Spectroscopy of Cosmic topology
  Einstein's theory of gravitation that governs the geometry of space-time, coupled with spectacular advance in cosmological observations, promises to deliver a `standard model' of cosmology in the near future. However, local geometry of space constrains, but does not dictate the topology of the cosmos. hence, Cosmic topology has remained an enigmatic aspect of the `standard model' of cosmology. Recent advance in the quantity and quality of observations has brought this issue within the realm of observational query. The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic consequence of non trivial cosmic topology arising from to the imposed `crystallographic' periodicity on the eigenstates of the Laplacian. The sky maps of Cosmic Microwave Background (CMB) anisotropy and polarization most promising observations that would carry signatures of a violation of statistical isotropy and homogeneity. Hence, a measurable spectroscopy of cosmic topology is made possible using the Bipolar power spectrum (BiPS) of the temperature and polarization that quantifies violation of statistical isotropy. 
Tarun Souradeep (IUCAA)