Indications about the Shape of the Universe from the Wilkinson Microwave Anisotropy Probe Data

It is shown that the recent observations of NASA's Explorer mission, “Wilkinson Microwave Anisotropy Probe,” hint that our Universe may possess a nontrivial topology. As an example we discuss the Picard space which is stretched out into an infinitely long horn but with finite volume.

Figure 1

The mean temperature correlation function $C(\vartheta )$ is shown as a dashed curve for the Picard universe with ${\Omega }_{\mathrm{m}\mathrm{a}\mathrm{t}}=0.30$ and ${\Omega }_{\Lambda }=0.65$. The $1\sigma$ deviation is shown as a gray band. The corresponding WMAP curve is shown as a solid curve. The dotted curve represents the best-fit $\Lambda \mathrm{C}\mathrm{D}\mathrm{M}$ model described in 4 and the shaded region is the corresponding $1\sigma$ deviation band.

Figure 2

The Picard cell is shown in the unit ball, where the latter is indicated by the yellow net. In addition, the eigenfunction belonging to $k=20.3003\cdots$ is shown.

Figure 3

The eigenfunction belonging to $k=60.0057\cdots$ is shown in the Picard cell.

Figure 4

The cumulative distribution of the $S$ statistic for $\alpha =60°$ for 300 Picard simulations in comparison to the concordance model. The vertical line shows the value of the $S$ statistic for the WMAP data.

Figure 5

The same as in Fig. 4, but for $\alpha =20°$.