What the small angle CMB really tells us about the curvature of the Universe

TL;DR

Small angle CMB observations primarily constrain the curvature near the last scattering surface, and allowing spatial curvature to vary locally permits significant inhomogeneity, impacting models like void explanations for cosmic acceleration.

Contribution

The paper reveals that small angle CMB data constrains curvature locally near the last scattering surface and explores the implications of spatially varying curvature for void models and cosmic acceleration explanations.

Findings

Curvature near the last scattering surface is tightly constrained by small angle CMB.

Allowing spatial curvature to vary locally permits significant inhomogeneity.

Void models with a homogeneous big bang can fit CMB data if the universe is positively curved.

Abstract

It is well known that observations of the cosmic microwave background (CMB) are highly sensitive to the spatial curvature of the Universe, k. Here we find that what is in fact being tightly constrained by small angle fluctuations is spatial curvature near the surface of last scattering, and that if we allow k to be a function of position, rather than taking a constant value everywhere, then considerable spatial curvature is permissible within our own locale. This result is of interest for the giant void models that attempt to explain the supernovae observations without Dark Energy. We find voids models with a homogeneous big bang can be compatible with the observed small angle CMB, but only if they exist in a positively curved universe. To be compatible with local measurements of H_0, however, we find that a radially varying bang time is required.