Parampreet Singh, Ph.D.
Parampreet Singh, PhD
Assistant Professor of Physics
Ph.D., 2004 - Inter-University Center for Astronomy & Astrophysics (IUCAA),
University of Pune
Louisiana State University
Department of Physics & Astronomy
255-A Nicholson Hall, Tower Dr.
Baton Rouge, LA 70803-4001
Quantum Gravity, Cosmology
Singularity theorems of Penrose and Hawking tell us that singularities such as the big bang are the generic features of Einstein's theory of general relativity (GR). These are the boundaries of spacetime where all known laws of physics end. Thus signaling that GR, based on assuming a continuum spacetime at arbitrary scales, must be replaced by a more fundamental theory. It is believed that a quantum theory of spacetime or quantum gravity would resolve the singularity problem in GR. One such theory is loop quantum gravity (LQG). Our majority of research focuses on understanding physical implications, in particular for singularity resolution, for various cosmological and black hole spacetimes in LQG.
Few years ago, in a collaboration with A. Ashtekar and T. Pawlowski, we showed that for simple models in loop quantum cosmology (LQC), a quantization of homogeneous spacetimes based on LQG, the big bang singularity can be successfully resolved. If a state corresponding to a classical universe at late times is evolved towards the big bang using quantum gravitational Hamiltonian, we find that instead of following classical trajectory in to the big bang, the state bounces to a contracting trajectory when the spacetime curvature reached close to the Planck value. The quantum bounce or the big bounce occurs due to quantum discreteness of the spacetime which is one of the predictions of the theory. These results have been shown to be robust by various groups around the World for a variety of models. Further, it has been shown, in collaboration with A. Ashtekar and A. Corichi, that the bounce occurs for a dense subspace of the physical Hilbert space, and that there are very strong constraints on the change of relative fluctuations across the bounce (in collaboration with A. Corichi and an independent analysis of W. Kaminski and T. Pawlowski). Recently, we have shown that all singularities in a spatially flat homogeneous and isotropic universe are resolved in LQC at an effective spacetime level.
These results, so far obtained for homogeneous models, have opened a new window to the spacetime beyond classical singularities. Various questions remain open and they form the focus of our current research. Some of these questions are: (i) What are the effects on structure formation due to quantum gravitational effects? Are these effects potentially observable for near future astronomical or gravitational wave observations? (ii) Is singularity resolution an artifact of assuming homogeneous spacetimes or is it a generic phenomena? (iii) What insights do we obtain on pre-inflationary branch, if inflation did occur? (iv) Can LQG lead to a viable non-singular alternative to inflation? (v) What is the physics of singularity resolution in black hole spacetimes? (vi) How do we understand the probability of events such as singularity or bounce in a quantum universe devoid of any external observers or environment? and finally (vii) Is there a non-singularity theorem in quantum gravity?
Apart from above topics, we are interested in topics on AdS/CFT correspondence and singularities in string theory, spin foam cosmologies, group field theory, problem of dark energy and early universe cosmology.
Current and Selected Publications
- B. Gupt, P. Singh, "Quantum gravitational Kasner transitions in Bianchi-I spacetime," Phys. Rev. D 86, 024034 (2012).
- E. Ranken, P. Singh, "Non-singular Power-law and Assisted inflation in Loop Quantum Cosmology," Phys. Rev. D 85, 104002 (2012).
- P. Singh, "Curvature invariants, geodesics and the strength of singularities in Bianchi-I loop quantum cosmology," Phys. Rev. D 85, 104011 (2012).
- B. Gupt, P. Singh, "Contrasting features of anisotropic loop quantum cosmologies: the role of spatial curvature," Phys. Rev. D 85, 044011 (2012).
- A. Ashtekar, P. Singh, "Loop Quantum Cosmology: A Status Report," Class. Quant. Grav. 28, 213001 (2011).
- P. Singh, F. Vidotto, "Exotic singularities and spatially curved Loop Quantum Cosmology," Phys. Rev. D 83, 064027 (2011).
- D. A. Craig, P. Singh, "Consistent Probabilities in Wheeler-DeWitt Quantum Cosmology," Phys. Rev. D 82, 123526 (2010).