Two-point Correlation Functions in Inhomogeneous and Anisotropic
  Cosmologies
  Two-point correlation functions are ubiquitous tools of modern cosmology,
appearing in disparate topics ranging from cosmological inflation to late-time
astrophysics. When the background spacetime is maximally symmetric, invariance
arguments can be used to fix the functional dependence of this function as the
invariant distance between any two points. In this paper we introduce a novel
formalism which fixes this functional dependence directly from the isometries
of the background metric, thus allowing one to quickly assess the overall
features of Gaussian correlators without resorting to the full machinery of
perturbation theory. As an application we construct the CMB temperature
correlation function in one inhomogeneous (namely, an off-center LTB model) and
two spatially flat and anisotropic (Bianchi) universes, and derive their
covariance matrices in the limit of almost Friedmannian symmetry. We show how
the method can be extended to arbitrary N -point correlation functions and
illustrate its use by constructing three-point correlation functions in some
simple geometries.
