Reviving QFT in $2+1$ de Sitter Spacetime

TL;DR

This paper demonstrates that a conformally coupled scalar quantum field theory on a 2+1 dimensional static Einstein universe can be viewed as a quantum field theory in 2+1 de Sitter space, with quantum revivals naturally defining the de Sitter time range.

Contribution

It introduces a novel approach to formulate QFT in 2+1 de Sitter space using a static Einstein universe, avoiding causal issues and identifying a complete mode basis.

Findings

Quantum revivals restrict the de Sitter time range.

Zonal harmonics form a complete basis for the theory.

UV cutoff basis dimension scales with Bekenstein-Hawking entropy.

Abstract

We consider a conformally coupled scalar QFT on $2+1$ dimensional static Einstein universe $R \times S^2$, and write down the free theory Hilbert space. We explain that this theory is secretly a QFT in $2+1$ de Sitter space because all the quantum observables experience {\it quantum revivals}, which naturally restricts the timelike $R$ to the appropriate de Sitter time range. Our construction circumvents the causal obstruction to formulating QFT in de Sitter due to event horizons. There aren't any in static Einstein. The `unitary gauge' description of the theory is realized by the zonal harmonics $P_\ell(\hat n \cdot \hat n')$. We verify that interactions with conformally invariant external sources are mediated only by these modes. Hence these modes comprise the complete basis of the "bulk" theory. When the theory is cut off in the UV the basis dimension scales as the Bekenstein-Hawking formula.