Silent initial conditions for cosmological perturbations with a change of space-time signature

TL;DR

This paper explores silent initial conditions for cosmological perturbations at the early Universe's Lorentzian-Euclidean transition, proposing a decoupled, uncorrelated state that could lead to a scale-invariant spectrum.

Contribution

It introduces the concept of silent initial conditions at the Lorentzian-Euclidean transition, analyzing their implications for cosmological perturbations and spectrum formation.

Findings

Support for white noise initial conditions from Euclidean vacuum analysis

Silent initial conditions may originate from loop-deformations of Poincaré algebra

Conversion to scale-invariant spectrum is possible from silent initial states

Abstract

Recent calculations in loop quantum cosmology suggest that a transition from a Lorentzian to an Euclidean space-time might take place in the very early Universe. The transition point leads to a state of silence, characterized by a vanishing speed of light. This behavior can be interpreted as a decoupling of different space points, similar to the one characterizing the BKL phase. In this study, we address the issue of imposing initial conditions for the cosmological perturbations at the transition point between the Lorentzian and Euclidean phases. Motivated by the decoupling of space points, initial conditions characterized by a lack of correlations are investigated. We show that the "white noise" gains some support from analysis of the vacuum state in the deep Euclidean regime. Furthermore, the possibility of imposing the silent initial conditions at the trans-Planckian surface, characterized by a vanishing speed for the propagation of modes with wavelengths of the order of the Planck length, is studied. Such initial conditions might result from a loop-deformations of the Poincar\'e algebra. The conversion of the silent initial power spectrum to a scale-invariant one is also examined.