2011/08/23 by Chris Clarkson, Clarkson, Chris
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory #astro-ph.CO #gr-qc
paper · pdf · doi:10.48550/arxiv.1108.4513
7 pages
arxiv created 2011/08/23 · openalex publication_date 2011/08/23 · arxiv updated 2011/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The relativistic theory of structure formation in cosmology is based mainly on linear perturbations about a homogeneous background. But we are now driven to understand the theory of higher-order perturbations in full detail, both from observational and theoretical points of view. An important aspect of this lies in defining gauge-invariant perturbations at any order. We present a new covariant approach to this based on a local separation of tensors into their scalar, vector and tensor parts. Such a local decomposition necessarily requires a trio of mutually annihilating differential operators which form the basis for defining gauge-invariant objects. It makes no use of non-local Green's functions or pre-defined gauges, and can be used to define families of scalar, vector and tensor modes at any order one chooses.