Report on 2009.03893v1
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 which 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 an 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, λ ≤ 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 period in terms of the conformal time.
Authors 7
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Affiliation as printed
Institute for Theoretical Particle Physics and Cosmology(TTK) , RWTH Aachen University , D-52056 , Aachen , Germany
Institute for Theoretical Particle Physics and Cosmology(TTK), RWTH Aachen University, D-52056, Aachen, Germany
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Sayantan Choudhury corresponding
Max Planck Institute for Gravitational Physics
Affiliation as printed
Quantum Gravity and Unified Theory and Theoretical Cosmology Group , Max Planck Institute for Gravitational Physics (Albert Einstein Institute) , Am Mühlenberg 1 , 14476 Potsdam-Golm , Germany
Quantum Gravity and Unified Theory and Theoretical Cosmology Group, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam-Golm, Germany
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National Institute of Science Education and Research · Homi Bhabha National Institute
Affiliation as printed
Homi Bhabha National Institute , Training School Complex , Anushakti Nagar , Mumbai - 400085 , India
National Institute of Science Education and Research , Bhubaneswar , Odisha - 752050 , India
Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai -400085, India
National Institute of Science Education and Research, Bhubaneswar, Odisha -752050, India
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National Institute of Technology Rourkela
Affiliation as printed
Department of Physics and Astronomy , National Institute of Technology , Rourkela , Odisha , 769001
Department of Physics and Astronomy, National Institute of Technology, Rourkela, Odisha, 769001
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Birla Institute of Technology and Science - Hyderabad Campus · Birla Institute of Technology and Science, Pilani
Affiliation as printed
Department of Physics , Birla Institute of Technology and Science , Pilani , Hyderabad Campus , Hyderabad - 500078 , India
Department of Physics, Birla Institute of Technology and Science, Pilani, Hyderabad Campus, Hyderabad -500078, India
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National Institute of Science Education and Research · Homi Bhabha National Institute
Affiliation as printed
Homi Bhabha National Institute , Training School Complex , Anushakti Nagar , Mumbai - 400085 , India
National Institute of Science Education and Research , Bhubaneswar , Odisha - 752050 , India
Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai -400085, India
National Institute of Science Education and Research, Bhubaneswar, Odisha -752050, India
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Affiliation as printed
University of Waterloo , 200 University Ave W , Waterloo , ON , Canada , N2L 3G1
University of Waterloo, 200 University Ave W, Waterloo, ON, Canada, N2L 3G1
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