String Corrected Scalar Field Inflation Compatible with the ACT Data

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.