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.
Simulated Rotation Measure Sky from Primordial Magnetic Fields
Universitá di Bologna（博洛尼亚大学）；Ilia State University（伊利亚州立大学）；INAF Istituto di Radioastronomia（意大利国家天体物理研究所射电天文研究所）；University of California, Los Angeles（加州大学洛杉矶分校）；Carnegie Observatories（卡内基观测站）；Universidad Complutense de Madrid（马德里康普顿斯大学）
