Newton gauge cosmological perturbations for static spherically symmetric
  modifications of the de Sitter metric
  Static coordinates can be convenient to solve the vacuum Einstein's equations
in presence of spherical symmetry, but for cosmological applications comoving
coordinates are more suitable to describe an expanding Universe, especially in
the framework of cosmological perturbation theory (CPT). Using CPT we develop a
method to transform static spherically symmetric (SSS) modifications of the de
Sitter solution from static coordinates to the Newton gauge. We test the method
with the Schwarzschild de Sitter (SDS) metric and then derive general
expressions for the Bardeen's potentials for a class of SSS metrics obtained by
adding to the de Sitter metric a term linear in the mass and proportional to a
general function of the radius. Using the gauge invariance of the Bardeen's
potentials we then obtain a gauge invariant definition of the turn around
radius. We apply the method to an SSS solution of the Brans-Dicke theory,
confirming the results obtained independently by solving the perturbation
equations in the Newton gauge. The Bardeen's potentials are then derived for
new SSS metrics involving logarithmic, power law and exponential modifications
of the de Sitter metric. We also apply the method to SSS metrics which give
flat rotation curves, computing the radial energy density profile in comoving
coordinates in presence of a cosmological constant.
