Aspects of modern cosmology: inflation, gravitational waves and dark matter

The remarkable progress in the observations of the universe in the past couple of decades has led to the establishment of a standard model of physical cosmology. In this talk, we begin by looking at the status of modern cosmology and then explore a number of issues of current interest e.g. (a) how well does the observational data constrain the shape of the primordial power spectrum?, (b) could the Hawking radiation during inflation help in solving the Higgs instability problem? (c) how well could we use the CMB data to constrain a radiation dominated era prior to inflation? (d) could we use the observations of Gravitational Waves to probe the nature of DM?