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de Sitter invariance of the dS graviton vacuum

Atsushi Higuchi, Donald Marolf, Ian A. Morrison

TL;DR

The paper resolves an infrared divergence in the linearized graviton two-point function on de Sitter space that arises in the standard transverse-traceless-synchronous gauge in Poincaré coordinates by applying explicit linearized diffeomorphisms to the mode functions. This gauge transformation yields a finite, de Sitter-invariant graviton vacuum at the linearized level, valid within any finite spatial region, though global gauge constraints prevent a single globally finite two-point function. The authors introduce a regulator via a decaying factor $e^{-\rho k}$ and consider compact spatial regions $K_0 \supset K_1$ to ensure pure-gauge modifications remain well-defined, with explicit results demonstrated for $d=4$. The work clarifies that certain infrared pathologies are gauge artifacts and reinforces the consistency of a de Sitter-invariant vacuum for linearized gravitons, while noting subtleties for interacting theories and global boundary conditions.

Abstract

The two-point function of linearized gravitons on de Sitter space is infrared divergent in the standard transverse traceless synchronous gauge defined by $k=0$ cosmological coordinates (also called conformal or Poincare coordinates). We show that this divergence can be removed by adding a linearized diffeomorphism to each mode function; i.e., by an explicit change of gauge. It follows that the graviton vacuum state is well-defined and de Sitter invariant in agreement with various earlier arguments.

de Sitter invariance of the dS graviton vacuum

TL;DR

The paper resolves an infrared divergence in the linearized graviton two-point function on de Sitter space that arises in the standard transverse-traceless-synchronous gauge in Poincaré coordinates by applying explicit linearized diffeomorphisms to the mode functions. This gauge transformation yields a finite, de Sitter-invariant graviton vacuum at the linearized level, valid within any finite spatial region, though global gauge constraints prevent a single globally finite two-point function. The authors introduce a regulator via a decaying factor and consider compact spatial regions to ensure pure-gauge modifications remain well-defined, with explicit results demonstrated for . The work clarifies that certain infrared pathologies are gauge artifacts and reinforces the consistency of a de Sitter-invariant vacuum for linearized gravitons, while noting subtleties for interacting theories and global boundary conditions.

Abstract

The two-point function of linearized gravitons on de Sitter space is infrared divergent in the standard transverse traceless synchronous gauge defined by cosmological coordinates (also called conformal or Poincare coordinates). We show that this divergence can be removed by adding a linearized diffeomorphism to each mode function; i.e., by an explicit change of gauge. It follows that the graviton vacuum state is well-defined and de Sitter invariant in agreement with various earlier arguments.

Paper Structure

This paper contains 4 sections, 14 equations, 1 figure.

Table of Contents

  1. Introduction
  2. A finite 2-pt function for the naive $k=0$ vacuum
  3. Discussion
  4. The explicit propagator for $\tilde{h}^{gf}_{ij}$ in $d=4$

Figures (1)

  • Figure 1: The region covered by conformally flat coordinates (\ref{['cc']}) is shown (shaded) on a conformal diagram of de Sitter space. Each point represents an $S^{d-2}$ which degenerates to zero size at the vertical lines at left and right. A surface of constant $\eta$ is also shown (curved line) which ends at the point $i^0$, corresponding to the region of large $\vec{x}$.