On the possibility for constraining cosmic topology from the celestial distribution of astronomical objects

TL;DR

This paper explores a method to constrain cosmic topology using celestial object distributions but finds it impractical due to low signal-to-noise ratio, emphasizing the need for 3D catalogs instead.

Contribution

The paper extends a 3D cosmic topology search method to celestial sphere projections and evaluates its practicality, concluding it is ineffective with current data.

Findings

The celestial distribution method is impractical due to low signal-to-noise ratio.

3D catalogs are necessary for constraining cosmic topology.

The proposed method is not feasible with realistic observational data.

Abstract

We present a method to constrain cosmic topology from the distribution of astronomical objects projected on the celestial sphere. This is an extension of the 3D method introduced in Fujii & Yoshii (2011) that is to search for a pair of pairs of observed objects (quadruplet) linked by a holonomy, i.e., the method we present here is to search for a pair of celestial sphere $n$-tuplets for $n \geq 3$. We find, however, that this method is impractical to apply in realistic situations due to the small signal to noise ratio. We conclude therefore that it is unrealistic to constrain the topology of the Universe from the celestial distribution, and the 3D catalogs are necessary for the purpose.