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Late-time Structure of the Bunch-Davies De Sitter Wavefunction

Dionysios Anninos, Tarek Anous, Daniel Z. Freedman, George Konstantinidis

TL;DR

The paper investigates the late-time structure of the Bunch-Davies wavefunction in de Sitter space by importing perturbative techniques from Euclidean AdS/CFT. It shows that interacting light fields, including massless and conformally coupled scalars, gauge fields, and gravitons, generate logarithmic growth in conformal time under certain conditions, with gravity showing no such growth at tree level due to the Fefferman–Graham expansion. The work interprets these logarithms within a holographic framework, relating them to conformal anomalies and shifts in operator weights in a putative dual 3d CFT, and extends the analysis to dS$_2$ to illustrate the universality of the structure across dimensions. The results provide a systematic perturbative scheme for BD wavefunctions and highlight several avenues for future exploration, including graviton and higher-spin effects, nonperturbative resummation, and connections to stochastic inflation.

Abstract

We examine the late time behavior of the Bunch-Davies wavefunction for interacting light fields in a de Sitter background. We use perturbative techniques developed in the framework of AdS/CFT, and analytically continue to compute tree and loop level contributions to the Bunch-Davies wavefunction. We consider self-interacting scalars of general mass, but focus especially on the massless and conformally coupled cases. We show that certain contributions grow logarithmically in conformal time both at tree and loop level. We also consider gauge fields and gravitons. The four-dimensional Fefferman-Graham expansion of classical asymptotically de Sitter solutions is used to show that the wavefunction contains no logarithmic growth in the pure graviton sector at tree level. Finally, assuming a holographic relation between the wavefunction and the partition function of a conformal field theory, we interpret the logarithmic growths in the language of conformal field theory.

Late-time Structure of the Bunch-Davies De Sitter Wavefunction

TL;DR

The paper investigates the late-time structure of the Bunch-Davies wavefunction in de Sitter space by importing perturbative techniques from Euclidean AdS/CFT. It shows that interacting light fields, including massless and conformally coupled scalars, gauge fields, and gravitons, generate logarithmic growth in conformal time under certain conditions, with gravity showing no such growth at tree level due to the Fefferman–Graham expansion. The work interprets these logarithms within a holographic framework, relating them to conformal anomalies and shifts in operator weights in a putative dual 3d CFT, and extends the analysis to dS to illustrate the universality of the structure across dimensions. The results provide a systematic perturbative scheme for BD wavefunctions and highlight several avenues for future exploration, including graviton and higher-spin effects, nonperturbative resummation, and connections to stochastic inflation.

Abstract

We examine the late time behavior of the Bunch-Davies wavefunction for interacting light fields in a de Sitter background. We use perturbative techniques developed in the framework of AdS/CFT, and analytically continue to compute tree and loop level contributions to the Bunch-Davies wavefunction. We consider self-interacting scalars of general mass, but focus especially on the massless and conformally coupled cases. We show that certain contributions grow logarithmically in conformal time both at tree and loop level. We also consider gauge fields and gravitons. The four-dimensional Fefferman-Graham expansion of classical asymptotically de Sitter solutions is used to show that the wavefunction contains no logarithmic growth in the pure graviton sector at tree level. Finally, assuming a holographic relation between the wavefunction and the partition function of a conformal field theory, we interpret the logarithmic growths in the language of conformal field theory.

Paper Structure

This paper contains 21 sections, 109 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Schrödinger equation in a fixed de Sitter background
  3. Bunch-Davies wavefunction
  4. A Euclidean AdS approach
  5. Interaction corrections to $Z_{\text{AdS}}$
  6. Self-interacting scalars in four-dimenions
  7. Tree level contributions for the massless theory
  8. Loop correction to the two-point function
  9. Tree level contributions to the conformally coupled case
  10. Comments for general massive fields
  11. Gauge fields and gravity in four-dimensions
  12. $SU(N)$ gauge fields
  13. Scalar QED
  14. Gravity
  15. 3d CFTs and (A)dS/CFT
  16. ...and 6 more sections

Figures (1)

  • Figure 1: Witten diagrams for the order $\lambda$ contributions to $Z_{\text{AdS}} [\varphi_{\vec{k}},z_c]$ in the theory with $\phi^4$ interaction.