The Noisy Universe

TL;DR

The paper investigates large-scale white noise (LSWN) arising from non-linear mode coupling in cosmic evolution and its imprint on the primordial spectrum. It develops a framework based on Leading Order Born Approximation (LOBA) and augments the CLASS Boltzmann code with a relic LSWN term parameterized by $k_{BH}$, then constrains this amplitude using a joint Planck/ACT/DESI data analysis via a modified CLASS/COBAYA pipeline. The key result is a tight upper bound $k_{BH} ≤ 1.80×10^{-13}$ Mpc$^{-1}$ (99% CL), which implies either a small-scale cutoff $k_{cut} ≤ 3$ pc$^{-1}$ or a negative running $\alpha_s ≤ -0.015$, and yields $k_{LSWN} ≤ 0.1$ Gpc$^{-1}$. This work provides a novel empirical handle on the small-scale primordial spectrum, revealing how non-linearities can modify large-scale power and offering a path to test early-universe physics with future data.

Abstract

We present observational constraints on large-scale white noise (LSWN) in the cosmic density field, a phenomenon predicted to arise from non-linear mode coupling during cosmological evolution. Building on the theoretical framework of Paper I, where we demonstrated that non-linearities inevitably redistribute power from small to large scales through mode mixing, we confront these predictions with current cosmological data. We modify the CLASS Boltzmann code to incorporate a white noise component $k_\mathrm{BH}/k$ in the primordial power spectrum and perform parameter estimation using current cosmological data. The non-detection of excess power on the largest observable scales places stringent upper bounds: $k_\mathrm{BH} \leq 1.80 \times 10^{-13}~\mathrm{Mpc}^{-1}$ at 99\% confidence. These constraints imply the primordial power spectrum must deviate from perfect scale invariance on small scales, either through a cutoff at $k_{\mathrm{cut}} \lesssim 3~\mathrm{pc}^{-1}$ or through running of the spectral index with $α_s \lesssim -0.015$. Our results demonstrate that LSWN provides a powerful probe of the primordial spectrum at scales orders of magnitude smaller than directly observable, offering unique constraints on early-universe physics.

Figures (1)

• Figure 1: Constraints on the 6-parameter base $\Lambda$CDM model (blue), and the 7-parameter model including the LSWN coefficient $k_{\rm BH}$ (red). The regions lie almost exactly on top of each other, confirming that $k_{\rm BH}$ is uncorrelated with standard cosmological parameters.