Viable Gauge Choices in Cosmologies with Non-Linear Structures

Abstract

A variety of gauges are used in cosmological perturbation theory. These are often chosen in order to attribute physical properties to a particular choice of coordinates, or otherwise to simplify the form of the resultant equations. Calculations are then performed with the understanding that they could have been done in any gauge, and that transformations between different gauges can be made at will. We show that this logic can be extended to the domain of large density contrasts, where different types of perturbative expansion are required, but that the way in which gauges can be chosen in the presence of such structures is severely constrained. In particular, most gauges that are commonly considered in the cosmology literature are found to be unviable in the presence of non-linear structures. This includes spatially flat gauge, synchronous gauge, comoving orthogonal gauge, total matter gauge, N-body gauge, and the uniform density gauge. In contrast, we find that the longitudinal gauge and the Newtonian motion gauge are both viable choices in both standard cosmological perturbation theory, and in the post-Newtonian perturbative expansions that are required in order to model non-linear structures.

arXiv comment15 pages, 2 figures

References in corpus (26)

• Efficient Computation of CMB anisotropies in closed FRW models
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
• A Line of Sight Approach to Cosmic Microwave Background Anisotropies
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples
• Dark Energy Survey Year 1 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
• Cosmological perturbations
• Backreaction in late-time cosmology
• Does the growth of structure affect our dynamical models of the universe? The averaging, backreaction and fitting problems in cosmology
• gevolution: a cosmological N-body code based on General Relativity
• The primordial deuterium abundance of the most metal-poor damped Lyman-alpha system
• Connection between Newtonian simulations and general relativity
• General relativistic corrections to $N$-body simulations and the Zel'dovich approximation
• Scale-dependent bias from primordial non-Gaussianity in general relativity
• The missing link: a nonlinear post-Friedmann framework for small and large scales
• A Concise Introduction to Perturbation Theory in Cosmology
• Relativistic Interpretation of Newtonian Simulations for Cosmic Structure Formation
• General relativistic weak-field limit and Newtonian N-body simulations
• Cosmology Without Averaging
• Post-Newtonian Cosmological Modelling
• Proper-Time Hypersurface of Non-Relativistic Matter Flows: Galaxy Bias in General Relativity
• A new approach to cosmological structure formation with massive neutrinos
• Cosmology on all scales: a two-parameter perturbation expansion
• The Poisson equation at second order in relativistic cosmology
• Perturbation theory for cosmologies with non-linear structure
• Relativistic Euler Equations in cosmologies with non-linear structures

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• Modelling the emergence of cosmic anisotropy from non-linear structures
• Reconciling a decelerating Universe with cosmological observations
• Multi-Scale Perturbation Theory I: Methodology and Leading-Order Bispectrum Corrections in the Matter-Dominated Era
• Scale-Dependent Gravitational Couplings in Parameterised Post-Newtonian Cosmology
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• Consistent cosmological structure formation on all scales in relativistic extensions of MOND
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• Multi-Scale Perturbation Theory II: Solutions and Leading-Order Bispectrum in the $\Lambda$CDM Universe
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