Einstein-singleton theory and its power spectra in de Sitter inflation

TL;DR

This paper analyzes the Einstein-singleton theory during de Sitter inflation, revealing its solutions and power spectrum behavior, and concludes it has ghost-instability issues making it unsuitable for slow-roll inflation models.

Contribution

It provides an exact solution to the degenerate fourth-order scalar equation in de Sitter space and analyzes its power spectrum behavior.

Findings

Power spectrum diverges negatively in superhorizon limit

Power spectrum is negatively scale-invariant in subhorizon limit

The theory exhibits ghost-instability issues

Abstract

We study the Einstein-singleton theory during de Sitter inflation since it provides a way of degenerate fourth-order scalar theory. We obtain an exact solution expressed in terms of the exponential-integral function by solving the degenerate fourth-order scalar equation in de Sitter spacetime. Furthermore, we find that its power spectrum blows negatively up in the superhorizon limit, while it is negatively scale-invariant in the subhorizon limit. This suggests that the Einstein-singleton theory contains the ghost-instability and thus, it is not suitable for developing a slow-roll inflation model.