Constructing analytical solutions of linear perturbations of inflation with modified dispersion relations

TL;DR

This paper presents a method to derive analytical solutions for linear inflation perturbations affected by nonlinear dispersion relations, accounting for quantum effects in the early universe, with detailed error analysis.

Contribution

It introduces a novel technique to obtain exact analytical solutions for inflation perturbations with modified dispersion relations, including error bounds.

Findings

Analytical solutions closely match numerical results.

Error bounds are rigorously established.

Method effectively captures quantum effects in early universe perturbations.

Abstract

We develop a technique to construct analytical solutions of the linear perturbations of inflation with a nonlinear dispersion relation, due to quantum effects of the early universe. Error bounds are given and studied in detail. The analytical solutions describe the exact evolution of the perturbations extremely well even when only the first-order approximations is used.