Cosmological Model Druine by Universal Vorticity - (Without Dark Matter or Dark Energy) | Standard GR

Abstract

Cosmological Model Druine by Universal Vorticity (MCDVU) The Cosmological Model Druine by Universal Vorticity (MCDVU) is an alternative cosmological framework formulated entirely within standard General Relativity. It describes a spatially homogeneous but anisotropic and rotating universe (Bianchi-type cosmology) containing only baryonic matter and radiation. No cold dark matter and no cosmological constant are introduced (Ω_cdm = 0, Λ = 0). Cosmic vorticity ω and residual shear σ modify the Friedmann and Raychaudhuri equations. The quadratic vorticity term ω² acts as an effective positive contribution that drives late-time accelerated expansion, thereby replacing the role traditionally assigned to dark energy: 3H² = 8πG ρ + ω² − σ² − 3k/a² ä/a = −(4πG/3)(ρ + 3p) + (1/3)(ω² − σ²) At galactic scales, the same cosmic rotation induces a gravitomagnetic (frame-dragging) effect that supplies the additional acceleration needed to produce flat rotation curves, eliminating the need for dark-matter halos: v²(r)/r = G M_b(r)/r² + 2 ω_cos v(r) The characteristic acceleration generated by this mechanism is: a_ω = 2 ω_cos c ≈ 1.2 × 10⁻⁸ cm s⁻² This value naturally coincides with the MOND acceleration scale a₀. The model recovers the classic Gödel relation ω² = 4πG ρ = −Λ_eff as an exact limiting case and remains compatible with current upper bounds on cosmic anisotropy from the CMB. While mathematically consistent, several observational challenges (baryon acoustic oscillations, large-scale structure growth, and the precise origin of primordial vorticity) remain open. In short, MCDVU shows that both the dark-energy and dark-matter phenomena can, in principle, emerge as purely geometric consequences of a rotating universe described by Einstein’s equations alone.