BAO Scale Distortion
Anisotropic expansion rates along different axes (a(t),b(t),c(t)a(t), b(t), c(t)) produce direction-dependent BAO scales.
This would manifest as ellipticity in the BAO ring, leading to small but measurable anisotropies in the two-point correlation function:
 (r,)=0(r)+2(r)P2()+...\xi(r, \mu) = \xi_0(r) + \xi_2(r) P_2(\mu) + \dots
 where \mu is the cosine of the angle to the line of sight, and 2\xi_2 is enhanced by anisotropy and vorticity.
Supernovae Luminosity Distance
Rotation and torsion modify the geodesics and hence the luminosity distance--redshift relation:
 dL(z)=(1+z)2dA(z)dL(z,),d_L(z) = (1 + z)^2 d_A(z) \rightarrow d_L(z, \theta),
 acquiring angular dependence due to spacetime anisotropy.This results in directional modulation of supernova brightness, potentially explaining reported dipole anisotropies in Type Ia supernova datasets (e.g. Union2, Pantheon).
5.3 Gravitational Lensing Distortions from Vorticity
In a rotating universe, the lensing of light rays is altered by both:
-
Geometrical anisotropy, and
Torsion-induced modifications to null geodesics.
The primary implications include:
