Inflation without quantum gravity

TL;DR

This paper argues that detecting inflationary gravitational waves is necessary to confirm quantum gravity, as scalar perturbations can be explained without quantising spacetime in a semiclassical framework.

Contribution

It demonstrates that in a semiclassical model, scalar perturbations can match inflationary predictions without quantum gravity, making gravitational wave detection essential for evidence of quantised spacetime.

Findings

Scalar spectrum depends on the hypersurface choice in semiclassical models.

In non-minimal coupling models, scalar perturbations are not scale-invariant.

Gravitational waves are negligible at second order, requiring direct detection for quantum gravity evidence.

Abstract

It is sometimes argued that observation of tensor modes from inflation would provide the first evidence for quantum gravity. However, in the usual inflationary formalism, also the scalar modes involve quantised metric perturbations. We consider the issue in a semiclassical setup in which only matter is quantised, and spacetime is classical. We assume that the state collapses on a spacelike hypersurface, and find that the spectrum of scalar perturbations depends on the hypersurface. For reasonable choices, we can recover the usual inflationary predictions for scalar perturbations in minimally coupled single-field models. In models where non-minimal coupling to gravity is important and the field value is sub-Planckian, we do not get a nearly scale-invariant spectrum of scalar perturbations. As gravitational waves are only produced at second order, the tensor-to-scalar ratio is negligible. We conclude that detection of inflationary gravitational waves would indeed be needed to have observational evidence of quantisation of gravity.