Lagrangian theory of structure formation in relativistic cosmology. V. Irrotational fluids

TL;DR

This paper extends relativistic Lagrangian perturbation theory to irrotational fluids with pressure, deriving equations for structure formation and analyzing differences from dust and Newtonian models.

Contribution

It develops a relativistic perturbation framework for pressure-supported fluids, including master equations for their evolution, expanding beyond dust models.

Findings

Derived first-order evolution equations for irrotational fluids with pressure.

Analyzed the impact of different equations of state on structure formation.

Compared relativistic results with Newtonian and dust models.

Abstract

We extend the general relativistic Lagrangian perturbation theory, recently developed for the formation of cosmic structures in a dust continuum, to the case of model universes containing a single fluid with a single-valued analytic equation of state. Using a coframe-based perturbation approach, we investigate evolution equations for structure formation in pressure-supported irrotational fluids that generate their rest-frame spacetime foliation. We provide master equations to first order for the evolution of the trace and traceless parts of barotropic perturbations that evolve in the perturbed space, where the latter describes the propagation of gravitational waves in the fluid. We illustrate the trace evolution for a linear equation of state and for a model equation of state describing isotropic velocity dispersion, and we discuss differences to the dust matter model, to the Newtonian case, and to standard perturbation approaches.