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Cosmic Variance from Superhorizon Mode Coupling

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We observe a finite subvolume of the universe, so CMB and large scale structure data may give us either a representative or a biased sample of statistics in the larger universe. Mode coupling (non-Gaussianity) in the primordial perturbations can introduce a bias of parameters measured in any subvolume due to coupling to superhorizon background modes longer than the size of the subvolume. This leads to a "cosmic variance" of statistics on smaller scales, as the long-wavelength background modes vary around the global mean. We study this bias for local non-Gaussianity and quantify how observed statistics such as the power spectrum of the primordial perturbations, spectral index (scale-dependence in the power spectrum), amplitude of non-Gaussianity, dark matter halo power spectrum, and primordial tensor modes, can differ from the same quantities averaged throughout a volume much larger than the observable universe. More general kinds of mode coupling can change the relative sensitivity to different background modes. Finally, we consider what observations can tell us about the possibility of biasing from superhorizon modes."