Observable circles-in-the-sky in flat universes

TL;DR

This paper discusses the potential for detecting non-trivial flat universe topologies through circles-in-the-sky in the CMB, highlighting that current searches may not exclude all possibilities due to geometric constraints.

Contribution

It derives upper bounds on the deviation from antipodicity of matching circles in flat universes, showing some topologies could evade current detection methods.

Findings

Current searches do not exclude all flat topologies.

Some flat topologies produce circles with large deviations from antipodicity.

Detectability depends on the universe's topology and observer's position.

Abstract

An important, and potentially detectable, signature of a non-trivial topology for the universe is the presence of so called circles-in-the-sky in the cosmic microwave background (CMB). Recent searches, confined to antipodal and nearly antipodal circles, have however failed to detect any. This outcome, coupled with recent theoretical results concerning the detectability of very nearly flat universes, is sufficient to exclude a detectable non-trivial cosmic topology for most observers in the inflationary limit ($0< |\Omega_{tot}-1| \lesssim 10^{-5}$). In a recent paper we have studied the consequences of these searches for circles if the Universe turns out to be exactly flat ($\Omega_{tot} = 1 $) as is often assumed. More specifically, we have derived the maximum angles of deviation possible from antipodicity of pairs of matching circles associated with the shortest closed geodesic for all multiply-connected flat orientable $3$-manifolds. These upper bounds on the deviation from antipodicity demonstrate that in a flat universe for some classes of topology there remains a substantial fraction of observers for whom the deviation from antipodicity of the matching circles is considerably larger than zero, which implies that the searches for circles-in-the-sky undertaken so far are not enough to exclude the possibility of a detectable non-trivial flat topology. Here we briefly review these results and discuss their consequences in the search for circles-in-the-sky in a flat universes.