We show that, the part of the universe that is observable today (in principle), could not have evolved out of a domain which was causally connected in the past. This and other issues related to horizon problem in inflationary models are discussed.

The evolution of Gaussian quantum states in the de Sitter phase of the early universe is investigated. The potential is approximated by that of an inverted oscillator. We study the origin and magnitude of the density perturbations with special emphasis on the nature of the semiclassical limits

In the computation of density perturbation in inflation it is conventional to assume the inflation field to be in the vacuum state. There are, however, some advantages in relaxing this assumption. In an earlier paper we have estimated the density perturbations in a Gaussian coherent state using a toy-model. Here we extend this work by doing an exact analysis of this problem. The advantages of this method is discussed and the results are compared with earlier results

The historical motivation for the Brans-Dicke theory and its connection with Mach’s principle has been discussed. Some examples of actions which can be reduced to the Brans-Dicke type have been given. Further, the recent developments in the theory in the context of inflationary cosmology have been briefly pointed out.

Origin of magnetic fields, its structure and effects on dynamical processes in stars to galaxies are not well understood. Lack of a direct probe has remained a problem for its study. The first phase of Square Kilometre Array (SKA-I), will have almost an order of magnitude higher sensitivity than the best existing radio telescope at GHz frequencies. In this contribution, we discuss specific science cases that are of interest to the Indian community concerned with astrophysical turbulence and magnetic fields. The SKA-I will allow observations of a large number of background sources with detectable polarization and measure their Faraday depths (FDs) through the Milky Way, other galaxies and their circum-galactic mediums. This will probe line-of-sight magnetic fields in these objects well and provide field configurations. Detailed comparison of observational data (e.g., pitch angles in spirals) with models which consider various processes giving rise to field amplification and maintenance (e.g., various types of dynamo models) will then be possible. Such observations will also provide the coherence scale of the fields and its random component through RM structure function. Measuring the random component is important to characterize turbulence in the medium. Observations of FDs with redshift will provide important information on magnetic field evolution as a function of redshift. The background sources could also be used to probe magnetic fields and its coherent scale in galaxy clusters and in bridges formed between interacting galaxies. Other than FDs, sensitive observations of synchrotron emission from galaxies will provide complimentary information on their magnetic field strengths in the sky plane. The core shift measurements of AGNs can provide more precise measurements of magnetic field in the sub parsec region near the black hole and its evolution. The low band of SKA-I will also be useful to study circularly polarized emission from Sun and comparing various models of field configurations with observations.