Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism
Bhargava, Parth, Choudhury, Sayantan, Chowdhury, Satyaki, Mishara, Anurag, Selvam, Sachin Panneer, Panda, Sudhakar, Pasquino, Gabriel D.
Abstract
$Circuit~ Complexity$, a well known computational technique has recently<br>become the backbone of the physics community to probe the chaotic behaviour and<br>random quantum fluctuations of quantum fields. This paper is devoted to the<br>study of out-of-equilibrium aspects and quantum chaos appearing in the universe<br>from the paradigm of two well known bouncing cosmological solutions viz.<br>$Cosine~ hyperbolic$ and $Exponential$ models of scale factors. Besides<br>$circuit~ complexity$, we use the $Out-of-Time~ Ordered~ correlation~ (OTOC)$<br>functions for probing the random behaviour of the universe both at early and<br>the late times. In particular, we use the techniques of well known two-mode<br>squeezed state formalism in cosmological perturbation theory as a key<br>ingredient for the purpose of our computation. To give an appropriate<br>theoretical interpretation that is consistent with the observational<br>perspective we use the scale factor and the number of e-foldings as a dynamical<br>variable instead of conformal time for this computation. From this study, we<br>found that the period of post bounce is the most interesting one. Though it may<br>not be immediately visible, but an exponential rise can be seen in the<br>$complexity$ once the post bounce feature is extrapolated to the present time<br>scales. We also find within the very small acceptable error range a universal<br>connecting relation between Complexity computed from two different kinds of<br>cost functionals-$linearly~ weighted$ and $geodesic~ weighted$ with the OTOC.<br>Furthermore, from the $complexity$ computation obtained from both the<br>cosmological models and also using the well known MSS bound on quantum Lyapunov<br>exponent, $\lambda\leq 2\pi/\beta$ for the saturation of chaos, we estimate the<br>lower bound on the equilibrium temperature of our universe at late time scale.<br>Finally, we provide a rough estimation of the scrambling time in terms of the<br>conformal time.<br>