Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-11-30
Class. Quantum Grav. 29 (2012) 015007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
To be published in Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/29/1/015007
We present a new approach to cosmological perturbations based on the theory of Lie groups and their representations. After re-deriving the standard covariant formalism from SO(3) considerations, we provide a new expansion of the perturbed Friedmann-Lemaitre-Robertson-Walker (FLRW) metric in terms of irreducible representations of the Lorentz group. The resulting decomposition splits into (scalar, scalar), (scalar, vector) and (vector, vector) terms. These equations directly correspond to the standard Lifshitz classification of cosmological perturbations using scalar, vector and tensor modes which arise from the irreducible SO(3) representation of the spatial part of the metric. While the Lorentz group basis matches the underlying local symmetries of the FLRW spacetime better than the SO(3), the new equations do not provide further simplification compared to the standard cosmological perturbation theory. We conjecture that this is due to the fact that the so(3,1) ~ su(2) x su(2) Lorentz algebra has no pair of commuting generators commuting with any of the translation group generators.
Czinner Viktor G.
Szapudi István
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