Cosmic Variance of the Spectral Index from Mode Coupling

TL;DR

This paper shows that local non-Gaussianity and mode coupling can cause significant cosmic variance in the observed spectral index and bispectrum, affecting inflationary model constraints.

Contribution

It introduces the concept that mode coupling and non-Gaussianity induce cosmic variance in spectral index and bispectrum measurements, impacting inflationary theory constraints.

Findings

Local non-Gaussianity causes scale-dependent cosmic variance.

Mode coupling affects observed tensor modes and spectral indices.

Future observations can constrain this cosmic variance effect.

Abstract

We demonstrate that local, scale-dependent non-Gaussianity can generate cosmic variance uncertainty in the observed spectral index of primordial curvature perturbations. In a universe much larger than our current Hubble volume, locally unobservable long wavelength modes can induce a scale-dependence in the power spectrum of typical subvolumes, so that the observed spectral index varies at a cosmologically significant level (|\Delta ns | ~ O(0.04)). Similarly, we show that the observed bispectrum can have an induced scale dependence that varies about the global shape. If tensor modes are coupled to long wavelength modes of a second field, the locally observed tensor power and spectral index can also vary. All of these effects, which can be introduced in models where the observed non-Gaussianity is consistent with bounds from the Planck satellite, loosen the constraints that observations place on the parameters of theories of inflation with mode coupling. We suggest observational constraints that future measurements could aim for to close this window of cosmic variance uncertainty.