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Quantum aspects of chaos and complexity from bouncing cosmology: A study with twomode single field squeezed state formalism
by Parth Bhargava, Sayantan Choudhury, Satyaki Chowdhury, Anurag Mishara, Sachin Panneer Selvam, Sudhakar Panda, Gabriel D. Pasquino
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Authors (as registered SciPost users):  Sayantan Choudhury 
Submission information  

Preprint Link:  https://arxiv.org/abs/2009.03893v1 (pdf) 
Date submitted:  20201026 13:37 
Submitted by:  Choudhury, Sayantan 
Submitted to:  SciPost Physics Core 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Phenomenological 
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 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 period in terms of conformal time.
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Reports on this Submission
Anonymous Report 1 on 202189 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2009.03893v1, delivered 20210809, doi: 10.21468/SciPost.Report.3365
Report
The authors use Circuit Complexity to probe into 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. They set their results along with the OutofTime Ordered correlation (OTOC) functions for probing the random behaviour of the universe. Use is made of the two mode squeezed state formalism in cosmological perturbation theory, for computations. They estimate the lower bound on the equilibrium temperature of the universe at the late time scale. Also, a rough estimation of the scrambling time period is provided.
The bringing together of various tools into the probe of the chaotic behaviour of the universe is appreciable.
I have a few suggestions:
(a). The notion of circuit complexity should be expanded upon.
(b). Use is made here of the linear cost functional and the quadratic cost functional. What would be the pros and cons of handling other types of cost functionals? A comment would be beneficial.
(c). The notion of the squeezed state formalism, central to the presentation, could benefit from further discussion.
Author: Sayantan Choudhury on 20210815 [id 1672]
(in reply to Report 1 on 20210809)The comments are carefully addressed in the attached .pdf file. Please look into the attachment.
Attachment:
Scipost_report.pdf
Anonymous on 20210908 [id 1744]
(in reply to Sayantan Choudhury on 20210815 [id 1672])The latest modified version of the draft is uploaded at https://arxiv.org/pdf/2009.03893v4.pdf.