What if Planck's Universe isn't flat?

TL;DR

If Planck detects a non-zero curvature parameter, it could indicate either local inhomogeneities or a fundamental deviation from flatness, challenging inflationary predictions and requiring further spectral analysis.

Contribution

This paper explores the implications of a potential non-zero curvature measurement by Planck, analyzing whether it signals local inhomogeneities or a true superhorizon curvature.

Findings

Local inhomogeneities can cause detectable spectral distortions in the CMB.

Spectral distortions can help distinguish between local and superhorizon curvature.

A non-zero Omega_K would prompt new investigations into inflation and universe geometry.

Abstract

Inflationary theory predicts that the observable Universe should be very close to flat, with a spatial-curvature parameter |Omega_K| < 10^-4. The WMAP satellite currently constrains |Omega_K| < 0.01, and the Planck satellite will be sensitive to values near 10^-3. Suppose that Planck were to find Omega_K to be non-zero at this level. Would this necessarily be a serious problem for inflation? We argue that an apparent departure from flatness could be due either to a local (wavelength comparable to the observable horizon) inhomogeneity, or a truly superhorizon departure from flatness. If there is a local inhomogeneity, then secondary CMB anisotropies distort the CMB frequency spectrum at a level potentially detectable by a next-generation experiment. We discuss how these spectral distortions would complement constraints on the Grishchuk-Zel'dovich effect from the CMB power spectrum at large angular scales in discovering the source of the departure from flatness.