Statistical Naturalness and Non-Gaussianity in a Finite Universe

Abstract

We study the behavior of n-point functions of the primordial curvature perturbations, assuming our observed universe is only a subset of a larger space with statistically homogeneous and isotropic perturbations. If the larger space has arbitrary n-point functions in a family of local type non-Gaussian statistics, sufficiently biased smaller volumes will have statistics from a 'natural' version of that family with moments that are weakly non-Gaussian and ordered, regardless of the statistics of the original field. We also describe the effect of this bias on the shape of the bispectrum.

Nonlocal bispectra from super cosmic variance

“…A Φ 2 that can generate the equilateral, orthogonal or local bispectral templates was derived by Scoccimarro 2 Note that ∂ n is not in general a genuine derivative operator because it does not obey the Leibniz rule,…”

“…If we are more restrictive and insist that the induced bispectrum has no piece proportional to either ∂φ l or ∂ 2 φ l in the bispectrum, the only solution is b i = 0 except for i = 1 (the local g NL term). Super cosmic variance from a local cubic term and beyond was previously considered in [2,26].…”

“…The bias from super horizon modes is completely unmeasurable, but the qualitative conclusions we draw about the origin of fluctuations can change when we allow for it [1][2][3][4][5][6][7][8][9]. Fortunately, no such mode coupling has been detected within our universe yet, but current observational limits (e.g., from the Planck satellite results [10] and the most recent constraints from quasars [11]) do not rule out this possibility.…”

Constraining primordial and gravitational mode coupling with the position-dependent bispectrum of the large-scale structure

“…The interesting feature of the local ansatz (in the bispectrum, trispectrum and beyond) is the significant coupling between long-and short-wavelength modes of the primordial perturbations. A convincing detection of such a coupling would have two important implications: it would introduce an additional source of cosmic variance in connecting observations to theory [10][11][12][13], and it would rule out the single-clock inflation models [14].…”

Cosmic variance in inflation with two light scalars

“…For example, the "local" bispectrum generated in curvaton scenarios [3][4][5][6][7][8] correlates the amplitude of short wavelength fluctuations with the amplitudes of much longer wavelength modes. This means that in the presence of local ansatz non-Gaussianity, the power spectrum measured in sub-volumes will vary depending on how much the background fluctuations deviate from the mean [9][10][11][12]. While the bispectrum can cause the power spectrum to vary in sub-volumes, the trispectrum can generate shifts to the bispectrum and the power spectrum in biased sub-volumes (that is, subvolumes whose long wavelength background is not the mean).…”