Circles-in-the-sky searches and observable cosmic topology in the inflationary limit

TL;DR

This paper develops a theoretical framework to interpret searches for matching circles in the cosmic microwave background, linking observational constraints to cosmological parameters and inflationary models, and assessing the detectability of cosmic topology.

Contribution

It provides a method to constrain circle parameters based on cosmological densities, aiding the interpretation of negative search results for cosmic topology.

Findings

Assuming a nearly flat universe, certain circle searches can exclude detectable topology for most observers.

The framework relates observer position and density parameters to the likelihood of detecting cosmic topology.

Negative results in specific circle searches can, under inflationary conditions, rule out non-trivial cosmic topology.

Abstract

While the topology of the Universe is at present not specified by any known fundamental theory, it may in principle be determined through observations. In particular, a non-trivial topology will generate pairs of matching circles of temperature fluctuations in maps of the cosmic microwave background, the so-called circles-in-the-sky. A general search for such pairs of circles would be extremely costly and would therefore need to be confined to restricted parameter ranges. To draw quantitative conclusions from the negative results of such partial searches for the existence of circles we need a concrete theoretical framework. Here we provide such a framework by obtaining constraints on the angular parameters of these circles as a function of cosmological density parameters and the observer's position. As an example of the application of our results, we consider the recent search restricted to pairs of nearly back-to-back circles with negative results. We show that assuming the Universe to be very nearly flat, with its total matter-energy density satisfying the bounds $ 0 <|\Omega_0 - 1| \lesssim 10^{-5}$, compatible with the predictions of typical inflationary models, this search, if confirmed, could in principle be sufficient to exclude a detectable non-trivial cosmic topology for most observers. We further relate explicitly the fraction of observers for which this result holds to the cosmological density parameters.