## Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism

Parth Bhargava, Sayantan Choudhury, Satyaki Chowdhury, Anurag Mishara, Sachin Panneer Selvam, Sudhakar Panda, Gabriel D. Pasquino

SciPost Phys. Core 4, 026 (2021) · published 7 October 2021

- doi: 10.21468/SciPostPhysCore.4.4.026
- Submissions/Reports

### 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 out-of-equilibrium 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 $Out-of-Time~ Ordered~ correlation~ (OTOC)$ 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 two-mode 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 e-foldings 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 functionals-$linearly~ weighted$ and $geodesic~ weighted$ with the OTOC. Furthermore, from the $complexity$ computation obtained from both the cosmological models and also using the well known MSS bound on quantum Lyapunov exponent, $\lambda\leq 2\pi/\beta$ for the saturation of chaos, we estimate the lower bound on the equilibrium temperature of our universe at late time scale. Finally, we provide a rough estimation of the scrambling time in terms of the conformal time.

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Parth Bhargava, -
^{2}^{3}^{4}Sayantan Choudhury, -
^{3}^{4}Satyaki Chowdhury, -
^{5}Anurag Mishara, -
^{6}Sachin Panneer Selvam, -
^{3}^{4}Sudhakar Panda, -
^{7}Gabriel D. Pasquino

^{1}Rheinisch-Westfälische Technische Hochschule Aachen / RWTH Aachen University [RWTH]^{2}Max-Planck-Institut für Gravitationsphysik / Max Planck Institute for Gravitational Physics [AEI]^{3}राष्ट्रीय विज्ञान शिक्षा एवं अनुसंधान संस्थान / National Institute of Science Education and Research [NISER]^{4}होमी भाभा राष्ट्रीय संस्थान / Homi Bhabha National Institute [HBNI]^{5}राष्ट्रीय प्रौद्योगिकी संस्थान, राउरकेला / National Institute of Technology Rourkela [NITR]^{6}Birla Institute of Technology and Science - Hyderabad Campus [BPHC]^{7}University of Waterloo [UW]

- Department of Science and Technology, Ministry of Science and Technology (through Organization: विज्ञान एवं प्रौद्योगिकी विभाग / Department of Science and Technology [DST])
- European Research Council [ERC]