Cosmological Perturbations from a Group Theoretical Point of View
  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.
