Inflation with the Trace Anomaly Action and Primordial Black Holes

TL;DR

This paper explores a modified inflationary model involving a trace anomaly scalar, leading to unique perturbation spectra and the potential formation of primordial black holes, with implications for dark matter and gravitational waves.

Contribution

It introduces a new inflationary framework with a trace anomaly scalar (anomalyon), showing how it affects perturbations and primordial black hole formation.

Findings

Standard inflationary background deviations are minimal.

Scalar perturbations include a nearly scale-invariant mode and a blue spectrum.

Primordial black holes could form at small scales and survive to today.

Abstract

We study inflation in a recently proposed gravitational effective field theory describing the trace anomaly. The theory requires an additional scalar which is massless in the early universe. This scalar -- referenced as an anomalyon -- couples to the familiar matter and radiation through the gauge field trace anomaly. We derive a class of cosmological solutions that deviate from the standard inflationary ones only slightly, in spite of the fact that the anomalyon has a sizable time dependent background. On the other hand, the scalar cosmological perturbations in this theory are different from the conventional inflationary perturbations. The inflaton and anomalyon perturbations mix, and one of the diagonal combinations gives the standard nearly scale-invariant adiabatic spectrum, while the other combination has a blue power spectrum at short distance scales. We argue that this blue spectrum can lead to the formation of primordial black holes (PBHs) at distance scales much shorter than the ones tested in CMB observations. The resulting PBHs can be heavy enough to survive to the present day universe. For natural values of the parameters involved the PBHs would constitute only a tiny fraction of the dark matter, but with fine-tunings perhaps all of dark matter could be accounted by them. We also show that the theory predicts primordial gravitational waves which are almost identical to the standard inflationary ones.