Inflation, holography, and the choice of vacuum in de Sitter space

TL;DR

The paper investigates a family of de Sitter vacua as plausible initial conditions for inflation and interprets them through de Sitter holography. It shows that a one-parameter subfamily of de Sitter invariant vacua arises from a Bogolubov transformation of the Euclidean BD vacuum, with modes created when their physical momentum equals $\Lambda$, leading to trans-Planckian corrections of order $\frac{H}{\Lambda}$ in the scalar spectrum. The analysis clarifies how these vacua differ from the BD vacuum (which is thermal) and how their Wightman functions introduce image-source singularities outside the horizon, while still preserving commutators and causal propagators. The study culminates in a holographic interpretation where CMBR fluctuations correspond to boundary correlators on $\mathcal{I}^{+}$, and discusses how holography might inform vacuum selection, including the idea that trans-Planckian effects map to $1/N$ corrections in the vacuum choice. Overall, the work connects trans-Planckian initial conditions, de Sitter invariant vacua, and holographic cosmology, with potential observational implications for the CMBR.

Abstract

A family of de Sitter vacua introduced in hep-th/0203198 as plausible initial conditions for inflation, are discussed from the point of view of de Sitter holography. The vacua are argued to be physically acceptable and the inflationary picture provides a physical interpretation of a subfamily of de Sitter invariant vacua. Some speculations on the issue of vacuum choice and the connection between the CMBR and holography are also provided.