Manifestly Covariant Gauge-invariant Cosmological Perturbation Theory

TL;DR

This paper develops a unique gauge-invariant cosmological perturbation theory applicable to various universe models, revealing new insights into density perturbations and their role in star formation after matter-radiation decoupling.

Contribution

It introduces a novel, manifestly gauge-invariant framework for cosmological perturbations, including new variables that clarify the evolution of density perturbations across different eras.

Findings

Unique gauge-invariant variable for energy density perturbation

Density perturbations in the radiation era oscillate with increasing amplitude

No back-reaction of perturbations on the universe's global expansion

Abstract

It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lema\^itre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy density and which becomes equal to the usual Newtonian energy density in the non-relativistic limit. The same holds true for the perturbation to the particle number density. Using these two new variables, a new manifestly gauge-invariant cosmological perturbation theory has been developed. Density perturbations evolve diabatically. Perturbations in the total energy density are gravitationally coupled to perturbations in the particle number density, irrespective of the nature of the particles. There is, in first-order, no back-reaction of perturbations to the global expansion of the universe. Small-scale perturbations in the radiation-dominated era oscillate with an increasing amplitude, whereas in older, less precise treatments, oscillating perturbations are found with a decreasing amplitude. This is a completely new and, obviously, important result, since it makes it possible to explain and understand the formation of massive stars after decoupling of matter and radiation.