Tensor ghosts in the inflationary cosmology

TL;DR

This paper explores how ghost modes in curvature squared theories of gravity, especially during inflation, can be managed through Euclidean path integrals, revealing modifications to tensor perturbations without necessarily indicating physical instabilities.

Contribution

It demonstrates that ghost degrees of freedom in curvature squared inflationary models can be integrated out using Euclidean path integrals, altering tensor perturbation amplitudes.

Findings

Tensor perturbation amplitude is modified by O(alpha^2 H^2)

Ghost modes can be integrated out without instability

Curvature squared corrections affect inflationary predictions

Abstract

Theories with curvature squared terms in the action are known to contain ghost modes in general. However, if we regard curvature squared terms as quantum corrections to the original theory, the emergence of ghosts may be simply due to the perturbative truncation of a full non-perturbative theory. If this is the case, there should be a way to live with ghosts. In this paper, we take the Euclidean path integral approach, in which ghost degrees of freedom can be, and are integrated out in the Euclideanized spacetime. We apply this procedure to Einstein gravity with a Weyl curvature squared correction in the inflationary background. We find that the amplitude of tensor perturbations is modified by a term of O(alpha^2 H^2) where alpha^2 is a coupling constant in front of the Weyl squared term and H is the Hubble parameter during inflation.