TITLE:
Kinematic and Geometric Origin of Apparent Cosmological Acceleration: A Rotating-Observer Model with Euclidean Embedding
AUTHORS:
Zaki Harari
KEYWORDS:
Cosmological Constant, Dark Energy, Cosmological Expansion, Kinematic Models, Higher-Dimensional Embeddings, Observational Cosmology
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.12 No.4,
October
9,
2026
ABSTRACT: The late-time accelerated expansion of the universe is canonically attributed to a cosmological constant Λ with energy density
ρ
Λ
≃6.9×
10
−27
kg⋅
m
−3
. We investigate a purely kinematic interpretation in which the apparent acceleration arises from the projection of inertial motion onto a non-inertial, radially constrained observational frame. Working first in a rotating-observer toy model and then in a higher-dimensional Euclidean embedding calibrated to cosmological scales (
r
0
~10 Mpc
,
v
0
=
H
0
r
0
), we show that an inertially moving particle is perceived by a central observer as radially accelerating. We present closed-form expressions for the apparent radial distance, velocity, and acceleration, and derive a dimensionless transverse energy fraction
Ω
k
(
t
)=
r
0
2
/
r
(
t
)
2
. At
r(
t
)≈1.2
r
0
(
t≈9.84 Gyr
),
Ω
k
≈0.685
, matching the observed
Ω
Λ
to within 1%. The energetic deficit inferred by the rotating observer, which is fully accounted for by the unobserved transverse degree of freedom, mimics dark energy. The asymptotic acceleration scales as
t
−3
, implying a decaying effective equation of state. While we do not claim to replace ΛCDM, this proof of concept demonstrates that a geometric projection effect can generate kinematic signatures indistinguishable from a positive cosmological constant. We discuss falsifiability, observational discriminants, and the need for a relativistic extension.