  The observed dipole asymmetry in Cosmic Microwave Background radiation may
have originated from the modulations of super-horizon long wavelength modes. In
this work we unveil different aspects of asymmetries generated from the long
wavelength mode modulations. We show that the same mechanism which leads to the
observed CMB power spectrum dipole asymmetry from the long mode modulations
also yields dipole asymmetry in (a): tensor perturbations power spectrum and
(b): the halo bias parameter. These are different phenomena relevant to
different cosmological histories but both share the same underlying mechanism
in generating asymmetries in the sky. We obtain the set of consistency
conditions relating the amplitude of dipole asymmetries generated on tensor
perturbations and halo bias parameter to the amplitude of dipole asymmetry
generated on CMB power spectrum. In addition, we show that this mechanism does
not produce dipole asymmetry in acceleration expansion in $\Lambda CDM$
universe because the super-horizon curvature perturbation is conserved in this
background.
