity (mimicking dark matter) at galactic scales, and
γ→
0
+
drives cosmic acceleration via
Λ(
γ
)→∞
. Crucially, allowing
x
to take negative values introduces
γ→
0
−
with
Λ(
γ
)→−∞
, enabling cyclic universe scenarios through curvature oscillations. The derived force law
F=γma
aligns with MOND phenomenology, bridging modified dynamics and geometric modulation. Furthermore, the model constructs a closed “Taiji-like” cosmic evolution loop in the
γ−x
plane, linking asymptotic states (
γ=±1
at
x=±∞
) via hyperbolic perturbations, symbolizing cyclic rebirth. By unifying cosmic dynamics under a geometric gauge framework, this work offers testable predictions for parameter calibration
(
k,
a
0
,
Λ
0
)
and establishes a philosophically resonant synthesis of mathematical physics and cosmological evolution.