Cosmological Complexity

Project Description: 

In recent years, quantum information theory (QIT) has become a melting pot for incorporating various branches of physics. Tools and techniques from QIT are bringing new perspectives into fields such as cosmology, inspiring new questions and research directions. One area that has seen significant recent progress is the field of quantum complexity. Quantum complexity, a tool from QIT, quantifies the complexity of generating a particular quantum state and can provide new insights into the evolution of our universe. On a very large scale, our universe is isotropic, meaning it looks the same in every direction. Experimental evidence for this is found in the cosmic microwave background (CMB), which consists of an almost sea of photons that fill space and capture snapshots of the very early universe. Interestingly, the CMB exhibits a uniform temperature, yet there are tiny fluctuations. These temperature fluctuations imply the existence of density perturbations, which originate from curvature perturbations in the early universe. According to the inflationary paradigm of cosmology, these perturbations were quantum in origin. One can utilize the scalar perturbation model to construct a quantum circuit. In some recent papers, we have employed this model and investigated the complexity of different cosmological epochs. The project will essentially entail a review of this work. It will revisit how the complexity evolves during inflation and the radiation era. The methodology involves both analytical and numerical computations, which can be performed using Mathematica or similar platforms. In recent years, quantum information theory (QIT) has become a melting pot for incorporating various branches of physics. Tools and techniques from QIT are bringing new perspectives into fields such as cosmology, inspiring new questions and research directions. One area that has seen significant recent progress is the field of quantum complexity. Quantum complexity, a tool from QIT, quantifies the complexity of generating a particular quantum state and can provide new insights into the evolution of our universe. On a very large scale, our universe is isotropic, meaning it looks the same in every direction. Experimental evidence for this is found in the cosmic microwave background (CMB), which consists of an almost sea of photons that fill space and capture snapshots of the very early universe. Interestingly, the CMB exhibits a uniform temperature, yet there are tiny fluctuations. These temperature fluctuations imply the existence of density perturbations, which originate from curvature perturbations in the early universe. According to the inflationary paradigm of cosmology, these perturbations were quantum in origin. One can utilize the scalar perturbation model to construct a quantum circuit. In some recent papers, we have employed this model and investigated the complexity of different cosmological epochs. The project will essentially entail a review of this work. It will revisit how the complexity evolves during inflation and the radiation era. The methodology involves both analytical and numerical computations, which can be performed using Mathematica or similar platforms. (UCT)

Supervisor

University of Cape Town (UCT)

Co-Supervisor