Looking for non-Gaussianity in all the right places: A new basis for non-separable bispectra

Non-Gaussianity in the distribution of inflationary perturbations, measurable in statistics of the cosmic microwave background (CMB) and large scale structure fluctuations, can be used to probe non-trivial initial quantum states for these perturbations. The bispectrum shapes predicted for generic non-Bunch-Davies initial states are non-factorizable (non-separable) and are highly oscillatory functions of the three constituent wavenumbers. This can make the computation of CMB bispectra, in particular, computationally intractable. To efficiently compare with CMB data one needs to construct a separable template that has a significant similarity with the actual shape in momentum space. In this paper we consider a variety of inflationary scenarios, with different non-standard initial conditions, and how best to construct viable template matches. In addition to implementing commonly used separable polynomial and Fourier bases, we introduce a basis of localized piecewise spline functions. The spline basis is naturally nearly orthogonal, making it easy to implement and to extend to many modes. We show that, in comparison to existing techniques, the spline basis can provide better fits to the true bispectrum, as measured by the cosine between shapes, for sectors of the theory space of general initial states. As such, it offers a useful approach to investigate non-trivial features generated by fundamental properties of the inflationary Universe.

Alignments in quasar polarizations: pseudoscalar-photon mixing in the presence of correlated magnetic fields

We investigate the effects of pseudoscalar-photon mixing on electromagnetic radiation in the presence of correlated extragalactic magnetic fields. We model the Universe as a collection of magnetic domains and study the propagation of radiation through them. This leads to correlations between Stokes parameters over large scales and consistently explains the observed large-scale alignment of quasar polarizations at different redshifts within the framework of the big bang model.

Signatures of Pseudoscalar Photon Mixing in CMB Radiation

We model the effect of photon and ultra-light pseudoscalar mixing on the propagation of electromagnetic radiation through the extragalactic medium. The medium is modelled as a large number of magnetic domains, uncorrelated with one another. We obtain an analytic expression for the different Stokes parameters in the limit of small mixing angle. The different Stokes parameters are found to increase linearly with the number of domains. We also verify this result by direct numerical simulations. We use this formalism to estimate the effect of pseudoscalar-photon mixing on the Cosmic Microwave Background (CMB) polarization. We impose limits on the model parameters by the CMB observations. We find that the currently allowed parameter range admits a CMB circular polarization up to order $10^{-7}$.