Scale-invariant scalar spectrum from the nonminimal derivative coupling with fourth-order term

TL;DR

This paper demonstrates that a gravity model with nonminimal derivative coupling and fourth-order terms can produce an exactly scale-invariant scalar perturbation spectrum during de Sitter inflation, extending the Lee-Wick scalar theory.

Contribution

It introduces a gravity model combining nonminimal derivative coupling with fourth-order terms that yields a healthy, ghost-free, exactly scale-invariant scalar spectrum during de Sitter space.

Findings

Achieves a scale-invariant spectrum from the model.

Recovers the Harrison-Zel'dovich spectrum via Fourier transform.

Provides a connection to Lee-Wick scalar theory.

Abstract

An exactly scale-invariant spectrum of scalar perturbation generated during de Sitter spacetime is found from the gravity model of the nonminimal derivative coupling with fourth-order term. The nonminimal derivative coupling term generates a healthy (ghost-free) fourth-order derivative term, while the fourth-order term provides an unhealthy (ghost) fourth-order derivative term. The Harrison-Zel'dovich spectrum obtained from Fourier transforming the fourth-order propagator in de Sitter space is recovered by computing the power spectrum in its momentum space directly. It shows that this model provides a truly scale-invariant spectrum, in addition to the Lee-Wick scalar theory.