Several unexpected features have been observed in the microwave sky at large angular scales, both by WMAP and by Planck. Among those features is a lack of both variance and correlation on the largest angular scales, alignment of the lowest multipole moments with one another and with the motion and geometry of the solar system, a hemispherical power asymmetry or dipolar power modulation, a preference for odd parity modes and an unexpectedly large cold spot in the Southern hemisphere. The individual p -values of the significance of these features are in the per mille to per cent level, when compared to the expectations of the best-fit inflationary ΛCDM model. Some pairs of those features are demonstrably uncorrelated, increasing their combined statistical significance and indicating a significant detection of CMB features at angular scales larger than a few degrees on top of the standard model. Despite numerous detailed investigations, we still lack a clear understanding of these large-scale features, which seem to imply a violation of statistical isotropy and scale invariance of inflationary perturbations. In this contribution we present a critical analysis of our current understanding and discuss several ideas of how to make further progress.

The large-angle (low-$\ell$) correlations of the cosmic microwave background exhibit several statistically significant anomalies compared to the standard inflationary cosmology. We show that the quadrupole plane and the three octopole planes are far more aligned than previously thought (99.9% C.L.). Three of these planes are orthogonal to the ecliptic at 99.1% C.L., and the normals to these planes are aligned at 99.6% C.L. with the direction of the cosmological dipole and with the equinoxes. The remaining octopole plane is orthogonal to the supergalactic plane at 99.6% C.L.

Considerable work has been devoted to the question of how best to parametrize the properties of dark energy, in particular, its equation of state $w$. We argue that, in the absence of a compelling model for dark energy, the parametrizations of functions about which we have no prior knowledge, such as $w(z)$, should be determined by the data rather than by our ingrained beliefs or familiar series expansions. We find the complete basis of orthonormal eigenfunctions in which the principal components [weights of $w(z)$] that are determined most accurately are separated from those determined most poorly. Furthermore, we show that keeping a few of the best-measured modes can be an effective way of obtaining information about $w(z)$.

There is evidence that Newton and Einstein’s theories of gravity cannot explain the dynamics of a universe made up solely of baryons and radiation. To be able to understand the properties of galaxies, clusters of galaxies and the universe on the whole it has become commonplace to invoke the presence of dark matter. An alternative approach is to modify the gravitational field equations to accommodate observations. We propose a new class of gravitational theories in which we add a new degree of freedom, the Aether, in the form of a vector field that is coupled covariantly, but nonminimally, with the space-time metric. We explore the Newtonian and non-Newtonian limits, discuss the conditions for these theories to be consistent and explore their effect on cosmology.

We propose a novel representation of cosmic microwave anisotropy maps, where each multipole order $\mathcal{l}$ is represented by $\mathcal{l}$ unit vectors pointing in directions on the sky and an overall magnitude. These “multipole vectors and scalars” transform as vectors under rotations. Like the usual spherical harmonics, multipole vectors form an irreducible representation of the proper rotation group $\mathrm{SO}\left(3\right).$ However, they are related to the familiar spherical harmonic coefficients $a_{\mathcal{l}m}$ in a nonlinear way and are therefore sensitive to different aspects of the cosmic microwave background (CMB) anisotropy. Nevertheless, it is straightforward to determine the multipole vectors for a given CMB map and we present an algorithm to compute them. A code implementing this algorithm is available at http://www.phys.cwru.edu/projects/mpvectors/. Using the Wilkinson Microwave Anisotropy Probe (WMAP) full-sky maps, we perform several tests of the hypothesis that the CMB anisotropy is statistically isotropic and Gaussian random. We find that the result from comparing the oriented area of planes defined by these vectors between multipole pairs $2<~{\mathcal{l}}_1\ne {\mathcal{l}}_2<~8$ is inconsistent with the isotropic Gaussian hypothesis at the 99.4% level for the internal linear combination map and at 98.9% level for the cleaned map of Tegmark et al. A particular correlation is suggested between the $\mathcal{l}=3\mathrm{}$ and $\mathcal{l}=8\mathrm{}$ multipoles, as well as several other pairs. This effect is entirely different from the now familiar planarity and alignment of the quadrupole and octupole: while the aforementioned is fairly unlikely, the multipole vectors indicate correlations not expected in Gaussian random skies that make them unusually likely. The result persists after accounting for pixel noise and after assuming a residual 10% dust contamination in the cleaned WMAP map. While the definitive analysis of these results will require more work, we hope that multipole vectors will become a valuable tool for various cosmological tests, in particular those of cosmic isotropy.