Assigning Quantum-Mechanical Initial Conditions to Cosmological Perturbations

TL;DR

This paper explores how different quantum initial conditions for cosmological perturbations influence the two-point functions and back-reaction effects, highlighting the importance of Hamiltonian choice in early universe models.

Contribution

It introduces a method to assign quantum initial conditions based on Hamiltonian minimization, analyzing their impact on cosmological fluctuations and back-reaction.

Findings

Adiabatic Hamiltonian minimization yields negligible back-reaction.

Non-adiabatic Hamiltonian minimization results in large corrections to two-point functions.

Initial states with high energetic content can significantly affect the background geometry.

Abstract

Quantum-mechanical initial conditions for the fluctuations of the geometry can be assigned in excess of a given physical wavelength. The two-point functions of the scalar and tensor modes of the geometry will then inherit corrections depending on which Hamiltonian is minimized at the initial stage of the evolution. The energy density of the background geometry is compared with the energy-momentum pseudo-tensor of the fluctuations averaged over the initial states, minimizing each different Hamiltonian. The minimization of adiabatic Hamiltonians leads to initial states whose back-reaction on the geometry is negligible. The minimization of non-adiabatic Hamiltonians, ultimately responsible for large corrections in the two-point functions, is associated with initial states whose energetic content is of the same order as the energy density of the background.