Statistics of a single sky: constrained random fields and the imprint of
  Bardeen potentials on galaxy clustering
  We explore the implications of a single observer's viewpoint on measurements
of galaxy clustering statistics. We focus on the Bardeen potentials, which
imprint characteristic scale-dependent signatures in the observed galaxy power
spectrum. The existence of an observer breaks homogeneity as it singles out
particular field values at her/his position, like a spontaneous symmetry
breaking. As a result, spatial averaging of the data must be performed while
holding the Bardeen potentials fixed at the observer's position. In practice,
this can be implemented with the formalism of constrained random fields. In the
traditional Cartesian Fourier decomposition, this constraint imprints a
signature in the observed galaxy power spectrum at wavenumber comparable to the
fundamental mode of the survey. This effect, which is well within the cosmic
variance, is the same for all observers regardless of their local environment
because differences of potential solely are observable. In a spherical Bessel
Fourier decomposition, this constraint affects the monopole of the observed
galaxy distribution solely, like in CMB data. As a corollary, the
scale-dependence of the non-Gaussian bias induced by a local primordial
non-Gaussianity is not significantly affected by the observer's viewpoint.
