Comoving distance

Abstract: We adopt a cosmographic approach in order to determine spatial curvature (i.e. Ω_K), combining the latest release of cosmic chronometer (CC) data, the Pantheon sample of Type Ia supernovae observations and baryon acoustic oscillation measurements. We use the expanded transverse comoving distance D_M(⁠|$z$|⁠) as a basic function for deriving H(⁠|$z$|⁠) and other cosmic distances. In this scenario, Ω_K can be constrained only by CC data. To overcome the convergence issues at high-redshift domains, two methods are applied: the Pade approximants and the Taylor series in terms of the new redshift y = |$z$|/(1 + |$z$|⁠). Adopting the Bayesian evidence, we find that there is positive evidence for the Pade approximant up to order (2,2) and weak evidence for the Taylor series up to third order against the ΛCDM + Ω_K model. The constraint results show that a closed Universe is preferred by present observations under all the approximations used in this study. Also, the tension level of the Hubble constant H_0 has less than 2σ significance between different approximations and the local distance ladder determination. For each assumed approximation, H_0 is anticorrelated with Ω_K and the sound horizon at the end of the radiation drag epoch, which indicates that the H_0 tension problem can be slightly relaxed by introducing Ω_K or any new physics that can reduce the sound horizon in the early Universe.

Abstract: Maps of cosmic microwave background (CMB) temperature and polarization from the 2015 release of Planck data provide the highestquality full-sky view of the surface of last scattering available to date. This enables us to detect possible departures from a globally isotropic cosmology. We present the first searches using CMB polarization for correlations induced by a possible non-trivial topology with a fundamental domain that intersects, or nearly intersects, the last-scattering surface (at comoving distance χrec), both via a direct scan for matched circular patterns at the intersections and by an optimal likelihood calculation for specific topologies. We specialize to flat spaces with cubic toroidal (T3) and slab (T1) topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology with a scale below the diameter of the last-scattering surface. The limits on the radius ℛi of the largest sphere inscribed in the fundamental domain (at log-likelihood ratio Δlnℒ > −5 relative to a simply-connected flat Planck best-fit model) are: ℛi > 0.97 χrec for the T3 cubic torus; and ℛi > 0.56 χrec for the T1 slab. The limit for the T3 cubic torus from the matched-circles search is numerically equivalent, ℛi > 0.97 χrec at 99% confidence level from polarization data alone. We also perform a Bayesian search for an anisotropic global Bianchi VIIh geometry. In the non-physical setting, where the Bianchi cosmology is decoupled from the standard cosmology, Planck temperature data favour the inclusion of a Bianchi component with a Bayes factor of at least 2.3 units of log-evidence. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. Fitting the induced polarization pattern for this model to the Planck data requires an amplitude of −0.10 ± 0.04 compared to the value of + 1 if the model were to be correct. In the physically motivated setting, where the Bianchi parameters are coupled and fitted simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VIIh cosmology and constrain the vorticity of such models to (ω/H)0 < 7.6 × 10-10 (95% CL).

Abstract: We test the FLRW cosmology by reconstructing in a model-independent way both the Hubble parameter $H(z)$ and the comoving distance $D(z)$ via the most recent Hubble and Supernovae Ia data. In particular we use: data binning with direct error propagation, the principal component analysis, the genetic algorithms and the Pad\'e approximation. Using our reconstructions we evaluate the Clarkson {\it et al} test known as $\Omega_K(z)$, whose value is constant in redshift for the standard cosmological model, but deviates elsewise. We find good agreement with the expected values of the standard cosmological model within the experimental errors. Finally, we provide forecasts, exploiting the Baryon Acoustic Oscillations measurements from the Euclid survey.

Abstract: We propose a new model-independent method to test the cosmic curvature by comparing the proper distance and transverse comoving distance. Using the measurements of the Hubble parameter H(z) and the angular diameter distance d A , the cosmic curvature parameter is constrained to be −0.09 ± 0.19, which is consistent with a flat universe. We also use a Monte Carlo simulation to test the validity and efficiency, and find that our method can give a reliable and efficient constraint on cosmic curvature. Compared with other model-independent methods testing the cosmic curvature, our method can avoid some drawbacks and give a better constraint.