http://arxiv.org/abs/2102.12014
We will consider the effects of non-trivial sound speed on the evolution of cosmological complexity in a method of squeezed quantum states. In the standard procedure, we will treat the vacuum state of the curvature perturbation as the squeezed vacuum state referring to the Gaussian state. Squeezed quantum states are obtained by acting a two-mode squeezed operator which is described by angle parameter $\phi_k$ and squeezing parameter $r_k$ on a squeezed vacuum state. Through $Schr\ddot{o}dinger$ equation, one can obtain the corresponding evolution equation of $\phi_k$ and $r_k$. Subsequently, the quantum circuit complexity between a squeezed vacuum state and squeezed states are evaluated in scalar curvature perturbation with a type of non-trivial sound speeds. Our result indicates that the evolution of complexity will not change dramatically at a late time, only by considering the effects of the non-trivial sound speed in an inflationary de-Sitter spacetime. However, compared to the case of $c^2_S=1$, the evolution of complexity at an early time shows the rapid oscillation.
L. Liu and A. Li
Thu, 25 Feb 21
45/50
Comments: 8 pages, 4 figures, comments are welcome