Kinematic and Geometric Origin of Apparent Cosmological Acceleration: A Rotating-Observer Model with Euclidean Embedding

The late-time accelerated expansion of the universe is canonically attributed to a cosmological constant Λ with energy density 𝜌Λ ≃ 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 (𝑟0 ∼ 10 Mpc, 𝑣0 = 𝐻0𝑟0), we show that a particle moving inertially in the embedding space 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 Ω𝑘 (𝑡) = 𝑟2 0/𝑟 (𝑡) 2. At 𝑟 (𝑡) ≈ 1.2 𝑟0 (𝑡 ≈ 9.9 Gyr), Ω𝑘 ≈ 0.685, matching the observed ΩΛ to within 1%. The energetic deficit inferred by the rotating observer is entirely accounted for by the unobserved transverse degree of freedom. 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.