A separate universe view of the asymmetric sky

TL;DR

This paper presents a unified theoretical framework using delta N formalism to describe the hemispherical asymmetry in the cosmic microwave background, accounting for super-horizon modes and their effects on observable quantities.

Contribution

It provides a comprehensive derivation of the power spectrum with broken translational invariance and unifies previous approaches, including phase dependence and non-linear effects.

Findings

Confirmed significant non-linear contributions to the CMB quadrupole from super-horizon modes.

Derived a general form of the power spectrum that incorporates the asymmetry-generating mode.

Identified parameter regimes explaining observed asymmetry without conflicting with other observations.

Abstract

We provide a unified description of the hemispherical asymmetry in the cosmic microwave background generated by the mechanism proposed by Erickcek, Kamionkowski, and Carroll, using a delta N formalism that consistently accounts for the asymmetry-generating mode throughout. We derive a general form for the power spectrum which explicitly exhibits the broken translational invariance. This can be directly compared to cosmic microwave background observables, including the observed quadrupole and fNL values, automatically incorporating the Grishchuk--Zel'dovich effect. Our calculation unifies and extends previous calculations in the literature, in particular giving the full dependence of observables on the phase of our location in the super-horizon mode that generates the asymmetry. We demonstrate how the apparently different results obtained by previous authors arise as different limiting cases. We confirm the existence of non-linear contributions to the microwave background quadrupole from the super-horizon mode identified by Erickcek et al. and further explored by Kanno et al., and show that those contributions are always significant in parameter regimes capable of explaining the observed asymmetry. We indicate example parameter values capable of explaining the observed power asymmetry without violating other observational bounds.