Quantum aspects of chaos and complexity from bouncing cosmology: A study with twomode single field squeezed state formalism
Abstract
Circuit Complexity, a well known computational technique has recently become the backbone of the physics community to probe the chaotic behaviour and random quantum fluctuations of quantum fields. This paper is devoted to the study of outofequilibrium aspects and quantum chaos appearing in the universe from the paradigm of two well known bouncing cosmological solutions viz. Cosine hyperbolic and Exponential models of scale factors. Besides circuit complexity, we use the OutofTime Ordered correlation (OTOC) functions for probing the random behaviour of the universe both at early and the late times. In particular, we use the techniques of well known twomode squeezed state formalism in cosmological perturbation theory as a key ingredient for the purpose of our computation. To give an appropriate theoretical interpretation that is consistent with the observational perspective we use the scale factor and the number of efoldings as a dynamical variable instead of conformal time for this computation. From this study, we found that the period of post bounce is the most interesting one. Though it may not be immediately visible but an exponential rise can be seen in the complexity once the post bounce feature is extrapolated to the present time scales. We also find within the very small acceptable error range a universal connecting relation between Complexity computed from two different kinds of cost functionalslinearly weighted and geodesic weighted with the OTOC. Furthermore, from the complexity computation obtained from both the cosmological models under consideration and also using the well known Maldacena (M) Shenker (S) Stanford (S) bound on quantum Lyapunov exponent, \lambda\leq 2\pi/\betaλ≤2π/β for the saturation of chaos, we estimate the lower bound on the equilibrium temperature of our universe at the late time scale. Finally, we provide a rough estimation of the scrambling time scale in terms of the conformal time.
 Publication:

SciPost Physics Core
 Pub Date:
 October 2021
 DOI:
 10.21468/SciPostPhysCore.4.4.026
 arXiv:
 arXiv:2009.03893
 Bibcode:
 2021ScPC....4...26B
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Disordered Systems and Neural Networks;
 General Relativity and Quantum Cosmology;
 Nonlinear Sciences  Chaotic Dynamics;
 Quantum Physics
 EPrint:
 104 pages, 41 figures, 9 tables, This project is the part of the nonprofit virtual international research consortium "Quantum Aspects of SpaceTime and Matter (QASTM)", Accepted for publication in SciPost Physics Core