A Search for Nontoroidal Topological Lensing in the Sloan Digital Sky Survey Quasar Catalog

Abstract

Flat space models with multiply connected topology, which have compact dimensions, are tested against the distribution of high-redshift (z 4) quasars of the Sloan Digital Sky Survey (SDSS). When the compact dimensions are smaller in size than the observed universe, topological lensing occurs, in which multiple images of single objects (ghost images) are observed. We improve on the recently introduced method to identify ghost images by means of four-point statistics. Our method is valid for any of the 17 multiply connected flat models, including nontoroidal ones that are compacted by screw motions or glide reflection. Applying the method to the data revealed one possible case of topological lensing caused by sixth-turn screw motion, however, it is consistent with the simply connected model by this test alone. Moreover, simulations suggest that we cannot exclude the other space models despite the absence of their signatures. This uncertainty mainly originates from the patchy coverage of SDSS in the south Galactic cap, and this situation will be improved by future wide-field spectroscopic surveys.

Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches

“…The most obvious observational consequence of such a topological structure would be the appearance of multiple images of distant cosmic objects: light coming from a far-away galaxy would arrive at our position via multiple different paths. Each manifold would exhibit a predictable pattern of images of each astrophysical source to each observer (that can depend on the position of each); hence the name cosmic crystallography [9][10][11][12][13][14][15][16] for the search for such patterns. Detection of topology through such multiple images is complicated by the fact that different light paths lead to views of sources (such as galaxies) from different vantage points and with different look-back times, so both the morphology and time evolution of a source must be well understood to identify its multiple images.…”

Doubt on the statistical significance of the Giant GRB Ring

“…Note also that, as a possible origin for the ring‐like shape of the GGR, Balázs et al (2018) mentioned a multiply‐connected topology of the universe but rejected the hypothesis based on recent observational results (Planck Collaboration et al 2016); see Luminet (2016) for a recent review. However, this claim is incorrect because ring‐like patterns will not appear unless one extracts “ghost” images, that is, multiple images of a single object formed by light rays that travel around compact spatial dimensions, from observational data by a statistical method (e.g., Fujii & Yoshii 2013; Roukema et al 2014, and references therein). Furthermore, it will hardly occur due to its short (≲1000 s) duration that a single GRB can be observed as ghosts multiple times.…”

Gravitational potential in spherical topologies

“…Equation ( 1) corresponds to Newton's second law for the spatial acceleration of the fluid spatial velocity (this is also the Navier-Stokes equation, since it is written for a fluid), with (∂ t − L β ) v a + v c D c v a being the spatial acceleration corresponding to the spatial velocity v in any coordinate system, i.e. covariantly defined; equations ( 2) and ( 3) are constraint equations on the gravitational field, which (3) constrains to be irrotational; equation ( 5) is the evolution equation for the spatial metric; equation ( 6) is the continuity equation; equation (7) is the expansion law for the volume of the manifold Σ.…”

“…In contrast, taking into account the presence of inhomogeneities allows for the search of the specific topology (e.g. multiply connected) of our Universe by searching for correlations of matter distributions using either catalogues of extragalactic objects (the methods of cosmic crystallography of type I pairs [2], type II pairs [3,4], or quadruplet methods to seek weak signals [5][6][7][8]), or the CMB map (the method of circles in the sky, [9][10][11][12]). These studies currently give typical lower bounds of around 10 to 20 (Gpc/h) 3 (e.g.…”