Nonlinear perturbations for dissipative and interacting relativistic fluids

Abstract

We develop a covariant formalism to study nonlinear perturbations of dissipative and interacting relativistic fluids. We derive nonlinear evolution equations for various covectors defined as linear combinations of the spatial gradients of the local number of e-folds and of some scalar quantities characterizing the fluid, such as the energy density or the particle number density. For interacting fluids we decompose perturbations into adiabatic and entropy components and derive their coupled evolution equations, recovering and extending the results obtained in the context of the linear theory. For non-dissipative and noninteracting fluids, these evolution equations reduce to the conservation equations that we have obtained in recent works. We also illustrate geometrically the meaning of the covectors that we have introduced.

21 pages. v2: minor changes, added a reference; v3: minor changes, published version

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• Unveiling dark fifth forces with linear cosmology
• Cosmological Backreaction from Perturbations
• Conserved cosmological perturbation in Galileon models
• Nonlinear perturbations of cosmological scalar fields with non-standard kinetic terms
• Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multi-component, curvature, and rotation
• General treatment of isocurvature perturbations and non-Gaussianities
• Covariant generalization of cosmological perturbation theory
• Flat limits of curved interacting cosmic fluids
• Vector and tensor contributions to the curvature perturbation at second order
• The Non-Minimal Ekpyrotic Trispectrum
• Singularities in cosmologies with interacting fluids
• Material models of dark energy
• Fully non-linear equivalence of delta N and covariant formalisms
• Covariant Bardeen Perturbation Formalism
• Non-Gaussianity in the Cosmic Microwave Background Induced by Dipolar Dark Matter
• $\Delta N$ Formalism and Conserved Currents in Cosmology
• Dipolar Dark Matter and Cosmology
• Non-linear effects in early Universe cosmology