Resilience of long modes in cosmological observables

TL;DR

This paper demonstrates that certain long-wavelength mode effects in cosmological observables are physical and cannot be removed by gauge transformations, impacting the interpretation of non-Gaussianity and relativistic effects in cosmology.

Contribution

The authors show that effects involving squeezed bispectrum configurations are physical and cannot be gauged away, refining the understanding of observable non-Gaussianities in cosmology.

Findings

Long-wavelength mode effects are physical and observable.

The Maldacena consistency relation is confirmed to be physically meaningful.

Relativistic non-linear evolution impacts dark matter bispectrum and halo bias.

Abstract

By a careful implementation of gauge transformations involving long-wavelength modes, we show that a variety of effects involving squeezed bispectrum configurations, for which one Fourier mode is much shorter than the other two, cannot be gauged away, except for the unphysical exactly infinite-wavelength ($k=0$) limit. Our result applies, in particular, to the Maldacena consistency relation for single-field inflation, yielding a local non-Gaussianity strength $f_{\rm NL}^{\rm local} = - (5/12)(n_S-1)$ (with $n_S$ the primordial spectral index of scalar perturbations), and to the $f_{\rm NL}^{\rm GR} = -5/3$ term, appearing in the dark matter bispectrum and in the halo bias, as a consequence of the general relativistic non-linear evolution of matter perturbations. Such effects are therefore physical and observable in principle by future high-sensitivity experiments.