Markov chain Monte Carlo analysis of Bianchi VII_h models

We have extended the analysis of Jaffe et al. to a complete Markov chain Monte Carlo (MCMC) study of the Bianchi type ${\rm VII_h}$ models including a dark energy density, using 1-year and 3-year Wilkinson Microwave Anisotropy Probe (WMAP) cosmic microwave background (CMB) data. Since we perform the analysis in a Bayesian framework our entire inference is contained in the multidimensional posterior distribution from which we can extract marginalised parameter constraints and the comparative Bayesian evidence. Treating the left-handed Bianchi CMB anisotropy as a template centred upon the `cold-spot' in the southern hemisphere, the parameter estimates derived for the total energy density, `tightness' and vorticity from 3-year data are found to be: $\Omega_{tot} = 0.43\pm 0.04$, $h = 0.32^{+0.02}_{-0.13}$, $\omega = 9.7^{+1.6}_{-1.5}\times 10^{-10}$ with orientation $\gamma = {337^{\circ}}^{+17}_{-23}$). This template is preferred by a factor of roughly unity in log-evidence over a concordance cosmology alone. A Bianchi type template is supported by the data only if its position on the sky is heavily restricted. The low total energy density of the preferred template, implies a geometry that is incompatible with cosmologies inferred from recent CMB observations. Jaffe et al. found that extending the Bianchi model to include a term in $\Omega_{\Lambda}$ creates a degeneracy in the $\Omega_m - \Omega_{\Lambda}$ plane. We explore this region fully by MCMC and find that the degenerate likelihood contours do not intersect areas of parameter space that 1 or 3 year WMAP data would prefer at any significance above $2\sigma$. Thus we can confirm that a physical Bianchi ${\rm VII_h}$ model is not responsible for this signature.Comment: 8 pages, 10 figures, significant update to include more accurate results and conclusions to match version accepted by MNRA

Accelerated expansion from structure formation

We discuss the physics of backreaction-driven accelerated expansion. Using the exact equations for the behaviour of averages in dust universes, we explain how large-scale smoothness does not imply that the effect of inhomogeneity and anisotropy on the expansion rate is small. We demonstrate with an analytical toy model how gravitational collapse can lead to acceleration. We find that the conjecture of the accelerated expansion being due to structure formation is in agreement with the general observational picture of structures in the universe, and more quantitative work is needed to make a detailed comparison.Comment: 44 pages, 1 figure. Expanded treatment of topics from the Gravity Research Foundation contest essay astro-ph/0605632. v2: Added references, clarified wordings. v3: Published version. Minor changes and corrections, added a referenc

Planck 2013 results. XXVI. Background geometry and topology of the Universe

Peer reviewe

Planck 2013 results. XXIII. Isotropy and statistics of the CMB

Peer reviewe

Planck 2013 results. XXV. Searches for cosmic strings and other topological defects

Peer reviewe

Planck 2013 results. I. Overview of products and scientific results

Peer reviewe

Planck 2015 results. XVIII. Background geometry and topology of the Universe

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)