Primordial Gravitational Wave Circuit Complexity

Symmetry, vol. 15, pp. 664

Abstract

In this article, we investigate the various physical implications of quantum circuit complexity using the squeezed state formalism of Primordial Gravitational Waves (PGW). Recently, quantum information-theoretic concepts, such as entanglement entropy and complexity, have played a pivotal role in understanding the dynamics of quantum systems, even in diverse fields such as high-energy physics and cosmology. This paper is devoted to studying the quantum circuit complexity of PGW for various cosmological models, such as de Sitter, inflation, radiation, reheating, matter, bouncing, cyclic and black hole gas models, etc. We compute complexity measures using both Covariance and Nielsen’s wave function method for three different choices of quantum initial vacua: Motta-Allen, α and Bunch–Davies. Besides computing circuit complexity, we also compute the Von Neumann entanglement entropy. By making the comparison between complexity and entanglement entropy, we are able to probe various features regarding the dynamics of evolution for different cosmological models. Because entanglement entropy is independent of the squeezing angle, we are able to understand more details of the system using Nielsen’s measure of complexity, which is dependent on both squeezing parameter and angle. This implies that quantum complexity could indeed be a useful probe to study quantum features on a cosmological scale. Quantum complexity is also becoming a powerful technique to understand the chaotic behaviour and random fluctuations of quantum fields. Using the growth of complexity, we are able to compute the quantum Lyapunov exponent for various cosmological models and comment on its chaotic nature.

Authors 4

1. Kiran Adhikari Aachen Department of Physics

   RWTH Aachen University

   Affiliation as printed

   Department of Physics, RWTH Aachen University, D-52056 Aachen, Germany

2. Sayantan Choudhury corresponding

   National Institute of Science Education and Research · Homi Bhabha National Institute · Shree Guru Gobind Singh Tricentenary University

   Affiliation as printed

   Centre For Cosmology and Science Popularization (CCSP), SGT University, Gurugram 122505, India

   Homi Bhabha National Institute, Training School Complex, Anushakti Nagar 400085, India

   National Institute of Science Education and Research, Bhubaneswar 752050, India

3. Hardey N. Pandya

   Pandit Deendayal Energy University

   Affiliation as printed

   School of Technology, Pandit Deendayal Energy University, Gandhinagar 382355, India

4. Rohan Srivastava

   Indian Institute of Technology Jodhpur

   Affiliation as printed

   Indian Institute of Technology Jodhpur, Jodhpur 342011, India