Research Interests
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My research interest lies in the gravity theories to understand the dynamical and physical nature of the cosmos on large scales. The famous Einstein theory and Einstein's equations make it clear that the curvature tensor plays a crucial role in understanding the geometry of the universe, and it reveals how space-time is related to the matter density of the universe. This theory gained tremendous success by explaining the perihelion precision of Mercury, gravitational waves, the cosmological constant problem, the redshift-distance relationship, and other phenomena. Despite huge successes, there are still some theoretical and observational challenges, such as dark matter, dark energy, accelerated expansion of the universe, and Hubble tensions, that motivate us to explore modified theories of gravity to accommodate these issues and also test those theories against the known cosmological and astrophysical phenomena.
Modified geometric foundations of gravity
Rather than curvature, two other fundamental geometric representations, such as torsions (which measure the distortion while the twisting of spacetime) and nonmetricity (responsible for measuring the length of a vector in a parallel transportation in the spacetime), can be introduced to understand the gravitational phnomenon. The following pictures nicely illustrate the geometrical meaning of these three terms. Interestingly, in all these three cases, the Lagrangians are equivalent apart from a boundary term and hence known as the geometric trinity of gravity. However, their generalizations are no longer equivalent, and hence it is interesting to study the cosmological phenomenon in it. Instead of the Levi-Civita connection in GR, in metric teleparallel theory, a metric-compatible curvatureless Weitzenböck connection is used, and in symmetric teleparallel theory, a curvatureless, torsionless affine connection is used to measure the parallel transportation in a spacetime. In my phd thesis, we investigate the effects of the non-Riemannian connection in teleparallel theories to understand the different epochs of cosmic evolution, starting from radiation to matter to dark energy-dominated eras.
Different ways to modify GR
One can modify the Einstein theory of general relativity, either by changing the geometry (left-hand side) or the matter (right-hand side) of the Einstein equations. Again, various possible ways are available to change the left-hand side, among them one is the geometric modifications (Listed in the green box in the figure), which is the main interesting starting point of my research.
Early Universe Cosmology
From the Big Bang to inflation and galaxy formation, this diagram clearly represents the evolution of the universe up to today and its various intermediate phases. We believed inflation happened in the very early stage of the universe, generated from a rapid expansion just after the Big Bang, as evidenced by the cosmic microwave background, large-scale structure formation of the universe, and the expansion history of the universe. My research is particularly interested in understanding the early universe cosmologies, primordial black hole gravitational waves generated from primordial blackhole, structure formations, and matter growth perturbations in various alternative formulations of gravity theories.
Dynamical system
Due to the complexity and nonlinearity in the modified Einstein field equations, there is indeed difficulty in finding analytic solutions of gravity theories. A dynamical system technique can be used to read this difficulty to transform the modified Einstein field equations to first-order ordinary differential equations or an autonomous dynamical system. This facilitates finding the fixed point of the system and makes it easier to analyze the nature of fixed points through a phase space analysis by looking into the phase space trajectories. This facilitates understanding the cosmic evolution of the universe in both the early and late times.
Hamiltonian analysis
Furthermore, my research explores Hamiltonian analysis in alternative theories to understand the physical viability, physical degrees of freedom, and the concepts of energy from a Hamiltonian perspective. First, we reformulate the Lagrangian formalism through a Legendre transformation, which maps the original fields and their velocities into coordinates and their conjugate momenta. This reformulation helps to build Hamiltonian equations, identify constraints, and separate unphysical from true degrees of freedom.
Tools used in research
Latex
xAct Mathematica for symbolic and component computations
Microsoft word
Python
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