Constraints on the Detectability of Cosmic Topology from Observational Uncertainties

TL;DR

This paper investigates how observational uncertainties in cosmological parameters affect the ability to detect cosmic topology, providing analytical and numerical methods to determine detectability conditions in nearly flat universes.

Contribution

It introduces two complementary methods to assess the detectability of cosmic topology considering observational uncertainties, with analytical conditions for undetectability at infinite redshift.

Findings

Analytical conditions for undetectability derived and confirmed

Methods yield similar results for high redshifts

Application to WMAP data illustrates practical utility

Abstract

Recent observational results suggest that our universe is nearly flat and well modelled within a $\Lambda$CDM framework. The observed values of $\Omega_{m}$ and $\Omega_{\Lambda}$ inevitably involve uncertainties. Motivated by this, we make a systematic study of the necessary and sufficient conditions for undetectability as well as detectability (in principle) of cosmic topology (using pattern repetition) in presence of such uncertainties. We do this by developing two complementary methods to determine detectability for nearly flat universes. Using the first method we derive analytical conditions for undetectability for infinite redshift, the accuracy of which is then confirmed by the second method. Estimates based on WMAP data together with other measurements of the density parameters are used to illustrate both methods, which are shown to provide very similar results for high redshifts.