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

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2009.03893.pdf

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SciPostPhysCore_4_4_026.pdf

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##### Citation

Bhargava, P., Choudhury, S., Chowdhury, S., Mishara, A., Selvam, S. P., Panda, S., et al. (2021).
Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism.* SciPost Physics Core,* *4*: 026. doi:10.21468/SciPostPhysCore.4.4.026.

Cite as: https://hdl.handle.net/21.11116/0000-0007-1A67-9

##### 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.

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.