A new, improved version of a cosmic crystallography method for constraining cosmic topology is introduced. Like the circles-inthe-sky method using CMB data, we work in a thin, shell-like region containing plenty of objects. Two pairs of objects (quadruplet) linked by a holonomy show a specific distribution pattern, and three filters of separation, vectorial condition, and lifetime of objects extract these quadruplets. Each object P i is assigned an integer s i , which is the number of candidate quadruplets including P i as their members. Then an additional device of s i -histogram is used to extract topological ghosts, which tend to have high values of s i . In this paper we consider flat spaces with Euclidean geometry, and the filters are designed to constrain their holonomies. As the second filter, we prepared five types that are specialized for constraining specific holonomies: one for translation, one for half-turn corkscrew motion and glide reflection, and three for nth turn corkscrew motion for n = 4, 3, and 6. Every multiconnected space has holonomies that are detected by at least one of these five filters. Our method is applied to the catalogs of toy quasars in flat Λ-CDM universes whose typical sizes correspond to z ∼ 5. With these simulations our method is found to work quite well. These are the situations in which type-II pair crystallography methods are insensitive because of the tiny number of ghosts. Moreover, in the flat cases, our method should be more sensitive than the type-I pair (or, in general, n-tuplet) methods because of its multifilter construction and its independence from n.

In the standard model of cosmology, the Universe is static in comoving coordinates; expansion occurs homogeneously and is represented by a global scale factor. The baryon acoustic oscillation (BAO) peak location is a statistical tracer that represents, in the standard model, a fixed comoving-length standard ruler. Recent gravitational collapse should modify the metric, rendering the effective scale factor, and thus the BAO standard ruler, spatially inhomogeneous. Using the Sloan Digital Sky Survey, we show to high significance (P < 0.001) that the spatial compression of the BAO peak location increases as the spatial paths' overlap with superclusters increases. Detailed observational and theoretical calibration of this BAO peak location environment dependence will be needed when interpreting the next decade's cosmological surveys.

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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.

The redshift of the cosmic microwave background (CMB) radiation in the R h = ct cosmology (Melia & Shevchuk 2012) is inferred from nearly model-independent measurements of the angular baryon acoustic oscillations and the first acoustic peak location of the CMB power spectrum, based on the assumption that the two phenomena occur at the same comoving scale in the R h = ct model (Melia & López-Corredoira 2017). The derived redshift, z * ≈ 23, which corresponds to the radiation temperature T * ≈ 65 K, is inconsistent with the standard interpretation of the CMB as the relic radiation of the Big Bang.