Perturbations of Matter Fields in the Second-order Gauge-invariant Cosmological Perturbation Theory

TL;DR

This paper develops second-order gauge-invariant cosmological perturbation theory formulas for matter fields, including fluids and scalar fields, ensuring gauge invariance without fixing gauges.

Contribution

It provides new gauge-invariant formulas for matter field perturbations and their equations of motion in second-order cosmological perturbation theory.

Findings

Derived gauge-invariant perturbation formulas for energy-momentum tensors.

Formulated equations of motion for perfect and imperfect fluids.

Extended the framework to scalar fields in cosmology.

Abstract

Some formulae for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe, which is developed in the papers [K.Nakamura, Prog.Theor.Phys., 117 (2007), 17.]. We derive the formulae for the perturbations of the energy momentum tensors and equations of motion for a perfect fluid, an imperfect fluid, and a signle scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing.