Mathematics and Physics Seminar: Quantum Cosmology in Loop Quantum Gravity



The quest for Quantum Gravity is among the most challenging and fascinating ones in theoretical physics. It's a one hundred year long journey addressed to the understanding of the nature of space and time at a more fundamental level, namely the scale where both gravity and quantum mechanics are expected to be relevant. It's an enterprise pioneered by the seminal work of the soviet physicist Bronstein in 1936, and still far to be accomplished. No experimental evidences so far have guided us towards this elusive regime of nature and different tracks have been explored, like the one pursued by String theory (ST), Loop quantum gravity (LQG) and Non commutative geometry (NCG), only to cite a few.
In this talk I give a broad introduction to the path followed by LQG and its implementation(s) to primordial cosmology. The quantization of symmetry reduced sectors of the theory is highly non trivial and far to be unique. I discuss different models for the quantum corrected Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry, as they emerge from two approaches called Loop Quantum Cosmology (LQC) and Quantum Reduced Loop Gravity (QRLG). In the two, the quantization and the symmetry reduction are reversed in order. The former is a mini-superspace quantization of FLRW geometry, the latter is a dynamical reduction of the quantum theory which is achieved by implementing a gauge fixing and a suitable restriction on the states. If they both provide a singularity resolution of the classical singularity, their resulting dynamics are completely different. I will discuss the relations between the two models and a recent extension to the anisotropic case, namely to the quantization of Bianchi I geometry in QRLG.


Dr Gabriele V. Stagno
Sapienza University of Rome, P.le Aldo Moro 5, (00185) Roma, Italy
Aix Marseille Univ., Univ. de Toulon, CNRS, CPT, UMR 7332, 13288 Marseille, France
Dr. Gabriele Stagno recently completed his Ph.D. in Physics from La Sapienza, University of Rome. His research focuses on the applications of loop quantum gravity to quantum cosmology.