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Hemispherical asymmetry from an isotropy violating stochastic gravitational wave background

Measurement of Cosmic Microwave Background (CMB) temperature by Planck has resulted in extremely tight constraints on the $Λ$CDM model. However the data indicates a evidence of dipole modulated temperature fluctuations at large angular scale which is beyond the standard Statistically Isotropic (SI) $Λ$CDM model. The signal measured by Planck requires a scale dependent modulation amplitude that is beyond the scope of the phenomenological model considered by Planck. We propose a phenomenological model with mixed modulation field for scalar and tensor perturbations which affect the temperature fluctuations at large angular scales. Hence this model is a possible route to explain the scale dependent nature of the modulation field. The salient prediction of this model is the direction dependent tensor to scalar ratio which results in anisotropic Stochastic Gravitational Wave Background (SGWB). This feature is potentially measurable from the $B$-mode polarization map of Planck and BICEP-2 and leads to determination of the modulation strength. Measurability of SI violated polarization field due to this model is estimated for Planck and PRISM. Absence of the signal in the polarization field can restrict the viability of the model.