Cosmological Krylov Complexity

• URL: http://arxiv.org/abs/2203.14330v5
• Date: Thu, 8 Jun 2023 02:03:01 GMT
• Title: Cosmological Krylov Complexity
• Authors: Kiran Adhikari, Sayantan Choudhury
• Abstract summary: We study the Krylov complexity ($K$) from the planar/inflationary patch of the de Sitter space using the two mode squeezed state formalism. We show that the Krylov complexity ($K$) for this system is equal to average particle numbers suggesting it's relation to the volume.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we study the Krylov complexity ($K$) from the planar/inflationary patch of the de Sitter space using the two mode squeezed state formalism in the presence of an effective field having sound speed $c_s$. From our analysis, we obtain the explicit behavior of Krylov complexity ($K$) and lancoz coefficients ($b_n$) with respect to the conformal time scale and scale factor in the presence of effective sound speed $c_s$. Since lancoz coefficients ($b_n$) grow linearly with integer $n$, this suggests that universe acts like a chaotic system during this period. We also obtain the corresponding Lyapunov exponent $\lambda$ in presence of effective sound speed $c_s$. We show that the Krylov complexity ($K$) for this system is equal to average particle numbers suggesting it's relation to the volume. Finally, we give a comparison of Krylov complexity ($K$) with entanglement entropy (Von-Neumann) where we found that there is a large difference between Krylov complexity ($K$) and entanglement entropy for large values of squeezing amplitude. This suggests that Krylov complexity ($K$) can be a significant probe for studying the dynamics of the cosmological system even after the saturation of entanglement entropy.

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