It is believed that the modification of Newtonian dynamics （MOND） is a possible alternative for dark matter hypothesis. Although Bekenstein＇s TeVeS supplies a relativistic version of MOND, one may still wish for a more concise covariant formulism of MOND. In this paper, within covariant geometrical framework, we present another version of MOND. We show the spacetime structure of MOND with properties of Tully-Fisher relation and Lorentz invariance violation.
The WMAP and Planck observations show that the quadrupole and octopole orientations of the CMB might align with each other. We reveal that the quadrupole-octopole alignment is a natural implication of the primordial power spectrum in an anisotropic spacetime. The primordial power spectrum is presented with a dipolar modulation. We obtain the privileged plane by employing the ＂power tensor＂ technique. At this plane, there is maximum correlation between quadrupole and octopole. The probability for the alignment is much larger than that in the isotropic universe. We find that this model would lead to deviations from the statistical isotropy only for low-l multipoles.
