String Corrected Scalar Field Inflation Compatible with the ACT Data

TL;DR

This paper develops a string-corrected scalar field inflation model that aligns with ACT and Planck data, emphasizing self-consistency in the slow-roll approximation.

Contribution

It introduces a self-consistent inflationary framework incorporating specific string corrections, compatible with observational constraints.

Findings

Derived an analytically tractable inflationary model with string corrections.

The model fits ACT and Planck observational constraints.

Identified a non-trivial, self-consistent correction term for inflation dynamics.

Abstract

We consider the impact of the first string corrections of minimally coupled single scalar field theory on inflationary dynamics. Specifically we consider separately the string corrections $\sim \alpha'\xi(\phi)c_2\,\left( \partial_{\mu}\phi \partial^{\mu}\phi\right)^2$ and $\sim \alpha'c \xi(\phi)\square \phi \partial_{\mu}\phi \partial^{\mu}\phi$, where $\alpha'$ is the square of the string scale. Our aim is to develop a theory which is self consistent in the sense that the field equations reproduce themselves in the slow-roll approximation. Such a requirement for the theory with $\sim \alpha'\xi(\phi) c_2\left( \partial_{\mu}\phi \partial^{\mu}\phi\right)^2$ resulted to a trivial non-minimal coupling function $\xi(\phi)$, however a self-consistent framework emerged from the theory with correction term $\sim \alpha' c \xi(\phi)\square \phi \partial_{\mu}\phi \partial^{\mu}\phi$. The resulting theory can easily be worked out analytically and we obtained an inflationary theory that can easily be fitted with the Atacama Cosmology Telescope constraints on the scalar spectral index and the updated Planck constraints on the tensor-to-scalar ratio.