Positive Running of the Spectral Index for Scalar Theory and Modified Gravity

TL;DR

This paper explores conditions under which inflationary models, including scalar field and modified gravity theories like $F(R)$ and Einstein-Gauss-Bonnet gravity, can produce a positive running of the spectral index, potentially aligning with recent ACT data.

Contribution

It demonstrates how certain scalar and modified gravity inflationary scenarios can naturally yield a positive spectral index running consistent with observational hints.

Findings

Scalar theories and $F(R)$ gravity are mostly compatible with Planck data and difficult to produce positive running.

Nuanced scalar field scenarios can match ACT data and yield positive running.

Einstein-Gauss-Bonnet theories can produce positive running while remaining viable for inflation.

Abstract

In this work we address the possibility of having a positive running of the spectral index in inflationary theories. The recent ACT data indicate mildly that the running of the spectral index might be positive, and several other physical indications point out this possibility. If the running of the spectral index is confirmed to be positive by future cosmic microwave background experiments, this can rule out quite popular inflationary scenarios. We investigate how it is possible to obtain a positive running of the spectral index in the context of minimally coupled scalar field gravity and modified gravity. For the modified gravity we choose two mainstream and of string origin candidate theories, $F(R)$ gravity and Einstein-Gauss-Bonnet gravity. In the case of scalar field inflation and $F(R)$ gravity inflation, we demonstrate the difficulties for obtaining a positive running of the spectral index for a viable inflationary regime, so scalar theories and $F(R)$ gravity are mostly compatible with the Planck data. But nuanced scalar field scenarios can be compatible with the ACT data and produce a positive running of the spectral index. In the context of Einstein-Gauss-Bonnet theories which are compatible with the GW170817 event, the running of the spectral index can easily be positive while in parallel having a viable inflationary era.