Phenomenological and Theoretical Aspects of Quantum Gravity

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Quantum Mechanics and General Relativity are two of the most successful physical theories. Yet they appear to be mutually incompatible. Candidate theories of Quantum Gravity (QG) such as Superstring Theory (ST) and Loop Quantum Gravity (LQG) aim to unify the two, and have made significant progress. However, there has not been a single experiment or observation which supports or refutes any theory. The main focus of my research is to find experimental signatures of QG. All QG theories predict a minimum measurable length. The research of my collaborators and I have shown that this implies universal QG effects in all quantum systems (Das, Vagenas, PRL101,221301(2008)). This has given rise to considerable optimism that despite the immensity of the Planck energy scale, about 1016 TeV, with continual improvement in measurement sensitivities, signatures of QG may be observable in the low energy laboratory. One of the most important applications of General Relativity is cosmology, which has made remarkable progress in our understanding of the large scale structure of the universe. Two main unresolved problems in this area are understanding of the true nature of dark matter and dark energy, which together make up 95% of our universe. We have recently shown that a Bose-Einstein condensate (BEC) of ultralight bosons is a viable candidate for both dark matter and dark energy. The density of the BEC accounts for the dark matter and the quantum potential with negative pressure that it generates accounts for the dark energy. Motivated by the above, and building on my expertise, the objective of my research is to investigate three key problems in the aforementioned areas. In the short (1-2 years) and medium term (3-5 years), I will:  1: Formulate a Lorentz covariant description of minimum length and the related Generalized Uncertainty Principle (GUP) in QG. Apply this to compute QG corrections in low energy systems. Measure GUP effects in the optomechanical laboratory.   2: Make quantitative predictions such as density profiles of the cosmic BEC and compare with available data.  3: Building on my team's recent work, study gravitational Higgs mechanism as a viable model of dimensional reduction and study its implications for QG.  My research will provide evidence for or against the existing theories of QG, on the fundamental dimension of spacetime and the BEC model of dark matter and dark energy. In the long term, it will give important insights into what the correct theory of quantum gravity is and how to extract its experimental signatures. It will help rule out some theories. It will also shed light on the nature of spacetime - whether it is fundamentally discrete or continuum. It will help us understand the origin and evolution of the universe via detailed information about its contents and the theory of gravity which governs it.  In order to accomplish these objectives, I will train HQP at all levels and collaborate nationally and internationally.