Research Overview
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I am a theoretical physicist/astrophysicist interested in a wide range of topics. Broadly, my research interests include gravitation, theoretical cosmology, and relativistic astrophysics.
I started my research career with a project on interacting dark energy and dark matter models. Then, I moved on to studying early universe (inflation). For my PhD dissertation, I worked on the classic (yet unresolved) problem of averaging in general relativity and cosmology. Recently, I have become interested in alternate theories of gravity and gravito-electromagnetism.
Gravitation
The theory of general relativity (GR) is a singular achievement of human intellect. Conceived in 1915 by the genius mind of Albert Einstein, the theory has been of great interest to mathematicians and physicists alike. GR postulates the concept of general covariance which simply means that the laws of physics must be invariant under arbitrary coordinate transformations. This simple demand leads to a geometric description of gravitation as the curvature of space-time. This description has been successfully verified using numerous experiments over the last 100 years. Predictions of GR such as expansion of the universe, bending of light due to gravity, and existence of black holes have enriched our understanding of the universe substantially.
The focus of my research so far has been the mathematical nature of the equations of GR (called Einstein field equations) and their solutions. The Einstein field equations (EFE) are a set of 10 non-linear coupled differential equations. Several of their solutions (there exist more than a 1000 of them) describe physical objects such as stars, black holes, and the whole Universe. I am interested in studying the structure of the exact space-times describing compact stars and black holes, both in GR and in other gravitational theories. Recently, I have also become interested in the study of geometric flows in the context of these theories. Details of a few projects that I (along with my students and colleagues) have worked on can be found here.
A timeline of the history of the universe (2009)
(source: NASA/WMAP Science Team)
Cosmology
Cosmology is the study of the nature and contents of the Universe as a whole. Modern cosmology is based on an exact solution of the Einstein field equations, called the Friedmann-Lemaitre-Robertson-Walker (FLRW) solution. This solution describes the space-time structure of the universe. Observations have told us that in addition to the ordinary matter that we see, the Universe also contains two exotic forms of matter-energy called dark energy and dark matter. One of the ways to explain the effects of dark energy is to include a constant term in the EFE, known as the cosmological constant.
I am interested in several aspects of relativistic cosmology. This includes topics like kinematics of geodesic bundles, 1+3 covariant formalism, the averaging problem and continuous media, cosmological perturbation theory, and inhomogeneous cosmological models.
The averaging problem in cosmology has constituted a major part of my research so far. It is an outstanding problem in GR that stems from the lack of a mathematically rigorous integration operation for tensor fields on curved space-times. I am interested in building cosmological models using various averaging schemes and putting observational constraints on them. Non-linear effects such as back-reaction and CMB non-Gaussianities can lead to important modifications to the standard model of cosmology. A recent interest of mine has been to analyse the effect of perturbations on the kinematics of paths of light bundles (which are related observables such as distances) in the Universe.
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