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Although the cosmic microwave background (CMB) is largely understood to behomogeneous and isotropic, the hemispherical power asymmetry anomaly seems tobreakdown the isotropy, since the difference between the power spectrum in thetwo hemispheres of the CMB is of the order of $10^{-2}$ at large angularscales. We argue that the existence of an anisotropic power spectrum can simplybe explained by considering the existence of two distinct power spectra in thetwo hemispheres of the CMB, without introducing any additional parameters. Wepropose a direct-sum vacuum structure for (single field) inflationary quantumfluctuations based on discrete spacetime transformations($\mathcal{P}\mathcal{T}$). As a result, we are able to reproduce the amplitudeof the observed dipolar asymmetry at different scales of $ 10^{-4} {\rmMpc^{-1}}\lesssim k\lesssim 1 {\rm Mpc^{-1}}$. We also predict that a similarHPA should arise for the primordial gravitational waves (PGWs) as well and wecompute the power asymmetry of PGW spectra at various wave numbers.

Hemispherical asymmetry of primordial power spectra