Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode 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 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 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.

Causality Constraint on Circuit Complexity from $COSMOEFT$

“…For more details on this issue see refs. [61,[64][65][66]. Here R(θ k (τ )) is the rotation operator which can be expressed as:…”

“…Applying these concepts, numerous significant contributions to a broad class of physics problems has been carried out. Various studies have been carried out in the framework of cosmological islands [61], inflationary cosmology [62,63], bouncing cosmology [64], primordial gravitational waves (PGW) [65], black hole gas in arbitrary dimensions [66], supersymmetric quantum field theory [67], quantum neural networks [25] and in many other important places. The underlying connecting relationship between quantum entanglement in wormholes and emergent gravitational space-time in terms of spooky action at a distance has been an active area of interest in recent times.…”

Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning

“…Using [42,43,45,[59][60][61], one can write down the following relation between OTOC and complexity:…”

“…and k is the constant to integration. The out-of-order correlator OTOC [42,43,45,60,61] is given by OTOC = exp(−C) which shows that out-of-order correlator can be represented as:…”

Four-mode squeezed states in de Sitter space: A study with two field interacting quantum system

“…These states are also now being used in gravitational wave physics [17][18][19] to enhance the sensitivity of gravitational wave detectors [20][21][22][23], such as the LIGO [24] and to improve measurement techniques in quantum metrology [25][26][27][28][29][30][31]. For a more broad class of application of squeezed states see [32][33][34][35][36][37][38][39][40][41][42][43][44].…”