Research Projects

The issue of the late time accelerating Universe which originated from supernovae observations has given a new dimension to the cosmological research programme, which are largely been directed at understanding the properties of dark energy (DE). Einstein’s GR has certain limitations in addressing this issue, hence the effort to modify GR has become inevitable. There can be two different ways to modify GR. In the first approach, some extra matter fields contributions are added to the energy-momentum tensor so as to explain the late time cosmic speed up issue. These methods may lead to the presence of ghost fields providing negative kinetic energy. On the other hand, the geometrical aspect of the Einstein-Hilbert action is modified to get accelerating models without the assumption of any exotic fluids. In theoretical cosmology, the present focus is on the parametrization of the geometrical parameters such as the Hubble parameter, deceleration parameter, jerk and snap parameter and so on. These parameters enabled us to distinguish between different dark energy models e.g. the expansion history, the accelerating phase or the present stage of the Universe. One of the key issue is the recent H₀ tension issue and also the issues related to other geometrical or cosmological parameters. The H₀ tension issue is basically the different ranges of value suggested by different cosmological observations on the present value of the Hubble parameter. Of course, issues of all other geometrical parameters can be directly or indirectly addressed if the H₀ tension is reduced. Theoretically we propose to constrain these cosmological parameters based on the teleparallel gravity and its extension. The field equations of teleparallel gravitational theories contain the Hubble expansion term and the functional form of f(T). We shall develop certain functional forms of f(T) and adjust the free parameters in such a way that it will be resulting in an accelerating model at late times. Not only this our main focus in this proposal is to identify a suitable form of the expansion H such that it provides a consistent result on all the geometrical parameters in addition to the present H₀ value leading to a possible reduction in the H₀ tension. Whenever we are ready with the accelerating models, we will test our models through the available cosmological data sets. In order to make the models robust, we may include the additional terms in the action such as, Gauss-Bonnet term, scalar field, trace of energy momentum tensor and so on. It is well known that it is extremely difficult to find the solution to a system of equations those are highly non-linear. So, one can use the method that allows some critical properties to be determined about the solutions without knowing the exact solution of the system of equations. In such an approach to a system of differential equations; a dynamical system is introduced by making the variables dimensionless.