Beecroft Institute for Particle Astrophysics and Cosmology

Abstract:

A scalar field with an exponential potential has the particular property that it is attracted into a solution in which its energy scales as the dominant component (radiation or matter) of the Universe, contributing a fixed fraction of the total energy density. We study the growth of perturbations in a CDM dominated $\Omega=1$ universe with this extra field, with an initial flat spectrum of adiabatic fluctuations. The observational constraints from structure formation are satisfied as well, or better, than in other models, with a contribution to the energy density from the scalar field $\Omega_\phi \sim 0.1$ which is small enough to be consistent with entry into the attractor prior to nucleosynthesis.

Abstract:

We propose a new method for constraining a primordial homogeneous magnetic field with the cosmic microwave background. Such a field will induce an observable parity odd cross correlation between the polarization anisotropy and the temperature anisotropy by Faraday rotation. We analyze the necessary experimental features to match, and improve, current constraints of such a field by measuring this correlation.

Abstract:

We discuss the requirements of good statistics for quantifying non-Gaussianity in the Cosmic Microwave Background. The importance of rotational invariance and statistical independence is stressed, but we show that these are sometimes incompatible. It is shown that the first of these requirements prefers a real space (or wavelet) formulation, whereas the latter favours quantities defined in Fourier space. Bearing this in mind we decide to be eclectic and define two new sets of statistics to quantify the level of non-Gaussianity. Both sets make use of the concept of cumulants of a distribution. However, one set is defined in real space, with reference to the wavelet transform, whereas the other is defined in Fourier space. We derive a series of properties concerning these statistics for a Gaussian random field and show how one can relate these quantities to the higher order moments of temperature maps. Although our frameworks lead to an infinite hierarchy of quantities we show how cosmic variance and experimental constraints give a natural truncation of this hierarchy. We then focus on the real space statistics and analyse the non-Gaussian signal generated by points sources obscured by large scale Gaussian fluctuations. We conclude by discussing the practical implementations of these techniques.