Implications of Conformal Symmetry in Cosmology

Symmetry has always played an important role in understanding Nature. At present most of our theoretical knowledge comes from the symmetry principles. In this talk I will discuss the implications of scale or conformal symmetry in Cosmology. First I will discuss a conformal model in which scalar fields are minimally coupled to the gravity. We propose a possible solution to the fine tuning problem of cosmological constant within the framework of softly broken conformally symmetric model. A major problem with the cosmological constant is that it gets very large quantum contributions from the matter sector at each order in perturbation theory. So we need to cancel these large contributions in order to maintain the small value of observed dark energy density, leading to an acute fine tuning problem. In our proposed solution we have shown that the matter sector will not contribute to the cosmological constant and hence we have solved the fine tuning problem. Here we have not considered the quantum gravity effects since quantum theory of gravity is not well formulated. This model also predicts the non-standard particles, which can be the possible candidates for dark matter. I will also discuss a model where scalar fields are non-minimally coupled to the gravity. In this case we need to go to the Einstein frame to study its cosmological implications.