Initial conditions for cosmological perturbations

TL;DR

This paper proposes a quantum generalization of Penrose's hypothesis to set initial conditions for the universe at the Planck scale, constraining it to be as homogeneous and isotropic as quantum mechanics allows.

Contribution

It introduces a quantum extension of Penrose's classical hypothesis, incorporating scalar and tensor modes to define initial conditions at the Planck regime.

Findings

Initial conditions constrain the universe to be nearly homogeneous and isotropic.

The approach incorporates quantum uncertainty principles into cosmological initial conditions.

Provides a framework linking quantum mechanics with early universe initial conditions.

Abstract

Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose's hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose's hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime \emph{as permitted by the Heisenberg uncertainty relations}.