Do scale-invariant fluctuations imply the breaking of de Sitter invariance?

TL;DR

This paper demonstrates that scale-invariant fluctuations do not necessarily imply the breaking of de Sitter invariance, challenging previous assumptions about the relationship between IR effects and symmetry breaking in de Sitter space.

Contribution

The authors show that de Sitter symmetry breaking is not required for scale-invariant spectra by employing Cesaro-summability to handle divergences in the two-point function.

Findings

De Sitter invariance can coexist with scale-invariant fluctuations.

Cesaro-summability effectively regularizes IR divergences.

Symmetry breaking is not an inevitable consequence of IR effects.

Abstract

The quantization of the massless minimally coupled (mmc) scalar field in de Sitter spacetime is known to be a non-trivial problem due to the appearance of strong infrared (IR) effects. In particular, the scale-invariance of the CMB power-spectrum - certainly one of the most successful predictions of modern cosmology - is widely believed to be inconsistent with a de Sitter invariant mmc two-point function. Using a Cesaro-summability technique to properly define an otherwise divergent Fourier transform, we show in this Letter that de Sitter symmetry breaking is \emph{not} a necessary consequence of the scale-invariant fluctuation spectrum. We also generalize our result to the tachyonic scalar fields, i.e the discrete series of representations of the de Sitter group, that suffer from similar strong IR effects.