Stability and the Gauge Problem in Non-Perturbative Cosmology

Abstract

In this paper, we describe the first steps towards fully non-perturbative cosmology. We explain why the conventional methods used by cosmologists based on the ADM formulation are generally inadequate for this purpose and why it is advantageous instead to adapt the harmonic formulation pioneered and utilized in mathematical and numerical relativity. Here we focus on using this approach to evaluating the linear mode stability in homogeneous and nearly homogeneous backgrounds and devising a valid scheme and diagnostics for numerical computation. We also briefly touch on the relevance of these methods for extracting cosmological observables from non-perturbative simulations.

arXiv comment43 pages

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• Gravitational Collapse in Cubic Horndeski Theories
• Hairy rotating black holes in cubic Galileon theory
• More about stable wormholes in beyond Horndeski theory
• Bounce in GR and higher-order derivative operators
• Cosmological Bounces Induced by a Fermion Condensate
• Cosmology using numerical relativity
• Robustness of inflation to kinetic inhomogeneities
• Numerical Relativity as a New Tool for Fundamental Cosmology
• Physical Hamiltonian for mimetic gravity
• Cosmological Evolution in Bimetric Gravity: Observational Constraints and LSS Signatures
• Gauge/frame invariant variables for the numerical relativity study of cosmological spacetimes
• Extremal cosmological black holes in Horndeski gravity and the anti-evaporation regime
• Covariant single-field formulation of effective cosmological bounces