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

Authors (as registered SciPost users): Sayantan Choudhury
Submission information
Preprint Link: https://arxiv.org/abs/2009.03893v1  (pdf)
Date submitted: 2020-10-26 13:37
Submitted by: Choudhury, Sayantan
Submitted to: SciPost Physics Core
Ontological classification
Academic field: Physics
Specialties:
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
  • Quantum Physics
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 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 period in terms of conformal time.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 1 on 2021-8-9 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2009.03893v1, delivered 2021-08-09, doi: 10.21468/SciPost.Report.3365

Report

The authors use Circuit Complexity to probe into 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. They set their results along with the Out-of-Time 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.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Author:  Sayantan Choudhury  on 2021-08-15  [id 1672]

(in reply to Report 1 on 2021-08-09)
Category:
answer to question

The comments are carefully addressed in the attached .pdf file. Please look into the attachment.

Attachment:

Scipost_report.pdf

Anonymous on 2021-09-08  [id 1744]

(in reply to Sayantan Choudhury on 2021-08-15 [id 1672])
Category:
remark

The latest modified version of the draft is uploaded at https://arxiv.org/pdf/2009.03893v4.pdf.

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