Large Scale White Noise and Cosmology

TL;DR

This paper discusses how unresolved small-scale dynamics generate unavoidable white noise on large cosmological scales, offering a new way to probe early universe phenomena through large-scale observations.

Contribution

It reveals that large-scale white noise is a fundamental feature of cosmological models and can be used to investigate small-scale physics of the early universe.

Findings

White noise arises from unresolved small-scale dynamics in non-linear systems.

Observation of large-scale white noise constrains early universe phenomena.

White noise presence or absence informs about small-scale physics and phase transitions.

Abstract

The generation of white noise on large scales is a generic property of the dynamics of physical systems described by local non-linear partial differential equations. Non-linearities prevent the small scale dynamics from being erased by smoothing. Unresolved small scale dynamics act as an uncorrelated (white or Poissonian) noise (seemingly stochastic but actually deterministic) contribution to large scale dynamics. This white noise exists even when the dynamics is very nearly linear. In cases where the power spectrum is sub-Poissonian on large scales, this noise will dominate on the largest scale power no matter the amplitude of the inhomogeneities. Such is the case in the standard model of cosmology, where the primordial density power spectrum is expected to have an almost Harrison-Zel'dovich, $P[k]\sim k$, spectrum on a much broader range of scales than can be observed. Even though linear gravitational evolution dominates non-linear corrections by a factor $\sim10^5$, the non-observation of white noise on the Hubble scale precludes the extrapolation of this power law below the comoving $1\,$pc scale. More generally, observation or non-observation of large scale white noise provides a powerful probe of the universe on very small scales in the early early universe. Gravitational radiation, phase transitions, vorticity, and running of the spectral index are all phenomena that can be probed with large scale white noise. Large scale white noise is a non-optional feature of all cosmological models but one which has not heretofore been appreciated.