Analysis of scalar perturbations in cosmological models with a non-local scalar field

TL;DR

This paper develops a formalism for analyzing cosmological scalar perturbations in models with a non-local scalar field derived from string theory, addressing complex roots and potential effects on curvature and entropy perturbations.

Contribution

It introduces a novel perturbation formalism for non-local scalar fields in cosmology, including cases with complex roots, expanding the understanding of their impact on cosmological perturbations.

Findings

Derived equations for energy density perturbations with arbitrary potentials.

Formulated a local system of equations for linearized perturbations.

Analyzed effects of complex quantities on curvature and entropy perturbations.

Abstract

We develop the cosmological perturbations formalism in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field in the presence of the arbitrary potential and formulate the local system of equations for perturbations in the linearized model when both simple and double roots of the characteristic equation are present. We carry out the general analysis related to the curvature and entropy perturbations and consider the most specific example of perturbations when important quantities in the model become complex.