Second order density perturbations for dust cosmologies

Understand

We present simple expressions for the relativistic first and second order fractional density perturbations for FL cosmologies with dust, in four different gauges: the Poisson, uniform curvature, total matter and synchronous gauges.

• We include a cosmological constant and arbitrary spatial curvature in the background.
• A distinctive feature of our approach is our description of the spatial dependence of the perturbations using a canonical set of quadratic differential expressions involving an arbitrary spatial function that arises as a conserved quantity.
• This enables us to unify, simplify and extend previous seemingly disparate results.