Cosmological perturbations

Understand

We review the study of inhomogeneous perturbations about a homogeneous and isotropic background cosmology.

• We adopt a coordinate based approach, but give geometrical interpretations of metric perturbations in terms of the expansion, shear and curvature of constant-time hypersurfaces and the orthogonal timelike vector field.
• We give the gauge transformation rules for metric and matter variables at first and second order.
• We show how gauge invariant variables are constructed by identifying geometric or matter variables in physically-defined coordinate systems, and give the relations between many commonly used gauge-invariant variables.