Causal perturbation theory in general FRW cosmologies I: energy momentum conservation and matching conditions

Abstract

We describe energy--momentum conservation in relativistic perturbation theory in general FRW backgrounds with causal source terms, such as the presence of cosmic defect networks. We provide a prescription for a linear energy--momentum pseudo-tensor in a curved FRW universe, decomposing it using eigenfunctions of the Helmholtz equation. We also construct conserved vector densities for the conformal geometry of these spacetimes and relate these to our pseudo-tensor, demonstrating the equivalence of these two approaches. We also relate these techniques to the role played by residual gauge freedom in establishing matching conditions at early phase transitions, which we can express in terms of components of our pseudo-tensor. This formalism is concise and geometrically sound on both sub- and superhorizon scales, thus extending existing work to a physically (and numerically) useful context.

28 pages. To be submitted to Physical Review D

References in corpus (33)

• Hybrid Inflation
• MAXIMA-1: A Measurement of the Cosmic Microwave Background Anisotropy on angular scales of 10 arcminutes to 5 degrees
• Cosmology from Maxima-1, Boomerang and COBE/DMR CMB Observations
• CMB Anisotropies: Total Angular Momentum Method
• Inflation and the dS/CFT Correspondence
• Power Spectra in Global Defect Theories of Cosmic Structure Formation
• Cosmic Structure Formation with Topological Defects
• On matching conditions for cosmological perturbations
• A Complete Treatment of CMB Anisotropies in a FRW Universe
• Relativistic conservation laws and integral constraints for large cosmological perturbations
• Cosmic microwave background anisotropy from wiggly strings
• The case against scaling defect models of cosmic structure formation
• Cosmic strings from preheating
• CMB Anisotropy Induced by Cosmic Strings on Angular Scales $>15^{\prime }$
• Constraining Isocurvature Perturbations with CMB Polarization
• Evidence against or for topological defects in the BOOMERanG data ?
• CMB polarization as a direct test of Inflation
• Inflation in Supersymmetric Unified Theories
• Cosmic Microwave Background Anisotropies from Scaling Seeds: Global Defect Models
• CMB and density fluctuations from strings plus inflation
• Distinguishing Causal Seeds from Inflation
• Structure formation by cosmic strings with a cosmological constant
• Large Angular Scale CMB Anisotropy Induced by Cosmic Strings
• A Causal Source which Mimics Inflation
• Cosmic-String-Seeded Structure Formation
• Causality and the Doppler Peaks
• Non-gaussian Features of Linear Cosmic String Models
• Conservation Laws and Cosmological Perturbations in Curved Universes
• Cosmic Microwave Background Anisotropies from Scaling Seeds: Fit to Observational Data
• Cosmological Perturbations seeded by Topological Defects: Setting the Initial Conditions
• Integral Constraints On cosmological Perturbations and their Energy
• Cosmic Defects and CMB anisotropy
• Non-Gaussian sampling effects on the CMB power spectrum estimation

Cited by in corpus (5)

• The Separate Universe Approach and the Evolution of Nonlinear Superhorizon Cosmological Perturbations
• Fluctuations in the CMB Induced by Cosmic Strings: Methods and Formalism
• Cosmological perturbation theory, instantaneous gauges and local inertial frames
• Covariant conserved currents for scalar-tensor Horndeski theory
• Affine Gravity, Palatini Formalism and Charges