Here are some current projects in cosmology involving undergraduate students.
Cyclic Inflation Model: Cyclic models envisage a universe that periodically expands and contracts, where time is endless not only in the future, but also in the past. The universe literally existed forever and there was never any beginning. If the cycles are asymmetric, that is in each the cycle the universe grows a bit more than it contracts, then over many-many such cycles the universe appears to "inflate" (grow exponentially). Below is a picture of the cyclic inflation phase followed by the usual slow power-law growth, a(t), represents the size of the universe.
That the universe once underwent an inflationary near-exponential growth has been pivotal to the success of the modern cosmological theory in explaining (and in some cases predicting) what one sees in our universe today. The cyclic inflation model, not only provides a viable mechanism to realize inflation but also comes with distinctive predictions for the cosmic microwave background radiation that our satellites are currently measuring. Here is a recent power point presentation on the subject.
Cyclic cosmologies in general provide an enigmatic alternative to the conventional monotonically expanding universe. There are quite a few interesting research projects in this direction that Dr. Biswas is planning to work on in the near future. If you are a physics or a math student who likes theoretical or computational work, you may want to explore the opportunity!
The Dark energy problem: Is the Dark energy just the Cosmological Constant as introduced by Einstein who later famously retracted it by saying that it was his “Biggest blunder”, or is there more to Dark energy than meets the “eye”? Cosmologists introduced dark energy to explain the cosmic speed-up, the fact that the expansion of our universe is speeding up rather than slowing down due to the gravitational attraction that exists between all "known" matter. In order to overcome gravity, dark energy has to have rather strange properties, such as having negative pressure and being impervious to dilution as the universe expands. This has lead many cosmologists to consider alternatives to the dark energy paradigm.
With collaborators and students, Dr. Biswas is currently looking into viable modifications of Einstein's theory of gravity that may be able to produce accelerating cosmologies without invoking dark energy. This is a follow up of his paper on viable gravitational theories on Minkowski background, including "non-local" (going beyond the paradigm that particles interact with each other at a given space-time point) modifications to Einstein's General theory of Relativity. Here is powerpoint presentation on the subject.