Conserved Quantities in Lemaitre-Tolman-Bondi Cosmology

Understand

We study linear perturbations to a Lema{\^\i}tre-Tolman-Bondi (LTB) background spacetime.

• Studying the transformation behaviour of the perturbations under gauge transformations, we construct gauge invariant quantities.
• We show, using the perturbed energy conservation equation, that there are conserved quantities in LTB, in particular a spatial metric trace perturbation, \zeta_{SMTP}, which is conserved on all scales.
• We then briefly extend our discussion to the Lema{\^\i}tre spacetime, and construct gauge-invariant perturbations in this extension of LTB spacetime.