Multi-connected Universe Research Articles

Electromagnetism in a Multiconnected Universe

Our raw intuition tells us that the topology of the universe shouldn't affect the behavior of a current-carrying wire, but when the wire wraps all the way around a multiconnected space, our intuition is wrong. While an infinitely long perfectly conducting wire in Euclidean space may carry a constant current, a simple application of the Ampere-Maxwell circuital law shows that the analogous wire in a 3-torus may not. Instead, we find that the current spontaneously oscillates, and the wire acts like an antenna, gradually radiating away its energy.

Wave computation on the Poincaré dodecahedral space

We compute the waves propagating on a compact 3-manifold of constant positive curvature with a non-trivial topology: the Poincaré dodecahedral space that is a plausible model of multi-connected universe. We transform the Cauchy problem to a mixed problem posed on a fundamental domain determined by the quaternionic calculus. We adopt a variational approach using a space of finite elements that is invariant under the action of the binary icosahedral group. The computation of the transient waves is validated with their spectral analysis by computing a lot of eigenvalues of the Laplace–Beltrami operator.

Hot pixel contamination in the CMB correlation function?

Recently, it was suggested that the map-making procedure, which is applied to the time-ordered cosmic microwave background data by the WMAP team, might be flawed by hot pixels. This could lead to a bias in the pixels having an angular distance of about 141° from hot pixels due to the differential measuring process of the satellite WMAP. Here, the bias is confirmed, and the temperature two-point correlation function C(ϑ) is reevaluated by excluding the affected pixels. It is shown that the most significant effect occurs in C(ϑ) at the largest angles near ϑ = 180°. Furthermore, the corrected correlation function C(ϑ) is applied to the cubic topology of the Universe, and it is found that such a multi-connected universe matches the temperature correlation better than the ΛCDM concordance model, provided the cubic length scale is close to L = 4 measured in units of the Hubble length.

CMB anisotropy of the Poincaré dodecahedron

We analyse the anisotropy of the cosmic microwave background (CMB) for the Poincaré dodecahedron which is an example of a multi-connected spherical universe. We compare the temperature correlation function and the angular power spectrum for the Poincaré dodecahedral universe with the first-year WMAP data and find that this multi-connected universe can explain the surprisingly low CMB anisotropy on large scales found by WMAP provided that the total energy density parameter Ωtot is in the range 1.016…1.020. The ensemble average over the primordial perturbations is assumed to be the scale-invariant Harrison–Zel'dovich spectrum. The circles-in-the-sky signature is studied and it is found that the signal of the six pairs of matched circles could be missed by current analyses of CMB sky maps.

Topological lensing in spherical spaces

This paper gives the construction and complete classification of all three-dimensional spherical manifolds and orders them by decreasing volume, in the context of multi-connected universe models with positive spatial curvature. It discusses which spherical topologies are likely to be detectable by crystallographic methods using three-dimensional catalogues of cosmic objects. The expected form of the pair separation histogram is predicted (including the location and height of the spikes) and is compared to computer simulations, showing that this method is stable with respect to observational uncertainties and is well suited for detecting spherical topologies.

The no-defect conjecture and its implications

When the topology of the universe is non-trivial, there exist constraints on the network of topological defects that may appear during a phase transition in the early universe. Here we review the main results of two recent papers by Uzan and Peter concerning topological defects in a multiconnected universe: the no-defect conjecture, the evaluation of the redshift at which all the defects (if formed) have disappeared and the consequence on the cosmic microwave background.