Ellipsoidal Universe Can Solve the Cosmic Microwave Background Quadrupole Problem

The recent 3 yr Wilkinson Microwave Anisotropy Probe data have confirmed the anomaly concerning the low quadrupole amplitude compared to the best-fit $\Lambda$–cold dark matter prediction. We show that by allowing the large-scale spatial geometry of our universe to be plane symmetric with eccentricity at decoupling or order ${10}^{-2}$, the quadrupole amplitude can be drastically reduced without affecting higher multipoles of the angular power spectrum of the temperature anisotropy.

Figure 1

Geometrical interpretation of the CMB anisotropy in an “ellipsoidal” universe. A photon emitted at point $E$ of the ellipsoidal surface of last scattering reaches the observer $O$ with an energy proportional to the distance between emitter and observer. This causes a quadrupole anisotropy in the CMB radiation.

Figure 2

Results from our numerical simulation with $N=250$ runs. Continuous gray lines in the left and right panels refer to Eqs. (26, 27), respectively. Left panel: The blue continuous line is the mean value Eq. (28), the green dashed line is Eq. (4), and the red dashed line is Eq. (5). Right panel: The blue continuous line is the mean value Eq. (29).